question
stringlengths 29
1.88k
| test_input
listlengths 0
10
| test_output
listlengths 0
10
| test_time_limit
int64 1
1
| test_method
stringclasses 1
value |
|---|---|---|---|---|
Catherine has a deck of n cards, each of which is either red, green, or blue. As long as there are at least two cards left, she can do one of two actions: take any two (not necessarily adjacent) cards with different colors and exchange them for a new card of the third color; take any two (not necessarily adjacent) cards with the same color and exchange them for a new card with that color.
She repeats this process until there is only one card left. What are the possible colors for the final card?
-----Input-----
The first line of the input contains a single integer n (1 ≤ n ≤ 200) — the total number of cards.
The next line contains a string s of length n — the colors of the cards. s contains only the characters 'B', 'G', and 'R', representing blue, green, and red, respectively.
-----Output-----
Print a single string of up to three characters — the possible colors of the final card (using the same symbols as the input) in alphabetical order.
-----Examples-----
Input
2
RB
Output
G
Input
3
GRG
Output
BR
Input
5
BBBBB
Output
B
-----Note-----
In the first sample, Catherine has one red card and one blue card, which she must exchange for a green card.
In the second sample, Catherine has two green cards and one red card. She has two options: she can exchange the two green cards for a green card, then exchange the new green card and the red card for a blue card. Alternatively, she can exchange a green and a red card for a blue card, then exchange the blue card and remaining green card for a red card.
In the third sample, Catherine only has blue cards, so she can only exchange them for more blue cards.
|
[
"2\nRB\n",
"3\nGRG\n",
"5\nBBBBB\n",
"1\nR\n",
"200\nBBRGRRBBRGGGBGBGBGRRGRGRGRBGRGRRBBGRGBGRRGRRRGGBBRGBGBGBRBBBBBBBGGBRGGRRRGGRGBGBGGBRRRRBRRRBRBBGGBGBRGRGBBBBGGBGBBBGBGRRBRRRGBGGBBBRBGRBRRGGGRRGBBBGBGRRRRRRGGRGRGBBBRGGGBGGGBRBBRRGBGRGRBRRRBRBGRGGBRBB\n",
"101\nRRRRRRRRRRRRRRRRRRRBRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRR\n",
"7\nBBBGBRG\n",
"5\nGRRGR\n",
"3\nGBR\n",
"1\nB\n"
] |
[
"G\n",
"BR\n",
"B\n",
"R\n",
"BGR\n",
"BG\n",
"BGR\n",
"BGR\n",
"BGR\n",
"B\n"
] | 1
|
stdio
|
Arpa is taking a geometry exam. Here is the last problem of the exam.
You are given three points a, b, c.
Find a point and an angle such that if we rotate the page around the point by the angle, the new position of a is the same as the old position of b, and the new position of b is the same as the old position of c.
Arpa is doubting if the problem has a solution or not (i.e. if there exists a point and an angle satisfying the condition). Help Arpa determine if the question has a solution or not.
-----Input-----
The only line contains six integers a_{x}, a_{y}, b_{x}, b_{y}, c_{x}, c_{y} (|a_{x}|, |a_{y}|, |b_{x}|, |b_{y}|, |c_{x}|, |c_{y}| ≤ 10^9). It's guaranteed that the points are distinct.
-----Output-----
Print "Yes" if the problem has a solution, "No" otherwise.
You can print each letter in any case (upper or lower).
-----Examples-----
Input
0 1 1 1 1 0
Output
Yes
Input
1 1 0 0 1000 1000
Output
No
-----Note-----
In the first sample test, rotate the page around (0.5, 0.5) by $90^{\circ}$.
In the second sample test, you can't find any solution.
|
[
"0 1 1 1 1 0\n",
"1 1 0 0 1000 1000\n",
"1 0 2 0 3 0\n",
"3 4 0 0 4 3\n",
"-1000000000 1 0 0 1000000000 1\n",
"49152 0 0 0 0 81920\n",
"1 -1 4 4 2 -3\n",
"-2 -2 1 4 -2 0\n",
"5 0 4 -2 0 1\n",
"-4 -3 2 -1 -3 4\n"
] |
[
"Yes\n",
"No\n",
"No\n",
"Yes\n",
"Yes\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n"
] | 1
|
stdio
|
One day Vasya was sitting on a not so interesting Maths lesson and making an origami from a rectangular a mm × b mm sheet of paper (a > b). Usually the first step in making an origami is making a square piece of paper from the rectangular sheet by folding the sheet along the bisector of the right angle, and cutting the excess part.
[Image]
After making a paper ship from the square piece, Vasya looked on the remaining (a - b) mm × b mm strip of paper. He got the idea to use this strip of paper in the same way to make an origami, and then use the remainder (if it exists) and so on. At the moment when he is left with a square piece of paper, he will make the last ship from it and stop.
Can you determine how many ships Vasya will make during the lesson?
-----Input-----
The first line of the input contains two integers a, b (1 ≤ b < a ≤ 10^12) — the sizes of the original sheet of paper.
-----Output-----
Print a single integer — the number of ships that Vasya will make.
-----Examples-----
Input
2 1
Output
2
Input
10 7
Output
6
Input
1000000000000 1
Output
1000000000000
-----Note-----
Pictures to the first and second sample test.
[Image]
|
[
"2 1\n",
"10 7\n",
"1000000000000 1\n",
"3 1\n",
"4 1\n",
"3 2\n",
"4 2\n",
"1000 700\n",
"959986566087 524054155168\n",
"4 3\n"
] |
[
"2\n",
"6\n",
"1000000000000\n",
"3\n",
"4\n",
"3\n",
"2\n",
"6\n",
"90\n",
"4\n"
] | 1
|
stdio
|
Vasya is studying number theory. He has denoted a function f(a, b) such that: f(a, 0) = 0; f(a, b) = 1 + f(a, b - gcd(a, b)), where gcd(a, b) is the greatest common divisor of a and b.
Vasya has two numbers x and y, and he wants to calculate f(x, y). He tried to do it by himself, but found out that calculating this function the way he wants to do that might take very long time. So he decided to ask you to implement a program that will calculate this function swiftly.
-----Input-----
The first line contains two integer numbers x and y (1 ≤ x, y ≤ 10^12).
-----Output-----
Print f(x, y).
-----Examples-----
Input
3 5
Output
3
Input
6 3
Output
1
|
[
"3 5\n",
"6 3\n",
"1000000009 1000000008\n",
"1000000007 1000000006\n",
"2000000018 2000000017\n",
"1000000000000 1\n",
"1000000000000 1000000000000\n",
"1 1000000000000\n",
"100000000000 100000000000\n",
"1 100000000000\n"
] |
[
"3\n",
"1\n",
"1000000008\n",
"1000000006\n",
"1000000009\n",
"1\n",
"1\n",
"1000000000000\n",
"1\n",
"100000000000\n"
] | 1
|
stdio
|
Gerald is very particular to eight point sets. He thinks that any decent eight point set must consist of all pairwise intersections of three distinct integer vertical straight lines and three distinct integer horizontal straight lines, except for the average of these nine points. In other words, there must be three integers x_1, x_2, x_3 and three more integers y_1, y_2, y_3, such that x_1 < x_2 < x_3, y_1 < y_2 < y_3 and the eight point set consists of all points (x_{i}, y_{j}) (1 ≤ i, j ≤ 3), except for point (x_2, y_2).
You have a set of eight points. Find out if Gerald can use this set?
-----Input-----
The input consists of eight lines, the i-th line contains two space-separated integers x_{i} and y_{i} (0 ≤ x_{i}, y_{i} ≤ 10^6). You do not have any other conditions for these points.
-----Output-----
In a single line print word "respectable", if the given set of points corresponds to Gerald's decency rules, and "ugly" otherwise.
-----Examples-----
Input
0 0
0 1
0 2
1 0
1 2
2 0
2 1
2 2
Output
respectable
Input
0 0
1 0
2 0
3 0
4 0
5 0
6 0
7 0
Output
ugly
Input
1 1
1 2
1 3
2 1
2 2
2 3
3 1
3 2
Output
ugly
|
[
"0 0\n0 1\n0 2\n1 0\n1 2\n2 0\n2 1\n2 2\n",
"0 0\n1 0\n2 0\n3 0\n4 0\n5 0\n6 0\n7 0\n",
"1 1\n1 2\n1 3\n2 1\n2 2\n2 3\n3 1\n3 2\n",
"0 0\n0 0\n0 0\n0 0\n0 0\n0 0\n0 0\n0 0\n",
"1000000 1000000\n1000000 999999\n1000000 999998\n999999 1000000\n999999 999998\n999998 1000000\n999998 999999\n999998 999998\n",
"0 0\n1 0\n0 1\n1 1\n0 2\n1 2\n0 3\n1 3\n",
"0 0\n2 1\n1 0\n0 2\n2 2\n1 0\n2 1\n0 2\n",
"0 0\n2 1\n1 0\n0 2\n2 2\n1 0\n2 1\n0 2\n",
"791649 383826\n10864 260573\n504506 185571\n899991 511500\n503197 876976\n688727 569035\n343255 961333\n439355 759581\n",
"750592 335292\n226387 434036\n299976 154633\n593197 600998\n62014 689355\n566268 571630\n381455 222817\n50555 288617\n"
] |
[
"respectable\n",
"ugly\n",
"ugly\n",
"ugly\n",
"respectable\n",
"ugly\n",
"ugly\n",
"ugly\n",
"ugly\n",
"ugly\n"
] | 1
|
stdio
|
Apart from Nian, there is a daemon named Sui, which terrifies children and causes them to become sick. Parents give their children money wrapped in red packets and put them under the pillow, so that when Sui tries to approach them, it will be driven away by the fairies inside.
Big Banban is hesitating over the amount of money to give out. He considers loops to be lucky since it symbolizes unity and harmony.
He would like to find a positive integer n not greater than 10^18, such that there are exactly k loops in the decimal representation of n, or determine that such n does not exist.
A loop is a planar area enclosed by lines in the digits' decimal representation written in Arabic numerals. For example, there is one loop in digit 4, two loops in 8 and no loops in 5. Refer to the figure below for all exact forms.
$0123456789$
-----Input-----
The first and only line contains an integer k (1 ≤ k ≤ 10^6) — the desired number of loops.
-----Output-----
Output an integer — if no such n exists, output -1; otherwise output any such n. In the latter case, your output should be a positive decimal integer not exceeding 10^18.
-----Examples-----
Input
2
Output
462
Input
6
Output
8080
|
[
"2\n",
"6\n",
"3\n",
"4\n",
"5\n",
"1000000\n",
"1\n",
"7\n",
"8\n",
"9\n"
] |
[
"8\n",
"888\n",
"86\n",
"88\n",
"886\n",
"-1\n",
"6\n",
"8886\n",
"8888\n",
"88886\n"
] | 1
|
stdio
|
NN is an experienced internet user and that means he spends a lot of time on the social media. Once he found the following image on the Net, which asked him to compare the sizes of inner circles: [Image]
It turned out that the circles are equal. NN was very surprised by this fact, so he decided to create a similar picture himself.
He managed to calculate the number of outer circles $n$ and the radius of the inner circle $r$. NN thinks that, using this information, you can exactly determine the radius of the outer circles $R$ so that the inner circle touches all of the outer ones externally and each pair of neighboring outer circles also touches each other. While NN tried very hard to guess the required radius, he didn't manage to do that.
Help NN find the required radius for building the required picture.
-----Input-----
The first and the only line of the input file contains two numbers $n$ and $r$ ($3 \leq n \leq 100$, $1 \leq r \leq 100$) — the number of the outer circles and the radius of the inner circle respectively.
-----Output-----
Output a single number $R$ — the radius of the outer circle required for building the required picture.
Your answer will be accepted if its relative or absolute error does not exceed $10^{-6}$.
Formally, if your answer is $a$ and the jury's answer is $b$. Your answer is accepted if and only when $\frac{|a-b|}{max(1, |b|)} \le 10^{-6}$.
-----Examples-----
Input
3 1
Output
6.4641016
Input
6 1
Output
1.0000000
Input
100 100
Output
3.2429391
|
[
"3 1\n",
"6 1\n",
"100 100\n",
"5 6\n",
"7 5\n",
"8 3\n",
"10 5\n",
"4 2\n",
"5 6\n",
"7 3\n"
] |
[
"6.4641016\n",
"1.0000000\n",
"3.2429391\n",
"8.5555200\n",
"3.8321081\n",
"1.8597432\n",
"2.2360680\n",
"4.8284271\n",
"8.5555200\n",
"2.2992648\n"
] | 1
|
stdio
|
There is the faculty of Computer Science in Berland. In the social net "TheContact!" for each course of this faculty there is the special group whose name equals the year of university entrance of corresponding course of students at the university.
Each of students joins the group of his course and joins all groups for which the year of student's university entrance differs by no more than x from the year of university entrance of this student, where x — some non-negative integer. A value x is not given, but it can be uniquely determined from the available data. Note that students don't join other groups.
You are given the list of groups which the student Igor joined. According to this information you need to determine the year of Igor's university entrance.
-----Input-----
The first line contains the positive odd integer n (1 ≤ n ≤ 5) — the number of groups which Igor joined.
The next line contains n distinct integers a_1, a_2, ..., a_{n} (2010 ≤ a_{i} ≤ 2100) — years of student's university entrance for each group in which Igor is the member.
It is guaranteed that the input data is correct and the answer always exists. Groups are given randomly.
-----Output-----
Print the year of Igor's university entrance.
-----Examples-----
Input
3
2014 2016 2015
Output
2015
Input
1
2050
Output
2050
-----Note-----
In the first test the value x = 1. Igor entered the university in 2015. So he joined groups members of which are students who entered the university in 2014, 2015 and 2016.
In the second test the value x = 0. Igor entered only the group which corresponds to the year of his university entrance.
|
[
"3\n2014 2016 2015\n",
"1\n2050\n",
"1\n2010\n",
"1\n2011\n",
"3\n2010 2011 2012\n",
"3\n2049 2047 2048\n",
"5\n2043 2042 2041 2044 2040\n",
"5\n2012 2013 2014 2015 2016\n",
"1\n2045\n",
"1\n2046\n"
] |
[
"2015\n",
"2050\n",
"2010\n",
"2011\n",
"2011\n",
"2048\n",
"2042\n",
"2014\n",
"2045\n",
"2046\n"
] | 1
|
stdio
|
Let $f_{x} = c^{2x-6} \cdot f_{x-1} \cdot f_{x-2} \cdot f_{x-3}$ for $x \ge 4$.
You have given integers $n$, $f_{1}$, $f_{2}$, $f_{3}$, and $c$. Find $f_{n} \bmod (10^{9}+7)$.
-----Input-----
The only line contains five integers $n$, $f_{1}$, $f_{2}$, $f_{3}$, and $c$ ($4 \le n \le 10^{18}$, $1 \le f_{1}$, $f_{2}$, $f_{3}$, $c \le 10^{9}$).
-----Output-----
Print $f_{n} \bmod (10^{9} + 7)$.
-----Examples-----
Input
5 1 2 5 3
Output
72900
Input
17 97 41 37 11
Output
317451037
-----Note-----
In the first example, $f_{4} = 90$, $f_{5} = 72900$.
In the second example, $f_{17} \approx 2.28 \times 10^{29587}$.
|
[
"5 1 2 5 3\n",
"17 97 41 37 11\n",
"4 1 1 1 1\n",
"1000000000000000000 1000000000 1000000000 1000000000 1000000000\n",
"27230 83472 9488 55320 2081\n",
"44618 45855 80403 31174 63416\n",
"67025 50601 5471 94645 97571\n",
"89432 31159 22014 66629 31727\n",
"11842 44412 71268 71316 98586\n",
"38100 49158 96330 34807 32742\n"
] |
[
"72900\n",
"317451037\n",
"1\n",
"607659049\n",
"791627460\n",
"468227325\n",
"252720835\n",
"100809399\n",
"543142695\n",
"231750081\n"
] | 1
|
stdio
|
Given are two strings s and t consisting of lowercase English letters. Determine if there exists an integer i satisfying the following condition, and find the minimum such i if it exists.
- Let s' be the concatenation of 10^{100} copies of s. t is a subsequence of the string {s'}_1{s'}_2\ldots{s'}_i (the first i characters in s').
-----Notes-----
- A subsequence of a string a is a string obtained by deleting zero or more characters from a and concatenating the remaining characters without changing the relative order. For example, the subsequences of contest include net, c, and contest.
-----Constraints-----
- 1 \leq |s| \leq 10^5
- 1 \leq |t| \leq 10^5
- s and t consists of lowercase English letters.
-----Input-----
Input is given from Standard Input in the following format:
s
t
-----Output-----
If there exists an integer i satisfying the following condition, print the minimum such i; otherwise, print -1.
-----Sample Input-----
contest
son
-----Sample Output-----
10
t = son is a subsequence of the string contestcon (the first 10 characters in s' = contestcontestcontest...), so i = 10 satisfies the condition.
On the other hand, t is not a subsequence of the string contestco (the first 9 characters in s'), so i = 9 does not satisfy the condition.
Similarly, any integer less than 9 does not satisfy the condition, either. Thus, the minimum integer i satisfying the condition is 10.
|
[
"contest\nson\n",
"contest\nprogramming\n",
"contest\nsentence\n",
"d\nd\n",
"j\nw\n",
"zv\nz\n",
"jh\nh\n",
"l\nll\n",
"s\nsv\n",
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iii\n"
] |
[
"10\n",
"-1\n",
"33\n",
"1\n",
"-1\n",
"1\n",
"2\n",
"2\n",
"-1\n",
"100000\n"
] | 1
|
stdio
|
[Image]
-----Input-----
The first line of the input is a string (between 1 and 50 characters long, inclusive). Each character will be a letter of English alphabet, lowercase or uppercase.
The second line of the input is an integer between 0 and 26, inclusive.
-----Output-----
Output the required string.
-----Examples-----
Input
AprilFool
14
Output
AprILFooL
|
[
"AprilFool\n14\n",
"abcdefabc\n3\n",
"fgWjSAlPOvcAbCdDEFjz\n7\n",
"sm\n26\n",
"GnlFOqPeZtPiBkvvLhaDvGPgFqBTnLgMT\n12\n",
"sPWSFWWqZBPon\n3\n",
"fQHHXCdeaintxHWcFcaSGWFvqnYMEByMlSNKumiFgnJB\n0\n",
"RtsUOGkraqKyjTktAXloOEmQj\n18\n",
"DuFhhnq\n4\n",
"RvpuYTxsbDiJDOLauRlfatcfwvtnDzKyaewGrZ\n22\n"
] |
[
"AprILFooL\n",
"ABCdefABC\n",
"FGwjsAlpovCABCDDEFjz\n",
"SM\n",
"GnLFoqpEztpIBKvvLHADvGpGFqBtnLGmt\n",
"spwsfwwqzBpon\n",
"fqhhxcdeaintxhwcfcasgwfvqnymebymlsnkumifgnjb\n",
"RtsuOGKRAQKyJtKtAxLOOEMQJ\n",
"Dufhhnq\n",
"RVPUyTxSBDIJDOLAURLFATCFwVTNDzKyAEwGRz\n"
] | 1
|
stdio
|
Now it's time of Olympiads. Vanya and Egor decided to make his own team to take part in a programming Olympiad. They've been best friends ever since primary school and hopefully, that can somehow help them in teamwork.
For each team Olympiad, Vanya takes his play cards with numbers. He takes only the cards containing numbers 1 and 0. The boys are very superstitious. They think that they can do well at the Olympiad if they begin with laying all the cards in a row so that: there wouldn't be a pair of any side-adjacent cards with zeroes in a row; there wouldn't be a group of three consecutive cards containing numbers one.
Today Vanya brought n cards with zeroes and m cards with numbers one. The number of cards was so much that the friends do not know how to put all those cards in the described way. Help them find the required arrangement of the cards or else tell the guys that it is impossible to arrange cards in such a way.
-----Input-----
The first line contains two integers: n (1 ≤ n ≤ 10^6) — the number of cards containing number 0; m (1 ≤ m ≤ 10^6) — the number of cards containing number 1.
-----Output-----
In a single line print the required sequence of zeroes and ones without any spaces. If such sequence is impossible to obtain, print -1.
-----Examples-----
Input
1 2
Output
101
Input
4 8
Output
110110110101
Input
4 10
Output
11011011011011
Input
1 5
Output
-1
|
[
"1 2\n",
"4 8\n",
"4 10\n",
"1 5\n",
"3 4\n",
"3 10\n",
"74 99\n",
"19 30\n",
"33 77\n",
"3342 3339\n"
] |
[
"101\n",
"110110110101\n",
"11011011011011\n",
"-1\n",
"1010101\n",
"-1\n",
"11011011011011011011011011011011011011011011011011011011011011011011011010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101\n",
"1101101101101101101101101101101010101010101010101\n",
"-1\n",
"-1\n"
] | 1
|
stdio
|
Let quasi-palindromic number be such number that adding some leading zeros (possible none) to it produces a palindromic string.
String t is called a palindrome, if it reads the same from left to right and from right to left.
For example, numbers 131 and 2010200 are quasi-palindromic, they can be transformed to strings "131" and "002010200", respectively, which are palindromes.
You are given some integer number x. Check if it's a quasi-palindromic number.
-----Input-----
The first line contains one integer number x (1 ≤ x ≤ 10^9). This number is given without any leading zeroes.
-----Output-----
Print "YES" if number x is quasi-palindromic. Otherwise, print "NO" (without quotes).
-----Examples-----
Input
131
Output
YES
Input
320
Output
NO
Input
2010200
Output
YES
|
[
"131\n",
"320\n",
"2010200\n",
"1\n",
"1000000000\n",
"999999999\n",
"999999998\n",
"102000\n",
"210000000\n",
"213443120\n"
] |
[
"YES\n",
"NO\n",
"YES\n",
"YES\n",
"YES\n",
"YES\n",
"NO\n",
"NO\n",
"NO\n",
"YES\n"
] | 1
|
stdio
|
Imp is in a magic forest, where xorangles grow (wut?)
[Image]
A xorangle of order n is such a non-degenerate triangle, that lengths of its sides are integers not exceeding n, and the xor-sum of the lengths is equal to zero. Imp has to count the number of distinct xorangles of order n to get out of the forest.
Formally, for a given integer n you have to find the number of such triples (a, b, c), that:
1 ≤ a ≤ b ≤ c ≤ n; $a \oplus b \oplus c = 0$, where $x \oplus y$ denotes the bitwise xor of integers x and y. (a, b, c) form a non-degenerate (with strictly positive area) triangle.
-----Input-----
The only line contains a single integer n (1 ≤ n ≤ 2500).
-----Output-----
Print the number of xorangles of order n.
-----Examples-----
Input
6
Output
1
Input
10
Output
2
-----Note-----
The only xorangle in the first sample is (3, 5, 6).
|
[
"6\n",
"10\n",
"3\n",
"4\n",
"5\n",
"2500\n",
"952\n",
"88\n",
"1216\n",
"2140\n"
] |
[
"1\n",
"2\n",
"0\n",
"0\n",
"0\n",
"700393\n",
"118547\n",
"536\n",
"160822\n",
"614785\n"
] | 1
|
stdio
|
Marina loves strings of the same length and Vasya loves when there is a third string, different from them in exactly t characters. Help Vasya find at least one such string.
More formally, you are given two strings s_1, s_2 of length n and number t. Let's denote as f(a, b) the number of characters in which strings a and b are different. Then your task will be to find any string s_3 of length n, such that f(s_1, s_3) = f(s_2, s_3) = t. If there is no such string, print - 1.
-----Input-----
The first line contains two integers n and t (1 ≤ n ≤ 10^5, 0 ≤ t ≤ n).
The second line contains string s_1 of length n, consisting of lowercase English letters.
The third line contain string s_2 of length n, consisting of lowercase English letters.
-----Output-----
Print a string of length n, differing from string s_1 and from s_2 in exactly t characters. Your string should consist only from lowercase English letters. If such string doesn't exist, print -1.
-----Examples-----
Input
3 2
abc
xyc
Output
ayd
Input
1 0
c
b
Output
-1
|
[
"3 2\nabc\nxyc\n",
"1 0\nc\nb\n",
"1 1\na\na\n",
"2 1\naa\naa\n",
"3 1\nbcb\nbca\n",
"4 3\nccbb\ncaab\n",
"4 2\nacbc\nacba\n",
"4 1\nbcbc\nacab\n",
"4 2\nacbb\nbabc\n",
"5 2\nabaac\nbbbaa\n"
] |
[
"bac",
"-1\n",
"b",
"ab",
"bcc",
"cbca",
"acab",
"-1\n",
"aaba",
"abbab"
] | 1
|
stdio
|
Luke Skywalker gave Chewbacca an integer number x. Chewbacca isn't good at numbers but he loves inverting digits in them. Inverting digit t means replacing it with digit 9 - t.
Help Chewbacca to transform the initial number x to the minimum possible positive number by inverting some (possibly, zero) digits. The decimal representation of the final number shouldn't start with a zero.
-----Input-----
The first line contains a single integer x (1 ≤ x ≤ 10^18) — the number that Luke Skywalker gave to Chewbacca.
-----Output-----
Print the minimum possible positive number that Chewbacca can obtain after inverting some digits. The number shouldn't contain leading zeroes.
-----Examples-----
Input
27
Output
22
Input
4545
Output
4444
|
[
"27\n",
"4545\n",
"1\n",
"9\n",
"8772\n",
"81\n",
"71723447\n",
"91730629\n",
"420062703497\n",
"332711047202\n"
] |
[
"22\n",
"4444\n",
"1\n",
"9\n",
"1222\n",
"11\n",
"21223442\n",
"91230320\n",
"420032203402\n",
"332211042202\n"
] | 1
|
stdio
|
Programmer Rostislav got seriously interested in the Link/Cut Tree data structure, which is based on Splay trees. Specifically, he is now studying the expose procedure.
Unfortunately, Rostislav is unable to understand the definition of this procedure, so he decided to ask programmer Serezha to help him. Serezha agreed to help if Rostislav solves a simple task (and if he doesn't, then why would he need Splay trees anyway?)
Given integers l, r and k, you need to print all powers of number k within range from l to r inclusive. However, Rostislav doesn't want to spent time doing this, as he got interested in playing a network game called Agar with Gleb. Help him!
-----Input-----
The first line of the input contains three space-separated integers l, r and k (1 ≤ l ≤ r ≤ 10^18, 2 ≤ k ≤ 10^9).
-----Output-----
Print all powers of number k, that lie within range from l to r in the increasing order. If there are no such numbers, print "-1" (without the quotes).
-----Examples-----
Input
1 10 2
Output
1 2 4 8
Input
2 4 5
Output
-1
-----Note-----
Note to the first sample: numbers 2^0 = 1, 2^1 = 2, 2^2 = 4, 2^3 = 8 lie within the specified range. The number 2^4 = 16 is greater then 10, thus it shouldn't be printed.
|
[
"1 10 2\n",
"2 4 5\n",
"18102 43332383920 28554\n",
"19562 31702689720 17701\n",
"11729 55221128400 313\n",
"5482 100347128000 342\n",
"3680 37745933600 10\n",
"17098 191120104800 43\n",
"10462 418807699200 2\n",
"30061 641846400000 3\n"
] |
[
"1 2 4 8 ",
"-1",
"28554 815330916 ",
"313325401 ",
"97969 30664297 9597924961 ",
"116964 40001688 13680577296 ",
"10000 100000 1000000 10000000 100000000 1000000000 10000000000 ",
"79507 3418801 147008443 6321363049 ",
"16384 32768 65536 131072 262144 524288 1048576 2097152 4194304 8388608 16777216 33554432 67108864 134217728 268435456 536870912 1073741824 2147483648 4294967296 8589934592 17179869184 34359738368 68719476736 137438953472 274877906944 ",
"59049 177147 531441 1594323 4782969 14348907 43046721 129140163 387420489 1162261467 3486784401 10460353203 31381059609 94143178827 282429536481 "
] | 1
|
stdio
|
There are N blocks arranged in a row. Let us paint these blocks.
We will consider two ways to paint the blocks different if and only if there is a block painted in different colors in those two ways.
Find the number of ways to paint the blocks under the following conditions:
- For each block, use one of the M colors, Color 1 through Color M, to paint it. It is not mandatory to use all the colors.
- There may be at most K pairs of adjacent blocks that are painted in the same color.
Since the count may be enormous, print it modulo 998244353.
-----Constraints-----
- All values in input are integers.
- 1 \leq N, M \leq 2 \times 10^5
- 0 \leq K \leq N - 1
-----Input-----
Input is given from Standard Input in the following format:
N M K
-----Output-----
Print the answer.
-----Sample Input-----
3 2 1
-----Sample Output-----
6
The following ways to paint the blocks satisfy the conditions: 112, 121, 122, 211, 212, and 221. Here, digits represent the colors of the blocks.
|
[
"3 2 1\n",
"100 100 0\n",
"60522 114575 7559\n",
"1 1 0\n",
"1 1 0\n",
"1 200000 0\n",
"1 200000 0\n",
"200000 1 0\n",
"200000 1 199999\n",
"200000 200000 0\n"
] |
[
"6\n",
"73074801\n",
"479519525\n",
"1\n",
"1\n",
"200000\n",
"200000\n",
"0\n",
"1\n",
"815343867\n"
] | 1
|
stdio
|
Given are a prime number p and a sequence of p integers a_0, \ldots, a_{p-1} consisting of zeros and ones.
Find a polynomial of degree at most p-1, f(x) = b_{p-1} x^{p-1} + b_{p-2} x^{p-2} + \ldots + b_0, satisfying the following conditions:
- For each i (0 \leq i \leq p-1), b_i is an integer such that 0 \leq b_i \leq p-1.
- For each i (0 \leq i \leq p-1), f(i) \equiv a_i \pmod p.
-----Constraints-----
- 2 \leq p \leq 2999
- p is a prime number.
- 0 \leq a_i \leq 1
-----Input-----
Input is given from Standard Input in the following format:
p
a_0 a_1 \ldots a_{p-1}
-----Output-----
Print b_0, b_1, \ldots, b_{p-1} of a polynomial f(x) satisfying the conditions, in this order, with spaces in between.
It can be proved that a solution always exists. If multiple solutions exist, any of them will be accepted.
-----Sample Input-----
2
1 0
-----Sample Output-----
1 1
f(x) = x + 1 satisfies the conditions, as follows:
- f(0) = 0 + 1 = 1 \equiv 1 \pmod 2
- f(1) = 1 + 1 = 2 \equiv 0 \pmod 2
|
[
"2\n1 0\n",
"3\n0 0 0\n",
"5\n0 1 0 1 0\n",
"2\n0 0\n",
"2\n0 1\n",
"2\n1 1\n",
"2999\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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0 0\n",
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Polycarp is a great fan of television.
He wrote down all the TV programs he is interested in for today. His list contains n shows, i-th of them starts at moment l_{i} and ends at moment r_{i}.
Polycarp owns two TVs. He can watch two different shows simultaneously with two TVs but he can only watch one show at any given moment on a single TV. If one show ends at the same moment some other show starts then you can't watch them on a single TV.
Polycarp wants to check out all n shows. Are two TVs enough to do so?
-----Input-----
The first line contains one integer n (1 ≤ n ≤ 2·10^5) — the number of shows.
Each of the next n lines contains two integers l_{i} and r_{i} (0 ≤ l_{i} < r_{i} ≤ 10^9) — starting and ending time of i-th show.
-----Output-----
If Polycarp is able to check out all the shows using only two TVs then print "YES" (without quotes). Otherwise, print "NO" (without quotes).
-----Examples-----
Input
3
1 2
2 3
4 5
Output
YES
Input
4
1 2
2 3
2 3
1 2
Output
NO
|
[
"3\n1 2\n2 3\n4 5\n",
"4\n1 2\n2 3\n2 3\n1 2\n",
"4\n0 1\n1 2\n2 3\n3 4\n",
"3\n1 2\n2 3\n2 4\n",
"3\n0 100\n0 100\n0 100\n",
"1\n0 1000000000\n",
"2\n0 1\n0 1\n",
"3\n2 3\n4 5\n1 6\n",
"5\n1 3\n1 4\n4 10\n5 8\n9 11\n",
"3\n1 2\n1 2\n2 3\n"
] |
[
"YES\n",
"NO\n",
"YES\n",
"NO\n",
"NO\n",
"YES\n",
"YES\n",
"YES\n",
"YES\n",
"NO\n"
] | 1
|
stdio
|
Sereja showed an interesting game to his friends. The game goes like that. Initially, there is a table with an empty cup and n water mugs on it. Then all players take turns to move. During a move, a player takes a non-empty mug of water and pours all water from it into the cup. If the cup overfills, then we assume that this player lost.
As soon as Sereja's friends heard of the game, they wanted to play it. Sereja, on the other hand, wanted to find out whether his friends can play the game in such a way that there are no losers. You are given the volumes of all mugs and the cup. Also, you know that Sereja has (n - 1) friends. Determine if Sereja's friends can play the game so that nobody loses.
-----Input-----
The first line contains integers n and s (2 ≤ n ≤ 100; 1 ≤ s ≤ 1000) — the number of mugs and the volume of the cup. The next line contains n integers a_1, a_2, ..., a_{n} (1 ≤ a_{i} ≤ 10). Number a_{i} means the volume of the i-th mug.
-----Output-----
In a single line, print "YES" (without the quotes) if his friends can play in the described manner, and "NO" (without the quotes) otherwise.
-----Examples-----
Input
3 4
1 1 1
Output
YES
Input
3 4
3 1 3
Output
YES
Input
3 4
4 4 4
Output
NO
|
[
"3 4\n1 1 1\n",
"3 4\n3 1 3\n",
"3 4\n4 4 4\n",
"2 1\n1 10\n",
"3 12\n5 6 6\n",
"4 10\n6 3 8 7\n",
"5 16\n3 3 2 7 9\n",
"6 38\n9 10 3 8 10 6\n",
"7 12\n4 4 5 2 2 4 9\n",
"8 15\n8 10 4 2 10 9 7 6\n"
] |
[
"YES\n",
"YES\n",
"NO\n",
"YES\n",
"YES\n",
"NO\n",
"YES\n",
"YES\n",
"NO\n",
"NO\n"
] | 1
|
stdio
|
Kolya loves putting gnomes at the circle table and giving them coins, and Tanya loves studying triplets of gnomes, sitting in the vertexes of an equilateral triangle.
More formally, there are 3n gnomes sitting in a circle. Each gnome can have from 1 to 3 coins. Let's number the places in the order they occur in the circle by numbers from 0 to 3n - 1, let the gnome sitting on the i-th place have a_{i} coins. If there is an integer i (0 ≤ i < n) such that a_{i} + a_{i} + n + a_{i} + 2n ≠ 6, then Tanya is satisfied.
Count the number of ways to choose a_{i} so that Tanya is satisfied. As there can be many ways of distributing coins, print the remainder of this number modulo 10^9 + 7. Two ways, a and b, are considered distinct if there is index i (0 ≤ i < 3n), such that a_{i} ≠ b_{i} (that is, some gnome got different number of coins in these two ways).
-----Input-----
A single line contains number n (1 ≤ n ≤ 10^5) — the number of the gnomes divided by three.
-----Output-----
Print a single number — the remainder of the number of variants of distributing coins that satisfy Tanya modulo 10^9 + 7.
-----Examples-----
Input
1
Output
20
Input
2
Output
680
-----Note-----
20 ways for n = 1 (gnome with index 0 sits on the top of the triangle, gnome 1 on the right vertex, gnome 2 on the left vertex): [Image]
|
[
"1\n",
"2\n",
"3\n",
"4\n",
"5\n",
"7\n",
"10\n",
"14\n",
"58000\n",
"6\n"
] |
[
"20",
"680",
"19340",
"529040",
"14332100",
"459529590",
"848178170",
"356372551",
"66667472",
"387302840"
] | 1
|
stdio
|
A wise man told Kerem "Different is good" once, so Kerem wants all things in his life to be different.
Kerem recently got a string s consisting of lowercase English letters. Since Kerem likes it when things are different, he wants all substrings of his string s to be distinct. Substring is a string formed by some number of consecutive characters of the string. For example, string "aba" has substrings "" (empty substring), "a", "b", "a", "ab", "ba", "aba".
If string s has at least two equal substrings then Kerem will change characters at some positions to some other lowercase English letters. Changing characters is a very tiring job, so Kerem want to perform as few changes as possible.
Your task is to find the minimum number of changes needed to make all the substrings of the given string distinct, or determine that it is impossible.
-----Input-----
The first line of the input contains an integer n (1 ≤ n ≤ 100 000) — the length of the string s.
The second line contains the string s of length n consisting of only lowercase English letters.
-----Output-----
If it's impossible to change the string s such that all its substring are distinct print -1. Otherwise print the minimum required number of changes.
-----Examples-----
Input
2
aa
Output
1
Input
4
koko
Output
2
Input
5
murat
Output
0
-----Note-----
In the first sample one of the possible solutions is to change the first character to 'b'.
In the second sample, one may change the first character to 'a' and second character to 'b', so the string becomes "abko".
|
[
"2\naa\n",
"4\nkoko\n",
"5\nmurat\n",
"6\nacbead\n",
"7\ncdaadad\n",
"25\npeoaicnbisdocqofsqdpgobpn\n",
"25\ntcqpchnqskqjacruoaqilgebu\n",
"13\naebaecedabbee\n",
"27\naaaaaaaaaaaaaaaaaaaaaaaaaaa\n",
"10\nbababbdaee\n"
] |
[
"1\n",
"2\n",
"0\n",
"1\n",
"4\n",
"12\n",
"7\n",
"8\n",
"-1\n",
"6\n"
] | 1
|
stdio
|
At regular competition Vladik and Valera won a and b candies respectively. Vladik offered 1 his candy to Valera. After that Valera gave Vladik 2 his candies, so that no one thought that he was less generous. Vladik for same reason gave 3 candies to Valera in next turn.
More formally, the guys take turns giving each other one candy more than they received in the previous turn.
This continued until the moment when one of them couldn’t give the right amount of candy. Candies, which guys got from each other, they don’t consider as their own. You need to know, who is the first who can’t give the right amount of candy.
-----Input-----
Single line of input data contains two space-separated integers a, b (1 ≤ a, b ≤ 10^9) — number of Vladik and Valera candies respectively.
-----Output-----
Pring a single line "Vladik’’ in case, if Vladik first who can’t give right amount of candy, or "Valera’’ otherwise.
-----Examples-----
Input
1 1
Output
Valera
Input
7 6
Output
Vladik
-----Note-----
Illustration for first test case:
[Image]
Illustration for second test case:
[Image]
|
[
"1 1\n",
"7 6\n",
"25 38\n",
"8311 2468\n",
"250708 857756\n",
"957985574 24997558\n",
"999963734 999994456\n",
"1000000000 1000000000\n",
"946 879\n",
"10819 45238\n"
] |
[
"Valera\n",
"Vladik\n",
"Vladik\n",
"Valera\n",
"Vladik\n",
"Valera\n",
"Vladik\n",
"Vladik\n",
"Valera\n",
"Vladik\n"
] | 1
|
stdio
|
Given an array $a$, consisting of $n$ integers, find:
$$\max\limits_{1 \le i < j \le n} LCM(a_i,a_j),$$
where $LCM(x, y)$ is the smallest positive integer that is divisible by both $x$ and $y$. For example, $LCM(6, 8) = 24$, $LCM(4, 12) = 12$, $LCM(2, 3) = 6$.
-----Input-----
The first line contains an integer $n$ ($2 \le n \le 10^5$) — the number of elements in the array $a$.
The second line contains $n$ integers $a_1, a_2, \dots, a_n$ ($1 \le a_i \le 10^5$) — the elements of the array $a$.
-----Output-----
Print one integer, the maximum value of the least common multiple of two elements in the array $a$.
-----Examples-----
Input
3
13 35 77
Output
1001
Input
6
1 2 4 8 16 32
Output
32
|
[
"3\n13 35 77\n",
"6\n1 2 4 8 16 32\n",
"2\n2 5\n",
"4\n12 9 1 8\n",
"4\n15 12 9 10\n",
"56\n15 10 44 38 12 7 20 17 16 3 43 10 32 4 31 38 8 15 21 8 37 44 19 21 26 24 22 21 16 43 45 36 29 36 41 44 39 34 7 8 42 49 5 31 50 34 22 13 22 38 38 45 14 15 18 45\n",
"74\n25 41 29 49 11 14 23 7 23 12 47 14 31 38 41 30 19 10 3 25 41 7 17 49 29 30 49 26 36 34 35 22 10 25 46 30 22 49 7 3 7 24 50 4 1 40 20 25 26 8 34 35 5 37 41 46 15 10 22 40 3 22 27 43 40 5 15 46 40 41 21 40 16 22\n",
"44\n155 188 95 86 212 468 137 23 465 239 104 109 427 176 344 266 55 10 334 224 489 99 483 137 159 341 91 364 52 113 248 346 439 271 468 309 382 93 320 351 337 429 125 196\n",
"62\n367 369 81 198 361 25 439 264 72 247 308 265 426 209 306 258 317 155 465 491 192 312 331 115 460 46 468 119 122 154 139 231 320 10 23 245 363 307 472 396 403 155 470 268 407 112 45 29 281 247 444 102 374 449 75 381 71 72 91 313 267 429\n",
"41\n2 30 1 1 3 1 1 21 27 12 1 1 18 2 1 15 1 9 3 15 15 3 1 1 6 2 2 1 2 12 18 18 2 1 30 1 15 1 2 30 15\n"
] |
[
"1001",
"32",
"10",
"72",
"90",
"2450",
"2450",
"214671",
"231752",
"270"
] | 1
|
stdio
|
VK news recommendation system daily selects interesting publications of one of $n$ disjoint categories for each user. Each publication belongs to exactly one category. For each category $i$ batch algorithm selects $a_i$ publications.
The latest A/B test suggests that users are reading recommended publications more actively if each category has a different number of publications within daily recommendations. The targeted algorithm can find a single interesting publication of $i$-th category within $t_i$ seconds.
What is the minimum total time necessary to add publications to the result of batch algorithm execution, so all categories have a different number of publications? You can't remove publications recommended by the batch algorithm.
-----Input-----
The first line of input consists of single integer $n$ — the number of news categories ($1 \le n \le 200\,000$).
The second line of input consists of $n$ integers $a_i$ — the number of publications of $i$-th category selected by the batch algorithm ($1 \le a_i \le 10^9$).
The third line of input consists of $n$ integers $t_i$ — time it takes for targeted algorithm to find one new publication of category $i$ ($1 \le t_i \le 10^5)$.
-----Output-----
Print one integer — the minimal required time for the targeted algorithm to get rid of categories with the same size.
-----Examples-----
Input
5
3 7 9 7 8
5 2 5 7 5
Output
6
Input
5
1 2 3 4 5
1 1 1 1 1
Output
0
-----Note-----
In the first example, it is possible to find three publications of the second type, which will take 6 seconds.
In the second example, all news categories contain a different number of publications.
|
[
"5\n3 7 9 7 8\n5 2 5 7 5\n",
"5\n1 2 3 4 5\n1 1 1 1 1\n",
"5\n12 4 19 18 19\n15467 14873 66248 58962 90842\n",
"40\n19 20 8 13 13 17 1 14 15 20 14 17 2 9 9 10 19 16 6 12 9 7 20 5 12 6 4 4 12 5 4 11 8 1 2 8 11 19 18 4\n52258 5648 46847 9200 63940 79328 64407 54479 1788 60107 8234 64215 15419 84411 50307 78075 92548 17867 43456 7970 1390 99373 97297 90662 82950 678 79356 51351 2794 82477 16508 19254 81295 9711 72350 11578 21595 69230 82626 25134\n",
"1\n204\n74562\n",
"1\n1\n72\n",
"1\n1\n40825\n",
"1\n5\n16\n",
"1\n4\n85648\n",
"1\n3\n31\n"
] |
[
"6\n",
"0\n",
"66248\n",
"6113465\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n"
] | 1
|
stdio
|
Calendars in widespread use today include the Gregorian calendar, which is the de facto international standard, and is used almost everywhere in the world for civil purposes. The Gregorian reform modified the Julian calendar's scheme of leap years as follows:
Every year that is exactly divisible by four is a leap year, except for years that are exactly divisible by 100; the centurial years that are exactly divisible by 400 are still leap years. For example, the year 1900 is not a leap year; the year 2000 is a leap year. [Image]
In this problem, you have been given two dates and your task is to calculate how many days are between them. Note, that leap years have unusual number of days in February.
Look at the sample to understand what borders are included in the aswer.
-----Input-----
The first two lines contain two dates, each date is in the format yyyy:mm:dd (1900 ≤ yyyy ≤ 2038 and yyyy:mm:dd is a legal date).
-----Output-----
Print a single integer — the answer to the problem.
-----Examples-----
Input
1900:01:01
2038:12:31
Output
50768
Input
1996:03:09
1991:11:12
Output
1579
|
[
"1900:01:01\n2038:12:31\n",
"1996:03:09\n1991:11:12\n",
"1999:12:31\n2000:02:29\n",
"1903:09:27\n1988:06:15\n",
"1913:11:14\n1901:05:11\n",
"1915:01:01\n2007:07:01\n",
"1925:07:15\n2010:06:22\n",
"1935:10:08\n1923:01:07\n",
"1986:08:24\n1926:04:13\n",
"1932:11:18\n2028:09:25\n"
] |
[
"50768\n",
"1579\n",
"60\n",
"30943\n",
"4570\n",
"33784\n",
"31023\n",
"4657\n",
"22048\n",
"35010\n"
] | 1
|
stdio
|
-----Input-----
The input contains a single integer a (1 ≤ a ≤ 40).
-----Output-----
Output a single string.
-----Examples-----
Input
2
Output
Adams
Input
8
Output
Van Buren
Input
29
Output
Harding
|
[
"2\n",
"8\n",
"29\n",
"1\n",
"3\n",
"4\n",
"5\n",
"6\n",
"7\n",
"9\n"
] |
[
"Adams\n",
"Van Buren\n",
"Harding\n",
"Washington\n",
"Jefferson\n",
"Madison\n",
"Monroe\n",
"Adams\n",
"Jackson\n",
"Harrison\n"
] | 1
|
stdio
|
Fox Ciel has some flowers: r red flowers, g green flowers and b blue flowers. She wants to use these flowers to make several bouquets. There are 4 types of bouquets:
To make a "red bouquet", it needs 3 red flowers. To make a "green bouquet", it needs 3 green flowers. To make a "blue bouquet", it needs 3 blue flowers. To make a "mixing bouquet", it needs 1 red, 1 green and 1 blue flower.
Help Fox Ciel to find the maximal number of bouquets she can make.
-----Input-----
The first line contains three integers r, g and b (0 ≤ r, g, b ≤ 10^9) — the number of red, green and blue flowers.
-----Output-----
Print the maximal number of bouquets Fox Ciel can make.
-----Examples-----
Input
3 6 9
Output
6
Input
4 4 4
Output
4
Input
0 0 0
Output
0
-----Note-----
In test case 1, we can make 1 red bouquet, 2 green bouquets and 3 blue bouquets.
In test case 2, we can make 1 red, 1 green, 1 blue and 1 mixing bouquet.
|
[
"3 6 9\n",
"4 4 4\n",
"0 0 0\n",
"0 3 6\n",
"7 8 9\n",
"8 8 9\n",
"15 3 999\n",
"32 62 92\n",
"123456789 123456789 123456789\n",
"3 5 5\n"
] |
[
"6\n",
"4\n",
"0\n",
"3\n",
"7\n",
"8\n",
"339\n",
"62\n",
"123456789\n",
"4\n"
] | 1
|
stdio
|
Valera is a little boy. Yesterday he got a huge Math hometask at school, so Valera didn't have enough time to properly learn the English alphabet for his English lesson. Unfortunately, the English teacher decided to have a test on alphabet today. At the test Valera got a square piece of squared paper. The length of the side equals n squares (n is an odd number) and each unit square contains some small letter of the English alphabet.
Valera needs to know if the letters written on the square piece of paper form letter "X". Valera's teacher thinks that the letters on the piece of paper form an "X", if: on both diagonals of the square paper all letters are the same; all other squares of the paper (they are not on the diagonals) contain the same letter that is different from the letters on the diagonals.
Help Valera, write the program that completes the described task for him.
-----Input-----
The first line contains integer n (3 ≤ n < 300; n is odd). Each of the next n lines contains n small English letters — the description of Valera's paper.
-----Output-----
Print string "YES", if the letters on the paper form letter "X". Otherwise, print string "NO". Print the strings without quotes.
-----Examples-----
Input
5
xooox
oxoxo
soxoo
oxoxo
xooox
Output
NO
Input
3
wsw
sws
wsw
Output
YES
Input
3
xpx
pxp
xpe
Output
NO
|
[
"5\nxooox\noxoxo\nsoxoo\noxoxo\nxooox\n",
"3\nwsw\nsws\nwsw\n",
"3\nxpx\npxp\nxpe\n",
"5\nliiil\nilili\niilii\nilili\nliiil\n",
"7\nbwccccb\nckcccbj\nccbcbcc\ncccbccc\nccbcbcc\ncbcccbc\nbccccdt\n",
"13\nsooooooooooos\nosoooooooooso\noosooooooosoo\nooosooooosooo\noooosooosoooo\nooooososooooo\noooooosoooooo\nooooososooooo\noooosooosoooo\nooosooooosooo\noosooooooosoo\nosoooooooooso\nsooooooooooos\n",
"3\naaa\naaa\naaa\n",
"3\naca\noec\nzba\n",
"15\nrxeeeeeeeeeeeer\nereeeeeeeeeeere\needeeeeeeeeeoee\neeereeeeeeeewee\neeeereeeeebeeee\nqeeeereeejedyee\neeeeeerereeeeee\neeeeeeereeeeeee\neeeeeerereeeeze\neeeeereeereeeee\neeeereeeeegeeee\neeereeeeeeereee\neereeeeeeqeeved\ncreeeeeeceeeere\nreeerneeeeeeeer\n",
"5\nxxxxx\nxxxxx\nxxxxx\nxxxxx\nxxxxx\n"
] |
[
"NO\n",
"YES\n",
"NO\n",
"YES\n",
"NO\n",
"YES\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n"
] | 1
|
stdio
|
Vasya is studying in the last class of school and soon he will take exams. He decided to study polynomials. Polynomial is a function P(x) = a_0 + a_1x^1 + ... + a_{n}x^{n}. Numbers a_{i} are called coefficients of a polynomial, non-negative integer n is called a degree of a polynomial.
Vasya has made a bet with his friends that he can solve any problem with polynomials. They suggested him the problem: "Determine how many polynomials P(x) exist with integer non-negative coefficients so that $P(t) = a$, and $P(P(t)) = b$, where $t, a$ and b are given positive integers"?
Vasya does not like losing bets, but he has no idea how to solve this task, so please help him to solve the problem.
-----Input-----
The input contains three integer positive numbers $t, a, b$ no greater than 10^18.
-----Output-----
If there is an infinite number of such polynomials, then print "inf" without quotes, otherwise print the reminder of an answer modulo 10^9 + 7.
-----Examples-----
Input
2 2 2
Output
2
Input
2 3 3
Output
1
|
[
"2 2 2\n",
"2 3 3\n",
"1 1 1\n",
"3 5 10\n",
"2 3 1000000000000000000\n",
"7 8 9\n",
"8 10 11\n",
"5 30 930\n",
"3 3 3\n",
"1 5 5\n"
] |
[
"2\n",
"1\n",
"inf\n",
"0\n",
"0\n",
"1\n",
"0\n",
"1\n",
"2\n",
"1\n"
] | 1
|
stdio
|
After several latest reforms many tourists are planning to visit Berland, and Berland people understood that it's an opportunity to earn money and changed their jobs to attract tourists. Petya, for example, left the IT corporation he had been working for and started to sell souvenirs at the market.
This morning, as usual, Petya will come to the market. Petya has n different souvenirs to sell; ith souvenir is characterised by its weight w_{i} and cost c_{i}. Petya knows that he might not be able to carry all the souvenirs to the market. So Petya wants to choose a subset of souvenirs such that its total weight is not greater than m, and total cost is maximum possible.
Help Petya to determine maximum possible total cost.
-----Input-----
The first line contains two integers n and m (1 ≤ n ≤ 100000, 1 ≤ m ≤ 300000) — the number of Petya's souvenirs and total weight that he can carry to the market.
Then n lines follow. ith line contains two integers w_{i} and c_{i} (1 ≤ w_{i} ≤ 3, 1 ≤ c_{i} ≤ 10^9) — the weight and the cost of ith souvenir.
-----Output-----
Print one number — maximum possible total cost of souvenirs that Petya can carry to the market.
-----Examples-----
Input
1 1
2 1
Output
0
Input
2 2
1 3
2 2
Output
3
Input
4 3
3 10
2 7
2 8
1 1
Output
10
|
[
"1 1\n2 1\n",
"2 2\n1 3\n2 2\n",
"4 3\n3 10\n2 7\n2 8\n1 1\n",
"5 5\n3 5\n2 6\n3 2\n1 1\n1 6\n",
"6 6\n1 6\n1 4\n1 8\n3 2\n3 2\n2 8\n",
"6 12\n1 7\n1 10\n2 8\n1 2\n2 9\n3 5\n",
"6 18\n3 3\n1 10\n2 10\n3 6\n1 3\n2 3\n",
"20 25\n2 13\n3 11\n1 32\n1 43\n3 85\n1 14\n2 57\n1 54\n1 38\n2 96\n2 89\n3 64\n1 79\n2 73\n1 73\n2 34\n1 52\n1 79\n1 42\n3 34\n",
"40 45\n2 82\n2 70\n2 48\n3 50\n2 15\n1 23\n1 80\n2 46\n1 20\n3 8\n3 81\n2 27\n1 59\n1 15\n3 95\n2 82\n2 40\n2 9\n2 61\n1 49\n2 5\n2 82\n1 55\n2 11\n1 26\n1 33\n1 2\n1 7\n3 57\n2 29\n1 59\n2 50\n3 63\n1 40\n1 99\n2 91\n2 39\n3 50\n1 75\n3 77\n",
"4 28\n2 2\n3 1\n3 10\n1 9\n"
] |
[
"0\n",
"3\n",
"10\n",
"13\n",
"26\n",
"41\n",
"35\n",
"990\n",
"1605\n",
"22\n"
] | 1
|
stdio
|
Snuke has an integer sequence A of length N.
He will make three cuts in A and divide it into four (non-empty) contiguous subsequences B, C, D and E.
The positions of the cuts can be freely chosen.
Let P,Q,R,S be the sums of the elements in B,C,D,E, respectively.
Snuke is happier when the absolute difference of the maximum and the minimum among P,Q,R,S is smaller.
Find the minimum possible absolute difference of the maximum and the minimum among P,Q,R,S.
-----Constraints-----
- 4 \leq N \leq 2 \times 10^5
- 1 \leq A_i \leq 10^9
- All values in input are integers.
-----Input-----
Input is given from Standard Input in the following format:
N
A_1 A_2 ... A_N
-----Output-----
Find the minimum possible absolute difference of the maximum and the minimum among P,Q,R,S.
-----Sample Input-----
5
3 2 4 1 2
-----Sample Output-----
2
If we divide A as B,C,D,E=(3),(2),(4),(1,2), then P=3,Q=2,R=4,S=1+2=3.
Here, the maximum and the minimum among P,Q,R,S are 4 and 2, with the absolute difference of 2.
We cannot make the absolute difference of the maximum and the minimum less than 2, so the answer is 2.
|
[
"5\n3 2 4 1 2\n",
"10\n10 71 84 33 6 47 23 25 52 64\n",
"7\n1 2 3 1000000000 4 5 6\n",
"4\n877914575 602436426 24979445 861648772\n",
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14250 71274 44263 16825 35572 98232 65136 98305 68763 53196 16067 35653 88670 66974 38746 67559 786 29148 8387 12895 40350 98087 77951 89271 58270 27569 69861 57965 77665 52229 90620 17620 56171 48991 10052 30323 66932 37200 79790 58628 58214 41788 91231 1014 41794 44091 26706 65164 90076 50075 85811 46684 69339 78076 12036 63793 48986 6611 68091 1834 91946 54728 20770 27896 41230 62999 53782 69188 38173 89587 44777 14534 95459 16959 42305 70799 93024 78451 7030 64000 33415 40445 83831 1425 54689 45053 26022 59659 5832 25159 183 71662 4908 75717 85622 63084 49009 74195 50942 41228 91151 95841 30850 5096 22737 93845 12743 65263 68311 83942 8872 91748 4852 52738 71793 23773 27728 75305 83269 71492 64358 88143 34041 99098 81991 88926 58614 43631 79062 23633 88762 83339 34731 69723 14168 15913 9264 95742 23603 58102 56646 72820 87431 20278 22465 17802 54945 73312 57608 71616 6850 32221 73142 89482 46783 25773 92988 17810 83652 60129 79740 46451 93772 97122 5103 73568 6667 90185 59681 45019 93701 82853 5552 10686 68916 57528 91568 82998 40581 7290 17097 96034 11835 40821 78071 1944 52139 85543 38538 81089 68255 60099 64964 76568 95283 73936 7997 272 13531 33416 55586 38059 35835 44251 53842 88931 93453 54026 49504 94404 17247 85708 10644 14448 86610 63820 65034 84986 27100 96584 75761 32715 40135 65908 8780 8673 89520 92213 68501 17675 44169 8327 65397 23662 95383 99416 49326 99651 67700 2250 13105 9910 45134 35733 21960 42121 68742 72578 21421 69967 74771 21809 54129 87473 3004 8916 94518 63916 6401 87986 63349 41553 37843 86917 538 35492 85368 93884 76771 32766 36744 9978 27748 87564 95346 60085 20805 45645 8952 62679 15778 28183 92718 69953 35658 39666 92671 57475 3202 92251 58472 97125 47583 42499 63227 73442 80239 27310 75262 31911 53937 86389 44201 98777 48376 66436 96716 29356 24844 284 83782 83724 91144 92498 61583 83096 74205 91086 97231 8290 40718 67118 89636 82832 22290 28992 51841 68286 24278 56555 32745 94458 64728 38887 33912 98631 86349 66784 59067 48315 9723 59703 16946 62976 16640 38689 84821 23478 52201 77734 67308 94640 50108 46339 32278 9715 4847 8264 13987 18842 1230 38171 31898 72148 96377 91476 88916 55812 45795 88575 6559 7872 44788 14333 86395 54547 69000 16611 84416 76636 78159 74073 28983 9805 27307 68380 83901 74828 91060 74972 85507 39797 64247 88255 99760 55189 85907 6172 4541 16785 63355 74529 45240 98365 17015 33998 84354 71622 90306 47544 55985 37737 70605 14151 3183 43897 39579 22775 68888 90493 19267 29019 28128 1135 22066 62261 78507 66814 65350 34112 83795 91949 22867 49383 95366 40626 48674 49994 8006 51256 52013 84352 99783 74525 96485 79152 84884 21396 33228 38199 12394 57029 74555 47141 314 21160 30269 4959 60588 30030 89778 93855 79735 88248 92045 56143 72106 94461 88503 15762 39302 53417 95594 48636 50370 41560 3798 46964 18918 39391 85599 26329 78928 82372 48605 12154 24050 54177 762 33949 69489 7205 95832 47065 97000 34610 87113 46331 27011 35360 17141 8357 88293 14361 1367 54314 98626 78619 12640 79412 22757 93849 96787 88127 620 54490 44935 44187 81703 1561 61577 71181 59260 24579 78455 9038 14630 11804 70085 8203 2161 24506 52956 63107 8000 6984 2038 83788 45928 72453 56036 47951 84146 64675 80488 17191 54268 22152 99899 82022 8409 1648 24264 53585 15213 585 22863 41887 7153 18453 43203 25309 81557 22444 27148 35693 73753 26263 23078 1442 75571 95926 59392 82053 91532 15963 69823 27476 70211 42125 40408 221 24008 47110 99193 1928 17826 10549 61504 4458 65034 32733 72354 26003 43310 35924 19366 67137 20847 34405 6344 60138 39171 70254 64790 27287 70387 80035 57590 21187 18750 64201 88382 60128 66165 69084 48667 19634 27453 99401 86091 27090 68240 29141 80099 98412 7868 21492 36265 417 24354 83954 5786 14406 88696 6894 67014 73603 95752 53050 85935 36662 22895 70909 69774 58669 14270 99633 6478 47375 4093 91461 687 15892 55715 67131 38212 78792 23231 33899 59349 4716 54258 96351 48574 97781 27795 44725 91662 47147 60393 11264 42473 27307 13493 32199 59207 30502 66693 84709 49075 42112 56482 66023 63148 47442 55203 58641 21447 21992 14199 25433 19275 63587 82784 63371 79667 45687 86066 1475 32208 44303 77656 5622 47205 44549 52848 52649 97033 97450 67434 64664 60584 56196 63436 91025 18818 3018 60209 36790 34603 35658 71845 11679 32809 43172 83659 31830 6618 67021 85047 5145 49931 60845 31733 32539 13569 9665 85600 34723 58644 30297 92363 56875 81199 83227 21372 67746 42994 40510 52492 93611 3248 58896 29320 27420 3697 19377 92467 73184 86545 69238 37538 9429 38879 40647 22750 34255 61759 65857 92678 12275 7145 82068 40970 18749 59048 8869 32081 93306 30331 57902 81236 52462 93847 66138 4352 41648 17379 58857 65176 11977 9786 77618 48817 78169 87501 24380 36821 23986 44863 96099 85761 12795 13255 65434 61286 54478 73361 96899 56939 94106 76317 82424 41417 20961 97631 27206 32430 57051 27197 77869 9499 8594 7988 23233 11558 37892 7988 16652 81753 76901 64543 97034 96849 17050 60622 73771 26975 34462 83980 71700 11627 8257 93241 81406 2924 356 45128 50582 20721 14142 75681 60763 43099 71162 25152 42276 63456 25143 69460 38967 52298 59526 75201 47027 18582 84784 43102 38631 52886 18606 99992 88312 38927 14607 18605 49855 4380 80149 95794 59625 21449 30936 31886 62421 31480 35937 94044 73562 68992 74096 30221 64638 60649 18359 97988 71072 40785 93 94040 4783 70570 74877 15125 88368 80281 53636 88475 5852 7481 80246 19198 81311 57910 13385 79108 48571 71827 97256 47274 72515 68868 51281 78048 81664 46772 37176 80296 71887 60993 36130 83227 35585 83771 23883 28484 89530 29992 87360 21218 74675 94115 16582 71498 27097 82649 9713 33635 97195 75402 28109 65417 50911 87918 26873 72747 76509 66669 49351 77933 71107 63078 25534 81639 5535 61449 72088 78915 94072 26717 10148 76195 44006 1723 28613 34552 51477 71792 52529 47660 20967 16319 88818 85722 74703 66909 73417 59120 27318 93715 27014 41876 98137 70016 84241 62268 91529 68053 99173 70548 29450 98679 66543 65948 16756 83456 96083 27688 5749 68957 67688 25278 60462 14033 83223 44091 47345 44049 40575 34575 458 81319 4628 59004 6835 56080 30940 62875 71389 7837 84401 11415 97230 12534 70113 93071 59582 52114 42961 25144 77177 5600 67158 65593 23296 59713 59162 48174 92967 93867 37149 96198 15289 77576 98097 90533 52943 22933 381 66498 74013 88323 50556 96362 87110 74458 18363 97851 28770 27953 29374 11978 33215 89047 70651 54046 2397 35309 39613 84274 87601 8106 97794 67095 86723 59478 72318 34191 75152 28367 68438 49556 38088 14247 37670 72623 53745 78531 86524 39425 57986 37534 78874 2365 40361 86436 89496 98028 76294 97687 15679 96744 1453 1582 76463 96641 9384 30865 20090 95675 92467 21662 29959 30894 14334 17063 27024 91045 2863 13586 88484 99135 57757 23224 3557 73681 77078 2662 57259 1123 31642 17631 51008 71022 65373 92599 57090 1476 54697 44025 30149 9288 79674 7779 28078 89329 77408 84357 77912 66860 20736 38534 45363 50423 37748 10783 96640 66919 8518 58173 57750 37955 96697 38915 56897 91750 98848 57510 80765 26369 59301 55407 3423 44310 59908 79965 90381 10174 25069 14400 16033 21925 91973 89695 31786 27112 26565 49587 32138 82302 19002 59434 44601 67436 41603 6277 45024 11151 59767 34458 72575 81495 4092 30514 4521 80166 89489 38476 61923 74324 45733 65112 744 99630 74461 62813 21287 92275 60466 58933 46403 438 34480 3659 45714 82015 46393 52548 47071 8170 82112 2995 71529 4166 3663 7810 35905 6806 74369 10256 44304 19604 5800 11374 98639 54345 23464 46401 748 60663 60538 44547 47340 39791 62666 68674 23587 65275 27834 52224 20638 79861 5629 47089 4762 98094 61628 76512 50378 88296 69077 28426 89844 98012 24151 19201 27636 10453 64039 92874 86969 87891 71037 66720 4931 40714 38664 84079 6155 30080 85190 53529 56347 18738 83725 6837 4305 17327 71333 8811 26273 43804 30668 55257 10320 97678 31184 26225 86426 88915 71160 27224 45740 65770 75036 50665 63754 59878 14504 46704 65867 2575 40797 52464 68312 41504 8496 24765 72305 64778 5450 9219 16903 60048 80166 19037 98083 53289 8245 56062 37406 87970 4637 71756 42151 14009 56086 2015 61568 35875 63884 76039 97185 19974 55488 61828 72788 38912 83399 77227 67287 26910 34185 26856 18109 33446 86851 34134 18253 55278 69286 72393 50946 30978 39029 88868 98121 67906 87147 7651 53094 17761 50419 86643 55471 62087 14222 90869 30575 75248 44017 88063 56229 31915 83044 78234 89410 40861 65316 79141 17071 48283 31169 56368 52708 94643 47425 94370 76658 62404 12187 66004 24347 12608 41917 45940 53076 42961 86439 8707 73738 95250 24750 82615 59130 17586 1786 8410 44183 4373 73864 34441 51047 65938 70280 69525 5255 80021 23168 54790 29475 56895 97767 39027 32574 59137 27339 86827 11792 27589 25964 12559 31459 54245 7870 43637 79254 98066 59691 11399 74106 44142 87055 21506 44567 26578 53434 48440 66408 5673 53297 99822 65242 88787 72942 37822 52818 17891 65339 65142 91716 53890 88315 80280 47068 15370 46082 16600 70873 97611 4983 49089 34701 92425 81177 22960 78303 96475 14807 88919 83624 91438 10903 94428 65369 50945 46576 67287 97908 85607 68847 94904 10127 59112 87830 95966 59925 76959 49240 62529 11748 41853 67199 79305 67407 97189 43367 73972 83773 62222 4896 87476 83080 61124 37135 74447 23424 98440 72461 5821 67398 44651 20039 62190 72177 95351 15996 92961 92652 34694 45059 67726 82294 86505 42210 80861 92608 28482 23896 2253 81555 32810 4564 70190 90215 73644 90779 73383 17165 74312 14534 21137 87495 45169 68225 85593 20490 86447 45934 70466\n"
] |
[
"2\n",
"36\n",
"999999994\n",
"852935130\n",
"226008843\n",
"325361182\n",
"549938604\n",
"218707676\n",
"728856976\n",
"36328\n"
] | 1
|
stdio
|
Ksenia has ordinary pan scales and several weights of an equal mass. Ksenia has already put some weights on the scales, while other weights are untouched. Ksenia is now wondering whether it is possible to put all the remaining weights on the scales so that the scales were in equilibrium.
The scales is in equilibrium if the total sum of weights on the left pan is equal to the total sum of weights on the right pan.
-----Input-----
The first line has a non-empty sequence of characters describing the scales. In this sequence, an uppercase English letter indicates a weight, and the symbol "|" indicates the delimiter (the character occurs in the sequence exactly once). All weights that are recorded in the sequence before the delimiter are initially on the left pan of the scale. All weights that are recorded in the sequence after the delimiter are initially on the right pan of the scale.
The second line contains a non-empty sequence containing uppercase English letters. Each letter indicates a weight which is not used yet.
It is guaranteed that all the English letters in the input data are different. It is guaranteed that the input does not contain any extra characters.
-----Output-----
If you cannot put all the weights on the scales so that the scales were in equilibrium, print string "Impossible". Otherwise, print the description of the resulting scales, copy the format of the input.
If there are multiple answers, print any of them.
-----Examples-----
Input
AC|T
L
Output
AC|TL
Input
|ABC
XYZ
Output
XYZ|ABC
Input
W|T
F
Output
Impossible
Input
ABC|
D
Output
Impossible
|
[
"AC|T\nL\n",
"|ABC\nXYZ\n",
"W|T\nF\n",
"ABC|\nD\n",
"A|BC\nDEF\n",
"|\nABC\n",
"|\nZXCVBANMIO\n",
"|C\nA\n",
"|\nAB\n",
"A|XYZ\nUIOPL\n"
] |
[
"AC|TL\n",
"XYZ|ABC\n",
"Impossible\n",
"Impossible\n",
"ADF|BCE\n",
"Impossible\n",
"XVAMO|ZCBNI\n",
"A|C\n",
"B|A\n",
"Impossible\n"
] | 1
|
stdio
|
Long time ago Alex created an interesting problem about parallelogram. The input data for this problem contained four integer points on the Cartesian plane, that defined the set of vertices of some non-degenerate (positive area) parallelogram. Points not necessary were given in the order of clockwise or counterclockwise traversal.
Alex had very nice test for this problem, but is somehow happened that the last line of the input was lost and now he has only three out of four points of the original parallelogram. He remembers that test was so good that he asks you to restore it given only these three points.
-----Input-----
The input consists of three lines, each containing a pair of integer coordinates x_{i} and y_{i} ( - 1000 ≤ x_{i}, y_{i} ≤ 1000). It's guaranteed that these three points do not lie on the same line and no two of them coincide.
-----Output-----
First print integer k — the number of ways to add one new integer point such that the obtained set defines some parallelogram of positive area. There is no requirement for the points to be arranged in any special order (like traversal), they just define the set of vertices.
Then print k lines, each containing a pair of integer — possible coordinates of the fourth point.
-----Example-----
Input
0 0
1 0
0 1
Output
3
1 -1
-1 1
1 1
-----Note-----
If you need clarification of what parallelogram is, please check Wikipedia page:
https://en.wikipedia.org/wiki/Parallelogram
|
[
"0 0\n1 0\n0 1\n",
"0 -1\n-1 0\n1 1\n",
"-1 -1\n0 1\n1 1\n",
"1000 1000\n-1000 -1000\n-1000 1000\n",
"-1000 1000\n1000 -1000\n-1000 -1000\n",
"-4 -5\n7 10\n3 -10\n",
"-86 25\n-55 18\n58 24\n",
"-301 -397\n192 317\n-98 729\n",
"1000 1000\n999 1000\n-1000 -1000\n",
"-1000 0\n999 0\n1000 1\n"
] |
[
"3\n1 -1\n-1 1\n1 1\n",
"3\n-2 -2\n2 0\n0 2\n",
"3\n-2 -1\n0 -1\n2 3\n",
"3\n1000 -1000\n1000 3000\n-3000 -1000\n",
"3\n1000 1000\n-3000 1000\n1000 -3000\n",
"3\n0 15\n-8 -25\n14 5\n",
"3\n-199 19\n27 31\n89 17\n",
"3\n-11 -809\n-591 15\n395 1443\n",
"3\n2999 3000\n-999 -1000\n-1001 -1000\n",
"3\n-1001 -1\n-999 1\n2999 1\n"
] | 1
|
stdio
|
For a positive integer n let's define a function f:
f(n) = - 1 + 2 - 3 + .. + ( - 1)^{n}n
Your task is to calculate f(n) for a given integer n.
-----Input-----
The single line contains the positive integer n (1 ≤ n ≤ 10^15).
-----Output-----
Print f(n) in a single line.
-----Examples-----
Input
4
Output
2
Input
5
Output
-3
-----Note-----
f(4) = - 1 + 2 - 3 + 4 = 2
f(5) = - 1 + 2 - 3 + 4 - 5 = - 3
|
[
"4\n",
"5\n",
"1000000000\n",
"1000000001\n",
"1000000000000000\n",
"100\n",
"101\n",
"102\n",
"103\n",
"104\n"
] |
[
"2\n",
"-3\n",
"500000000\n",
"-500000001\n",
"500000000000000\n",
"50\n",
"-51\n",
"51\n",
"-52\n",
"52\n"
] | 1
|
stdio
|
You are given a string $s$ consisting of $n$ lowercase Latin letters.
You have to remove at most one (i.e. zero or one) character of this string in such a way that the string you obtain will be lexicographically smallest among all strings that can be obtained using this operation.
String $s = s_1 s_2 \dots s_n$ is lexicographically smaller than string $t = t_1 t_2 \dots t_m$ if $n < m$ and $s_1 = t_1, s_2 = t_2, \dots, s_n = t_n$ or there exists a number $p$ such that $p \le min(n, m)$ and $s_1 = t_1, s_2 = t_2, \dots, s_{p-1} = t_{p-1}$ and $s_p < t_p$.
For example, "aaa" is smaller than "aaaa", "abb" is smaller than "abc", "pqr" is smaller than "z".
-----Input-----
The first line of the input contains one integer $n$ ($2 \le n \le 2 \cdot 10^5$) — the length of $s$.
The second line of the input contains exactly $n$ lowercase Latin letters — the string $s$.
-----Output-----
Print one string — the smallest possible lexicographically string that can be obtained by removing at most one character from the string $s$.
-----Examples-----
Input
3
aaa
Output
aa
Input
5
abcda
Output
abca
-----Note-----
In the first example you can remove any character of $s$ to obtain the string "aa".
In the second example "abca" < "abcd" < "abcda" < "abda" < "acda" < "bcda".
|
[
"3\naaa\n",
"5\nabcda\n",
"2\nzz\n",
"2\nok\n",
"4\nabcd\n",
"5\naabbb\n",
"2\nas\n",
"7\nabcdeef\n",
"2\nab\n",
"3\nabc\n"
] |
[
"aa\n",
"abca\n",
"z\n",
"k\n",
"abc\n",
"aabb\n",
"a\n",
"abcdee\n",
"a\n",
"ab\n"
] | 1
|
stdio
|
Two players are playing a game. First each of them writes an integer from 1 to 6, and then a dice is thrown. The player whose written number got closer to the number on the dice wins. If both payers have the same difference, it's a draw.
The first player wrote number a, the second player wrote number b. How many ways to throw a dice are there, at which the first player wins, or there is a draw, or the second player wins?
-----Input-----
The single line contains two integers a and b (1 ≤ a, b ≤ 6) — the numbers written on the paper by the first and second player, correspondingly.
-----Output-----
Print three integers: the number of ways to throw the dice at which the first player wins, the game ends with a draw or the second player wins, correspondingly.
-----Examples-----
Input
2 5
Output
3 0 3
Input
2 4
Output
2 1 3
-----Note-----
The dice is a standard cube-shaped six-sided object with each side containing a number from 1 to 6, and where all numbers on all sides are distinct.
You can assume that number a is closer to number x than number b, if |a - x| < |b - x|.
|
[
"2 5\n",
"2 4\n",
"5 3\n",
"1 6\n",
"5 1\n",
"6 3\n",
"2 3\n",
"5 6\n",
"4 4\n",
"1 1\n"
] |
[
"3 0 3\n",
"2 1 3\n",
"2 1 3\n",
"3 0 3\n",
"3 1 2\n",
"2 0 4\n",
"2 0 4\n",
"5 0 1\n",
"0 6 0\n",
"0 6 0\n"
] | 1
|
stdio
|
Little boy Petya loves stairs very much. But he is bored from simple going up and down them — he loves jumping over several stairs at a time. As he stands on some stair, he can either jump to the next one or jump over one or two stairs at a time. But some stairs are too dirty and Petya doesn't want to step on them.
Now Petya is on the first stair of the staircase, consisting of n stairs. He also knows the numbers of the dirty stairs of this staircase. Help Petya find out if he can jump through the entire staircase and reach the last stair number n without touching a dirty stair once.
One has to note that anyway Petya should step on the first and last stairs, so if the first or the last stair is dirty, then Petya cannot choose a path with clean steps only.
-----Input-----
The first line contains two integers n and m (1 ≤ n ≤ 10^9, 0 ≤ m ≤ 3000) — the number of stairs in the staircase and the number of dirty stairs, correspondingly. The second line contains m different space-separated integers d_1, d_2, ..., d_{m} (1 ≤ d_{i} ≤ n) — the numbers of the dirty stairs (in an arbitrary order).
-----Output-----
Print "YES" if Petya can reach stair number n, stepping only on the clean stairs. Otherwise print "NO".
-----Examples-----
Input
10 5
2 4 8 3 6
Output
NO
Input
10 5
2 4 5 7 9
Output
YES
|
[
"10 5\n2 4 8 3 6\n",
"10 5\n2 4 5 7 9\n",
"10 9\n2 3 4 5 6 7 8 9 10\n",
"5 2\n4 5\n",
"123 13\n36 73 111 2 92 5 47 55 48 113 7 78 37\n",
"10 10\n7 6 4 2 5 10 8 3 9 1\n",
"12312 0\n",
"9817239 1\n6323187\n",
"1 1\n1\n",
"5 4\n4 2 5 1\n"
] |
[
"NO",
"YES",
"NO",
"NO",
"YES",
"NO",
"YES",
"YES",
"NO",
"NO"
] | 1
|
stdio
|
Okabe needs bananas for one of his experiments for some strange reason. So he decides to go to the forest and cut banana trees.
Consider the point (x, y) in the 2D plane such that x and y are integers and 0 ≤ x, y. There is a tree in such a point, and it has x + y bananas. There are no trees nor bananas in other points. Now, Okabe draws a line with equation $y = - \frac{x}{m} + b$. Okabe can select a single rectangle with axis aligned sides with all points on or under the line and cut all the trees in all points that are inside or on the border of this rectangle and take their bananas. Okabe's rectangle can be degenerate; that is, it can be a line segment or even a point.
Help Okabe and find the maximum number of bananas he can get if he chooses the rectangle wisely.
Okabe is sure that the answer does not exceed 10^18. You can trust him.
-----Input-----
The first line of input contains two space-separated integers m and b (1 ≤ m ≤ 1000, 1 ≤ b ≤ 10000).
-----Output-----
Print the maximum number of bananas Okabe can get from the trees he cuts.
-----Examples-----
Input
1 5
Output
30
Input
2 3
Output
25
-----Note----- [Image]
The graph above corresponds to sample test 1. The optimal rectangle is shown in red and has 30 bananas.
|
[
"1 5\n",
"2 3\n",
"4 6\n",
"6 3\n",
"1 1\n",
"10 1\n",
"20 10\n",
"1000 10000\n",
"139 9252\n",
"859 8096\n"
] |
[
"30\n",
"25\n",
"459\n",
"171\n",
"1\n",
"55\n",
"40326\n",
"74133360011484445\n",
"1137907933561080\n",
"29032056230649780\n"
] | 1
|
stdio
|
-----Input-----
The input consists of a single string of uppercase letters A-Z. The length of the string is between 1 and 10 characters, inclusive.
-----Output-----
Output "YES" or "NO".
-----Examples-----
Input
NEAT
Output
YES
Input
WORD
Output
NO
Input
CODER
Output
NO
Input
APRILFOOL
Output
NO
Input
AI
Output
YES
Input
JUROR
Output
YES
Input
YES
Output
NO
|
[
"NEAT\n",
"WORD\n",
"CODER\n",
"APRILFOOL\n",
"AI\n",
"JUROR\n",
"YES\n",
"Q\n",
"PUG\n",
"SOURPUSS\n"
] |
[
"YES\n",
"NO\n",
"NO\n",
"NO\n",
"YES\n",
"YES\n",
"NO\n",
"YES\n",
"YES\n",
"YES\n"
] | 1
|
stdio
|
You are given n points on a plane. All the points are distinct and no three of them lie on the same line. Find the number of parallelograms with the vertices at the given points.
-----Input-----
The first line of the input contains integer n (1 ≤ n ≤ 2000) — the number of points.
Each of the next n lines contains two integers (x_{i}, y_{i}) (0 ≤ x_{i}, y_{i} ≤ 10^9) — the coordinates of the i-th point.
-----Output-----
Print the only integer c — the number of parallelograms with the vertices at the given points.
-----Example-----
Input
4
0 1
1 0
1 1
2 0
Output
1
|
[
"4\n0 1\n1 0\n1 1\n2 0\n",
"1\n0 0\n",
"1\n6 6\n",
"5\n1 5\n4 2\n4 4\n8 1\n8 2\n",
"10\n1 7\n2 14\n3 7\n3 13\n5 13\n13 10\n15 12\n17 1\n18 8\n19 0\n",
"20\n0 17\n1 8\n1 9\n2 5\n2 11\n3 0\n5 10\n5 13\n6 7\n7 3\n12 13\n13 7\n14 16\n15 10\n15 18\n17 2\n17 12\n18 14\n19 18\n20 17\n",
"2\n2 5\n10 7\n",
"4\n7 9\n10 2\n12 20\n15 13\n",
"10\n2 14\n5 9\n10 16\n12 5\n16 19\n26 23\n30 37\n32 26\n37 33\n40 28\n",
"4\n0 0\n0 1\n1 2\n1 1\n"
] |
[
"1\n",
"0\n",
"0\n",
"0\n",
"2\n",
"18\n",
"0\n",
"1\n",
"10\n",
"1\n"
] | 1
|
stdio
|
Neko is playing with his toys on the backyard of Aki's house. Aki decided to play a prank on him, by secretly putting catnip into Neko's toys. Unfortunately, he went overboard and put an entire bag of catnip into the toys...
It took Neko an entire day to turn back to normal. Neko reported to Aki that he saw a lot of weird things, including a trie of all correct bracket sequences of length $2n$.
The definition of correct bracket sequence is as follows: The empty sequence is a correct bracket sequence, If $s$ is a correct bracket sequence, then $(\,s\,)$ is a correct bracket sequence, If $s$ and $t$ are a correct bracket sequence, then $st$ is also a correct bracket sequence.
For example, the strings "(())", "()()" form a correct bracket sequence, while ")(" and "((" not.
Aki then came up with an interesting problem: What is the size of the maximum matching (the largest set of edges such that there are no two edges with a common vertex) in this trie? Since the answer can be quite large, print it modulo $10^9 + 7$.
-----Input-----
The only line contains a single integer $n$ ($1 \le n \le 1000$).
-----Output-----
Print exactly one integer — the size of the maximum matching in the trie. Since the answer can be quite large, print it modulo $10^9 + 7$.
-----Examples-----
Input
1
Output
1
Input
2
Output
3
Input
3
Output
9
-----Note-----
The pictures below illustrate tries in the first two examples (for clarity, the round brackets are replaced with angle brackets). The maximum matching is highlighted with blue. [Image] [Image]
|
[
"1\n",
"2\n",
"3\n",
"4\n",
"5\n",
"6\n",
"7\n",
"8\n",
"9\n",
"10\n"
] |
[
"1\n",
"3\n",
"9\n",
"27\n",
"84\n",
"270\n",
"892\n",
"3012\n",
"10350\n",
"36074\n"
] | 1
|
stdio
|
During the winter holidays, the demand for Christmas balls is exceptionally high. Since it's already 2018, the advances in alchemy allow easy and efficient ball creation by utilizing magic crystals.
Grisha needs to obtain some yellow, green and blue balls. It's known that to produce a yellow ball one needs two yellow crystals, green — one yellow and one blue, and for a blue ball, three blue crystals are enough.
Right now there are A yellow and B blue crystals in Grisha's disposal. Find out how many additional crystals he should acquire in order to produce the required number of balls.
-----Input-----
The first line features two integers A and B (0 ≤ A, B ≤ 10^9), denoting the number of yellow and blue crystals respectively at Grisha's disposal.
The next line contains three integers x, y and z (0 ≤ x, y, z ≤ 10^9) — the respective amounts of yellow, green and blue balls to be obtained.
-----Output-----
Print a single integer — the minimum number of crystals that Grisha should acquire in addition.
-----Examples-----
Input
4 3
2 1 1
Output
2
Input
3 9
1 1 3
Output
1
Input
12345678 87654321
43043751 1000000000 53798715
Output
2147483648
-----Note-----
In the first sample case, Grisha needs five yellow and four blue crystals to create two yellow balls, one green ball, and one blue ball. To do that, Grisha needs to obtain two additional crystals: one yellow and one blue.
|
[
"4 3\n2 1 1\n",
"3 9\n1 1 3\n",
"12345678 87654321\n43043751 1000000000 53798715\n",
"12 12\n3 5 2\n",
"770 1390\n170 442 311\n",
"3555165 6693472\n1499112 556941 3075290\n",
"0 0\n1000000000 1000000000 1000000000\n",
"1 1\n0 1 0\n",
"117708228 562858833\n118004008 360437130 154015822\n",
"999998118 700178721\n822106746 82987112 547955384\n"
] |
[
"2\n",
"1\n",
"2147483648\n",
"0\n",
"12\n",
"3089339\n",
"7000000000\n",
"0\n",
"738362681\n",
"1753877029\n"
] | 1
|
stdio
|
Amr loves Geometry. One day he came up with a very interesting problem.
Amr has a circle of radius r and center in point (x, y). He wants the circle center to be in new position (x', y').
In one step Amr can put a pin to the border of the circle in a certain point, then rotate the circle around that pin by any angle and finally remove the pin.
Help Amr to achieve his goal in minimum number of steps.
-----Input-----
Input consists of 5 space-separated integers r, x, y, x' y' (1 ≤ r ≤ 10^5, - 10^5 ≤ x, y, x', y' ≤ 10^5), circle radius, coordinates of original center of the circle and coordinates of destination center of the circle respectively.
-----Output-----
Output a single integer — minimum number of steps required to move the center of the circle to the destination point.
-----Examples-----
Input
2 0 0 0 4
Output
1
Input
1 1 1 4 4
Output
3
Input
4 5 6 5 6
Output
0
-----Note-----
In the first sample test the optimal way is to put a pin at point (0, 2) and rotate the circle by 180 degrees counter-clockwise (or clockwise, no matter).
[Image]
|
[
"2 0 0 0 4\n",
"1 1 1 4 4\n",
"4 5 6 5 6\n",
"10 20 0 40 0\n",
"9 20 0 40 0\n",
"5 -1 -6 -5 1\n",
"99125 26876 -21414 14176 17443\n",
"8066 7339 19155 -90534 -60666\n",
"100000 -100000 -100000 100000 100000\n",
"10 20 0 41 0\n"
] |
[
"1\n",
"3\n",
"0\n",
"1\n",
"2\n",
"1\n",
"1\n",
"8\n",
"2\n",
"2\n"
] | 1
|
stdio
|
Consider the infinite sequence of integers: 1, 1, 2, 1, 2, 3, 1, 2, 3, 4, 1, 2, 3, 4, 5.... The sequence is built in the following way: at first the number 1 is written out, then the numbers from 1 to 2, then the numbers from 1 to 3, then the numbers from 1 to 4 and so on. Note that the sequence contains numbers, not digits. For example number 10 first appears in the sequence in position 55 (the elements are numerated from one).
Find the number on the n-th position of the sequence.
-----Input-----
The only line contains integer n (1 ≤ n ≤ 10^14) — the position of the number to find.
Note that the given number is too large, so you should use 64-bit integer type to store it. In C++ you can use the long long integer type and in Java you can use long integer type.
-----Output-----
Print the element in the n-th position of the sequence (the elements are numerated from one).
-----Examples-----
Input
3
Output
2
Input
5
Output
2
Input
10
Output
4
Input
55
Output
10
Input
56
Output
1
|
[
"3\n",
"5\n",
"10\n",
"55\n",
"56\n",
"1000000000000\n",
"847194127849\n",
"294719472984\n",
"999999911791\n",
"999999911792\n"
] |
[
"2\n",
"2\n",
"4\n",
"10\n",
"1\n",
"88209\n",
"255708\n",
"593358\n",
"1414213\n",
"1\n"
] | 1
|
stdio
|
You are given a complete undirected graph. For each pair of vertices you are given the length of the edge that connects them. Find the shortest paths between each pair of vertices in the graph and return the length of the longest of them.
-----Input-----
The first line of the input contains a single integer N (3 ≤ N ≤ 10).
The following N lines each contain N space-separated integers. jth integer in ith line a_{ij} is the length of the edge that connects vertices i and j. a_{ij} = a_{ji}, a_{ii} = 0, 1 ≤ a_{ij} ≤ 100 for i ≠ j.
-----Output-----
Output the maximum length of the shortest path between any pair of vertices in the graph.
-----Examples-----
Input
3
0 1 1
1 0 4
1 4 0
Output
2
Input
4
0 1 2 3
1 0 4 5
2 4 0 6
3 5 6 0
Output
5
-----Note-----
You're running short of keywords, so you can't use some of them:define
do
for
foreach
while
repeat
until
if
then
else
elif
elsif
elseif
case
switch
|
[
"3\n0 1 1\n1 0 4\n1 4 0\n",
"4\n0 1 2 3\n1 0 4 5\n2 4 0 6\n3 5 6 0\n",
"10\n0 16 67 7 82 44 25 13 25 42\n16 0 24 37 63 20 19 87 55 99\n67 24 0 81 19 71 35 6 20 91\n7 37 81 0 82 89 34 80 7 32\n82 63 19 82 0 42 66 96 42 99\n44 20 71 89 42 0 65 94 24 45\n25 19 35 34 66 65 0 97 100 22\n13 87 6 80 96 94 97 0 10 58\n25 55 20 7 42 24 100 10 0 29\n42 99 91 32 99 45 22 58 29 0\n",
"10\n0 1 1 1 1 1 1 1 1 100\n1 0 1 1 1 1 1 1 1 1\n1 1 0 1 1 1 1 1 1 1\n1 1 1 0 1 1 1 1 1 1\n1 1 1 1 0 1 1 1 1 1\n1 1 1 1 1 0 1 1 1 1\n1 1 1 1 1 1 0 1 1 1\n1 1 1 1 1 1 1 0 1 1\n1 1 1 1 1 1 1 1 0 1\n100 1 1 1 1 1 1 1 1 0\n",
"10\n0 1 100 100 100 100 100 100 100 100\n1 0 1 100 100 100 100 100 100 100\n100 1 0 1 100 100 100 100 100 100\n100 100 1 0 1 100 100 100 100 100\n100 100 100 1 0 1 100 100 100 100\n100 100 100 100 1 0 1 100 100 100\n100 100 100 100 100 1 0 1 100 100\n100 100 100 100 100 100 1 0 1 100\n100 100 100 100 100 100 100 1 0 1\n100 100 100 100 100 100 100 100 1 0\n",
"3\n0 1 1\n1 0 1\n1 1 0\n",
"6\n0 74 60 92 18 86\n74 0 96 55 30 81\n60 96 0 6 28 30\n92 55 6 0 5 89\n18 30 28 5 0 11\n86 81 30 89 11 0\n",
"6\n0 92 9 24 50 94\n92 0 70 73 57 87\n9 70 0 31 14 100\n24 73 31 0 66 25\n50 57 14 66 0 81\n94 87 100 25 81 0\n",
"8\n0 6 39 40 67 19 77 93\n6 0 25 9 67 48 26 65\n39 25 0 72 62 45 26 88\n40 9 72 0 69 19 88 4\n67 67 62 69 0 2 51 1\n19 48 45 19 2 0 60 14\n77 26 26 88 51 60 0 1\n93 65 88 4 1 14 1 0\n",
"6\n0 67 17 21 20 86\n67 0 32 80 24 36\n17 32 0 20 37 90\n21 80 20 0 58 98\n20 24 37 58 0 22\n86 36 90 98 22 0\n"
] |
[
"2\n",
"5\n",
"64\n",
"2\n",
"9\n",
"1\n",
"48\n",
"87\n",
"31\n",
"63\n"
] | 1
|
stdio
|
You are given an array a consisting of n integers, and additionally an integer m. You have to choose some sequence of indices b_1, b_2, ..., b_{k} (1 ≤ b_1 < b_2 < ... < b_{k} ≤ n) in such a way that the value of $\sum_{i = 1}^{k} a_{b_{i}} \operatorname{mod} m$ is maximized. Chosen sequence can be empty.
Print the maximum possible value of $\sum_{i = 1}^{k} a_{b_{i}} \operatorname{mod} m$.
-----Input-----
The first line contains two integers n and m (1 ≤ n ≤ 35, 1 ≤ m ≤ 10^9).
The second line contains n integers a_1, a_2, ..., a_{n} (1 ≤ a_{i} ≤ 10^9).
-----Output-----
Print the maximum possible value of $\sum_{i = 1}^{k} a_{b_{i}} \operatorname{mod} m$.
-----Examples-----
Input
4 4
5 2 4 1
Output
3
Input
3 20
199 41 299
Output
19
-----Note-----
In the first example you can choose a sequence b = {1, 2}, so the sum $\sum_{i = 1}^{k} a_{b_{i}}$ is equal to 7 (and that's 3 after taking it modulo 4).
In the second example you can choose a sequence b = {3}.
|
[
"4 4\n5 2 4 1\n",
"3 20\n199 41 299\n",
"5 10\n47 100 49 2 56\n",
"5 1000\n38361 75847 14913 11499 8297\n",
"10 10\n48 33 96 77 67 59 35 15 14 86\n",
"10 1000\n16140 63909 7177 99953 35627 40994 29288 7324 44476 36738\n",
"30 10\n99 44 42 36 43 82 99 99 10 79 97 84 5 78 37 45 87 87 11 11 79 66 47 100 8 50 27 98 32 27\n",
"30 1000\n81021 18939 94456 90340 76840 78808 27921 71826 99382 1237 93435 35153 71691 25508 96732 23778 49073 60025 95231 88719 61650 50925 34416 73600 7295 14654 78340 72871 17324 77484\n",
"35 10\n86 66 98 91 61 71 14 58 49 92 13 97 13 22 98 83 85 29 85 41 51 16 76 17 75 25 71 10 87 11 9 34 3 6 4\n",
"35 1000\n33689 27239 14396 26525 30455 13710 37039 80789 26268 1236 89916 87557 90571 13710 59152 99417 39577 40675 25931 14900 86611 46223 7105 64074 41238 59169 81308 70534 99894 10332 72983 85414 73848 68378 98404\n"
] |
[
"3\n",
"19\n",
"9\n",
"917\n",
"9\n",
"999\n",
"9\n",
"999\n",
"9\n",
"999\n"
] | 1
|
stdio
|
Every year, hundreds of people come to summer camps, they learn new algorithms and solve hard problems.
This is your first year at summer camp, and you are asked to solve the following problem. All integers starting with 1 are written in one line. The prefix of these line is "123456789101112131415...". Your task is to print the n-th digit of this string (digits are numbered starting with 1.
-----Input-----
The only line of the input contains a single integer n (1 ≤ n ≤ 1000) — the position of the digit you need to print.
-----Output-----
Print the n-th digit of the line.
-----Examples-----
Input
3
Output
3
Input
11
Output
0
-----Note-----
In the first sample the digit at position 3 is '3', as both integers 1 and 2 consist on one digit.
In the second sample, the digit at position 11 is '0', it belongs to the integer 10.
|
[
"3\n",
"11\n",
"12\n",
"13\n",
"29\n",
"30\n",
"1000\n",
"999\n",
"100\n",
"123\n"
] |
[
"3\n",
"0\n",
"1\n",
"1\n",
"9\n",
"2\n",
"3\n",
"9\n",
"5\n",
"6\n"
] | 1
|
stdio
|
Last week, Hamed learned about a new type of equations in his math class called Modular Equations. Lets define i modulo j as the remainder of division of i by j and denote it by $i \operatorname{mod} j$. A Modular Equation, as Hamed's teacher described, is an equation of the form $a \operatorname{mod} x = b$ in which a and b are two non-negative integers and x is a variable. We call a positive integer x for which $a \operatorname{mod} x = b$ a solution of our equation.
Hamed didn't pay much attention to the class since he was watching a movie. He only managed to understand the definitions of these equations.
Now he wants to write his math exercises but since he has no idea how to do that, he asked you for help. He has told you all he knows about Modular Equations and asked you to write a program which given two numbers a and b determines how many answers the Modular Equation $a \operatorname{mod} x = b$ has.
-----Input-----
In the only line of the input two space-separated integers a and b (0 ≤ a, b ≤ 10^9) are given.
-----Output-----
If there is an infinite number of answers to our equation, print "infinity" (without the quotes). Otherwise print the number of solutions of the Modular Equation $a \operatorname{mod} x = b$.
-----Examples-----
Input
21 5
Output
2
Input
9435152 272
Output
282
Input
10 10
Output
infinity
-----Note-----
In the first sample the answers of the Modular Equation are 8 and 16 since $21 \operatorname{mod} 8 = 21 \operatorname{mod} 16 = 5$
|
[
"21 5\n",
"9435152 272\n",
"10 10\n",
"0 1000000000\n",
"11 2\n",
"1 0\n",
"0 0\n",
"121 0\n",
"772930485 686893955\n",
"257424 24\n"
] |
[
"2\n",
"282\n",
"infinity\n",
"0\n",
"2\n",
"1\n",
"infinity\n",
"3\n",
"0\n",
"127\n"
] | 1
|
stdio
|
Johny likes numbers n and k very much. Now Johny wants to find the smallest integer x greater than n, so it is divisible by the number k.
-----Input-----
The only line contains two integers n and k (1 ≤ n, k ≤ 10^9).
-----Output-----
Print the smallest integer x > n, so it is divisible by the number k.
-----Examples-----
Input
5 3
Output
6
Input
25 13
Output
26
Input
26 13
Output
39
|
[
"5 3\n",
"25 13\n",
"26 13\n",
"1 1\n",
"8 8\n",
"14 15\n",
"197 894\n",
"6058 8581\n",
"97259 41764\n",
"453145 333625\n"
] |
[
"6\n",
"26\n",
"39\n",
"2\n",
"16\n",
"15\n",
"894\n",
"8581\n",
"125292\n",
"667250\n"
] | 1
|
stdio
|
You are given $q$ queries in the following form:
Given three integers $l_i$, $r_i$ and $d_i$, find minimum positive integer $x_i$ such that it is divisible by $d_i$ and it does not belong to the segment $[l_i, r_i]$.
Can you answer all the queries?
Recall that a number $x$ belongs to segment $[l, r]$ if $l \le x \le r$.
-----Input-----
The first line contains one integer $q$ ($1 \le q \le 500$) — the number of queries.
Then $q$ lines follow, each containing a query given in the format $l_i$ $r_i$ $d_i$ ($1 \le l_i \le r_i \le 10^9$, $1 \le d_i \le 10^9$). $l_i$, $r_i$ and $d_i$ are integers.
-----Output-----
For each query print one integer: the answer to this query.
-----Example-----
Input
5
2 4 2
5 10 4
3 10 1
1 2 3
4 6 5
Output
6
4
1
3
10
|
[
"5\n2 4 2\n5 10 4\n3 10 1\n1 2 3\n4 6 5\n",
"5\n1 1000000000 1\n1 1000000000 1000000000\n2 1000000000 1\n1 999999999 1000000000\n5 6 5\n",
"1\n1 1 1\n",
"1\n2 5 6\n",
"1\n80 100 80\n",
"10\n1 1000000000 1\n1 1000000000 1\n1 1000000000 1\n1 1000000000 1\n1 1000000000 1\n1 1000000000 1\n1 1000000000 1\n1 1000000000 1\n1 1000000000 1\n1 1000000000 1\n",
"20\n1 1000000000 1\n1 1000000000 1\n1 1000000000 1\n1 1000000000 1\n1 1000000000 1\n1 1000000000 1\n1 1000000000 1\n1 1000000000 1\n1 1000000000 1\n1 1000000000 1\n1 1000000000 1\n1 1000000000 1\n1 1000000000 1\n1 1000000000 1\n1 1000000000 1\n1 1000000000 1\n1 1000000000 1\n1 1000000000 1\n1 1000000000 1\n1 1000000000 1\n",
"1\n5 5 5\n",
"5\n80 100 10\n5 10 4\n3 10 1\n1 2 3\n4 6 5\n",
"16\n1 1000000000 1\n1 1000000000 1\n1 1000000000 1\n1 1000000000 1\n1 1000000000 1\n1 1000000000 1\n1 1000000000 1\n1 1000000000 1\n1 1000000000 1\n1 1000000000 1\n1 1000000000 1\n1 1000000000 1\n1 1000000000 1\n1 1000000000 1\n1 1000000000 1\n1 1000000000 1\n"
] |
[
"6\n4\n1\n3\n10\n",
"1000000001\n2000000000\n1\n1000000000\n10\n",
"2\n",
"6\n",
"160\n",
"1000000001\n1000000001\n1000000001\n1000000001\n1000000001\n1000000001\n1000000001\n1000000001\n1000000001\n1000000001\n",
"1000000001\n1000000001\n1000000001\n1000000001\n1000000001\n1000000001\n1000000001\n1000000001\n1000000001\n1000000001\n1000000001\n1000000001\n1000000001\n1000000001\n1000000001\n1000000001\n1000000001\n1000000001\n1000000001\n1000000001\n",
"10\n",
"10\n4\n1\n3\n10\n",
"1000000001\n1000000001\n1000000001\n1000000001\n1000000001\n1000000001\n1000000001\n1000000001\n1000000001\n1000000001\n1000000001\n1000000001\n1000000001\n1000000001\n1000000001\n1000000001\n"
] | 1
|
stdio
|
HAI
I HAS A TUX
GIMMEH TUX
I HAS A FOO ITS 0
I HAS A BAR ITS 0
I HAS A BAZ ITS 0
I HAS A QUZ ITS 1
TUX IS NOW A NUMBR
IM IN YR LOOP NERFIN YR TUX TIL BOTH SAEM TUX AN 0
I HAS A PUR
GIMMEH PUR
PUR IS NOW A NUMBR
FOO R SUM OF FOO AN PUR
BAR R SUM OF BAR AN 1
BOTH SAEM BIGGR OF PRODUKT OF FOO AN QUZ AN PRODUKT OF BAR BAZ AN PRODUKT OF FOO AN QUZ
O RLY?
YA RLY
BAZ R FOO
QUZ R BAR
OIC
IM OUTTA YR LOOP
BAZ IS NOW A NUMBAR
VISIBLE SMOOSH QUOSHUNT OF BAZ QUZ
KTHXBYE
-----Input-----
The input contains between 1 and 10 lines, i-th line contains an integer number x_{i} (0 ≤ x_{i} ≤ 9).
-----Output-----
Output a single real number. The answer is considered to be correct if its absolute or relative error does not exceed 10^{ - 4}.
-----Examples-----
Input
3
0
1
1
Output
0.666667
|
[
"3\n0\n1\n1\n",
"1\n0\n",
"1\n1\n",
"2\n0\n1\n",
"9\n0\n0\n0\n0\n0\n0\n0\n0\n1\n",
"5\n1\n1\n1\n0\n1\n",
"9\n1\n0\n0\n1\n0\n1\n1\n1\n1\n",
"9\n1\n1\n1\n0\n0\n1\n1\n1\n0\n",
"9\n1\n0\n0\n0\n0\n1\n1\n1\n1\n",
"6\n0\n0\n1\n1\n1\n0\n"
] |
[
"0.666667\n",
"0\n",
"1\n",
"0.5\n",
"0.111111\n",
"1\n",
"1\n",
"1\n",
"1\n",
"0.6\n"
] | 1
|
stdio
|
-----Input-----
The input contains a single integer a (0 ≤ a ≤ 35).
-----Output-----
Output a single integer.
-----Examples-----
Input
3
Output
8
Input
10
Output
1024
|
[
"3\n",
"10\n",
"35\n",
"0\n",
"1\n",
"2\n",
"4\n",
"5\n",
"6\n",
"7\n"
] |
[
"8\n",
"1024\n",
"33940307968\n",
"1\n",
"2\n",
"4\n",
"16\n",
"32\n",
"64\n",
"128\n"
] | 1
|
stdio
|
Kolya is very absent-minded. Today his math teacher asked him to solve a simple problem with the equation $a + 1 = b$ with positive integers $a$ and $b$, but Kolya forgot the numbers $a$ and $b$. He does, however, remember that the first (leftmost) digit of $a$ was $d_a$, and the first (leftmost) digit of $b$ was $d_b$.
Can you reconstruct any equation $a + 1 = b$ that satisfies this property? It may be possible that Kolya misremembers the digits, and there is no suitable equation, in which case report so.
-----Input-----
The only line contains two space-separated digits $d_a$ and $d_b$ ($1 \leq d_a, d_b \leq 9$).
-----Output-----
If there is no equation $a + 1 = b$ with positive integers $a$ and $b$ such that the first digit of $a$ is $d_a$, and the first digit of $b$ is $d_b$, print a single number $-1$.
Otherwise, print any suitable $a$ and $b$ that both are positive and do not exceed $10^9$. It is guaranteed that if a solution exists, there also exists a solution with both numbers not exceeding $10^9$.
-----Examples-----
Input
1 2
Output
199 200
Input
4 4
Output
412 413
Input
5 7
Output
-1
Input
6 2
Output
-1
|
[
"1 2\n",
"4 4\n",
"5 7\n",
"6 2\n",
"9 1\n",
"1 1\n",
"8 9\n",
"9 8\n",
"9 9\n",
"2 4\n"
] |
[
"1 2\n",
"40 41\n",
"-1\n",
"-1\n",
"9 10\n",
"10 11\n",
"8 9\n",
"-1\n",
"90 91\n",
"-1\n"
] | 1
|
stdio
|
Do you remember how Kai constructed the word "eternity" using pieces of ice as components?
Little Sheldon plays with pieces of ice, each piece has exactly one digit between 0 and 9. He wants to construct his favourite number t. He realized that digits 6 and 9 are very similar, so he can rotate piece of ice with 6 to use as 9 (and vice versa). Similary, 2 and 5 work the same. There is no other pair of digits with similar effect. He called this effect "Digital Mimicry".
Sheldon favourite number is t. He wants to have as many instances of t as possible. How many instances he can construct using the given sequence of ice pieces. He can use any piece at most once.
-----Input-----
The first line contains integer t (1 ≤ t ≤ 10000). The second line contains the sequence of digits on the pieces. The length of line is equal to the number of pieces and between 1 and 200, inclusive. It contains digits between 0 and 9.
-----Output-----
Print the required number of instances.
-----Examples-----
Input
42
23454
Output
2
Input
169
12118999
Output
1
-----Note-----
This problem contains very weak pretests.
|
[
"42\n23454\n",
"169\n12118999\n",
"1\n1\n",
"7\n777\n",
"18\n8118\n",
"33\n33333333\n",
"1780\n8170880870810081711018110878070777078711\n",
"2\n5255\n",
"5\n22252\n",
"9\n666969\n"
] |
[
"2\n",
"1\n",
"1\n",
"3\n",
"2\n",
"4\n",
"10\n",
"4\n",
"5\n",
"6\n"
] | 1
|
stdio
|
Mahmoud and Ehab are on the third stage of their adventures now. As you know, Dr. Evil likes sets. This time he won't show them any set from his large collection, but will ask them to create a new set to replenish his beautiful collection of sets.
Dr. Evil has his favorite evil integer x. He asks Mahmoud and Ehab to find a set of n distinct non-negative integers such the bitwise-xor sum of the integers in it is exactly x. Dr. Evil doesn't like big numbers, so any number in the set shouldn't be greater than 10^6.
-----Input-----
The only line contains two integers n and x (1 ≤ n ≤ 10^5, 0 ≤ x ≤ 10^5) — the number of elements in the set and the desired bitwise-xor, respectively.
-----Output-----
If there is no such set, print "NO" (without quotes).
Otherwise, on the first line print "YES" (without quotes) and on the second line print n distinct integers, denoting the elements in the set is any order. If there are multiple solutions you can print any of them.
-----Examples-----
Input
5 5
Output
YES
1 2 4 5 7
Input
3 6
Output
YES
1 2 5
-----Note-----
You can read more about the bitwise-xor operation here: https://en.wikipedia.org/wiki/Bitwise_operation#XOR
For the first sample $1 \oplus 2 \oplus 4 \oplus 5 \oplus 7 = 5$.
For the second sample $1 \oplus 2 \oplus 5 = 6$.
|
[
"5 5\n",
"3 6\n",
"3 0\n",
"1 0\n",
"3 3\n",
"32 32\n",
"32 31\n",
"1 1\n",
"2 0\n",
"3 1\n"
] |
[
"YES\n1 2 131072 131078 0 \n",
"YES\n131072 131078 0 \n",
"YES\n393216 131072 262144\n",
"YES\n0\n",
"YES\n131072 131075 0 \n",
"YES\n1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 131072 131105 0 \n",
"YES\n1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 131072 131102 0 \n",
"YES\n1\n",
"NO\n",
"YES\n131072 131073 0 \n"
] | 1
|
stdio
|
[Image]
-----Input-----
The input contains two integers a_1, a_2 (0 ≤ a_{i} ≤ 32), separated by a single space.
-----Output-----
Output a single integer.
-----Examples-----
Input
1 1
Output
0
Input
3 7
Output
0
Input
13 10
Output
1
|
[
"1 1\n",
"3 7\n",
"13 10\n",
"6 12\n",
"14 14\n",
"19 14\n",
"21 18\n",
"29 18\n",
"0 24\n",
"16 24\n"
] |
[
"0\n",
"0\n",
"1\n",
"1\n",
"0\n",
"0\n",
"1\n",
"0\n",
"0\n",
"1\n"
] | 1
|
stdio
|
The cows have just learned what a primitive root is! Given a prime p, a primitive root $\operatorname{mod} p$ is an integer x (1 ≤ x < p) such that none of integers x - 1, x^2 - 1, ..., x^{p} - 2 - 1 are divisible by p, but x^{p} - 1 - 1 is.
Unfortunately, computing primitive roots can be time consuming, so the cows need your help. Given a prime p, help the cows find the number of primitive roots $\operatorname{mod} p$.
-----Input-----
The input contains a single line containing an integer p (2 ≤ p < 2000). It is guaranteed that p is a prime.
-----Output-----
Output on a single line the number of primitive roots $\operatorname{mod} p$.
-----Examples-----
Input
3
Output
1
Input
5
Output
2
-----Note-----
The only primitive root $\operatorname{mod} 3$ is 2.
The primitive roots $\operatorname{mod} 5$ are 2 and 3.
|
[
"3\n",
"5\n",
"7\n",
"11\n",
"17\n",
"19\n",
"1583\n",
"997\n",
"2\n",
"1987\n"
] |
[
"1\n",
"2\n",
"2\n",
"4\n",
"8\n",
"6\n",
"672\n",
"328\n",
"1\n",
"660\n"
] | 1
|
stdio
|
Consider a linear function f(x) = Ax + B. Let's define g^{(0)}(x) = x and g^{(}n)(x) = f(g^{(}n - 1)(x)) for n > 0. For the given integer values A, B, n and x find the value of g^{(}n)(x) modulo 10^9 + 7.
-----Input-----
The only line contains four integers A, B, n and x (1 ≤ A, B, x ≤ 10^9, 1 ≤ n ≤ 10^18) — the parameters from the problem statement.
Note that the given value n can be too large, so you should use 64-bit integer type to store it. In C++ you can use the long long integer type and in Java you can use long integer type.
-----Output-----
Print the only integer s — the value g^{(}n)(x) modulo 10^9 + 7.
-----Examples-----
Input
3 4 1 1
Output
7
Input
3 4 2 1
Output
25
Input
3 4 3 1
Output
79
|
[
"3 4 1 1\n",
"3 4 2 1\n",
"3 4 3 1\n",
"1 1 1 1\n",
"3 10 723 6\n",
"14 81 51 82\n",
"826504481 101791432 76 486624528\n",
"475965351 844435993 96338 972382431\n",
"528774798 650132512 6406119 36569714\n",
"632656975 851906850 1 310973933\n"
] |
[
"7\n",
"25\n",
"79\n",
"2\n",
"443623217\n",
"908370438\n",
"621999403\n",
"83709654\n",
"505858307\n",
"230360736\n"
] | 1
|
stdio
|
Ilya got tired of sports programming, left university and got a job in the subway. He was given the task to determine the escalator load factor.
Let's assume that n people stand in the queue for the escalator. At each second one of the two following possibilities takes place: either the first person in the queue enters the escalator with probability p, or the first person in the queue doesn't move with probability (1 - p), paralyzed by his fear of escalators and making the whole queue wait behind him.
Formally speaking, the i-th person in the queue cannot enter the escalator until people with indices from 1 to i - 1 inclusive enter it. In one second only one person can enter the escalator. The escalator is infinite, so if a person enters it, he never leaves it, that is he will be standing on the escalator at any following second. Ilya needs to count the expected value of the number of people standing on the escalator after t seconds.
Your task is to help him solve this complicated task.
-----Input-----
The first line of the input contains three numbers n, p, t (1 ≤ n, t ≤ 2000, 0 ≤ p ≤ 1). Numbers n and t are integers, number p is real, given with exactly two digits after the decimal point.
-----Output-----
Print a single real number — the expected number of people who will be standing on the escalator after t seconds. The absolute or relative error mustn't exceed 10^{ - 6}.
-----Examples-----
Input
1 0.50 1
Output
0.5
Input
1 0.50 4
Output
0.9375
Input
4 0.20 2
Output
0.4
|
[
"1 0.50 1\n",
"1 0.50 4\n",
"4 0.20 2\n",
"2000 0.61 2000\n",
"100 1.00 200\n",
"417 0.57 742\n",
"100 0.01 53\n",
"300 0.05 55\n",
"1400 0.02 200\n",
"2000 0.01 234\n"
] |
[
"0.500000000000000\n",
"0.937500000000000\n",
"0.400000000000000\n",
"1219.999999999999545\n",
"100.000000000000000\n",
"414.074442142061741\n",
"0.530000000000000\n",
"2.750000000000001\n",
"3.999999999999999\n",
"2.340000000000000\n"
] | 1
|
stdio
|
There are n cards (n is even) in the deck. Each card has a positive integer written on it. n / 2 people will play new card game. At the beginning of the game each player gets two cards, each card is given to exactly one player.
Find the way to distribute cards such that the sum of values written of the cards will be equal for each player. It is guaranteed that it is always possible.
-----Input-----
The first line of the input contains integer n (2 ≤ n ≤ 100) — the number of cards in the deck. It is guaranteed that n is even.
The second line contains the sequence of n positive integers a_1, a_2, ..., a_{n} (1 ≤ a_{i} ≤ 100), where a_{i} is equal to the number written on the i-th card.
-----Output-----
Print n / 2 pairs of integers, the i-th pair denote the cards that should be given to the i-th player. Each card should be given to exactly one player. Cards are numbered in the order they appear in the input.
It is guaranteed that solution exists. If there are several correct answers, you are allowed to print any of them.
-----Examples-----
Input
6
1 5 7 4 4 3
Output
1 3
6 2
4 5
Input
4
10 10 10 10
Output
1 2
3 4
-----Note-----
In the first sample, cards are distributed in such a way that each player has the sum of numbers written on his cards equal to 8.
In the second sample, all values a_{i} are equal. Thus, any distribution is acceptable.
|
[
"6\n1 5 7 4 4 3\n",
"4\n10 10 10 10\n",
"100\n2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n",
"4\n82 46 8 44\n",
"2\n35 50\n",
"8\n24 39 49 38 44 64 44 50\n",
"100\n23 44 35 88 10 78 8 84 46 19 69 36 81 60 46 12 53 22 83 73 6 18 80 14 54 39 74 42 34 20 91 70 32 11 80 53 70 21 24 12 87 68 35 39 8 84 81 70 8 54 73 2 60 71 4 33 65 48 69 58 55 57 78 61 45 50 55 72 86 37 5 11 12 81 32 19 22 11 22 82 23 56 61 84 47 59 31 38 31 90 57 1 24 38 68 27 80 9 37 14\n",
"12\n22 83 2 67 55 12 40 93 83 73 12 28\n",
"16\n10 33 36 32 48 25 31 27 45 13 37 26 22 21 15 43\n",
"20\n18 13 71 60 28 10 20 65 65 12 13 14 64 68 6 50 72 7 66 58\n"
] |
[
"1 3\n6 2\n4 5\n",
"1 4\n2 3\n",
"1 100\n2 99\n3 98\n4 97\n5 96\n6 95\n7 94\n8 93\n9 92\n10 91\n11 90\n12 89\n13 88\n14 87\n15 86\n16 85\n17 84\n18 83\n19 82\n20 81\n21 80\n22 79\n23 78\n24 77\n25 76\n26 75\n27 74\n28 73\n29 72\n30 71\n31 70\n32 69\n33 68\n34 67\n35 66\n36 65\n37 64\n38 63\n39 62\n40 61\n41 60\n42 59\n43 58\n44 57\n45 56\n46 55\n47 54\n48 53\n49 52\n50 51\n",
"3 1\n4 2\n",
"1 2\n",
"1 6\n4 8\n2 3\n5 7\n",
"92 31\n52 90\n55 4\n71 41\n21 69\n7 84\n45 46\n49 8\n98 19\n5 80\n34 74\n72 47\n78 13\n16 97\n40 35\n73 23\n24 63\n100 6\n22 27\n10 51\n76 20\n30 68\n38 54\n18 48\n77 37\n79 32\n1 59\n81 11\n39 95\n93 42\n96 57\n87 83\n89 64\n33 53\n75 14\n56 86\n29 60\n3 91\n43 62\n12 82\n70 67\n99 61\n88 50\n94 25\n26 36\n44 17\n28 66\n2 58\n65 85\n9 15\n",
"3 8\n6 9\n11 2\n1 10\n12 4\n7 5\n",
"1 5\n10 9\n15 16\n14 11\n13 3\n6 2\n12 4\n8 7\n",
"15 17\n18 3\n6 14\n10 19\n2 9\n11 8\n12 13\n1 4\n7 20\n5 16\n"
] | 1
|
stdio
|
It seems that Borya is seriously sick. He is going visit n doctors to find out the exact diagnosis. Each of the doctors needs the information about all previous visits, so Borya has to visit them in the prescribed order (i.e. Borya should first visit doctor 1, then doctor 2, then doctor 3 and so on). Borya will get the information about his health from the last doctor.
Doctors have a strange working schedule. The doctor i goes to work on the s_{i}-th day and works every d_{i} day. So, he works on days s_{i}, s_{i} + d_{i}, s_{i} + 2d_{i}, ....
The doctor's appointment takes quite a long time, so Borya can not see more than one doctor per day. What is the minimum time he needs to visit all doctors?
-----Input-----
First line contains an integer n — number of doctors (1 ≤ n ≤ 1000).
Next n lines contain two numbers s_{i} and d_{i} (1 ≤ s_{i}, d_{i} ≤ 1000).
-----Output-----
Output a single integer — the minimum day at which Borya can visit the last doctor.
-----Examples-----
Input
3
2 2
1 2
2 2
Output
4
Input
2
10 1
6 5
Output
11
-----Note-----
In the first sample case, Borya can visit all doctors on days 2, 3 and 4.
In the second sample case, Borya can visit all doctors on days 10 and 11.
|
[
"3\n2 2\n1 2\n2 2\n",
"2\n10 1\n6 5\n",
"3\n6 10\n3 3\n8 2\n",
"4\n4 8\n10 10\n4 2\n8 2\n",
"5\n7 1\n5 1\n6 1\n1 6\n6 8\n",
"6\n1 3\n2 5\n4 7\n7 5\n6 8\n8 8\n",
"10\n4 10\n8 7\n6 5\n2 1\n2 3\n8 8\n2 4\n2 2\n6 7\n7 9\n",
"1\n1 1\n",
"1\n1000 1000\n",
"42\n1 2\n1 2\n1 2\n1 2\n1 2\n1 2\n1 2\n1 2\n1 2\n1 2\n1 2\n1 2\n1 2\n1 2\n1 2\n1 2\n1 2\n1 2\n1 2\n1 2\n1 2\n1 2\n1 2\n1 2\n1 2\n1 2\n1 2\n1 2\n1 2\n1 2\n1 2\n1 2\n1 2\n1 2\n1 2\n1 2\n1 2\n1 2\n1 2\n1 2\n1 2\n1 2\n"
] |
[
"4\n",
"11\n",
"10\n",
"14\n",
"14\n",
"16\n",
"34\n",
"1\n",
"1000\n",
"83\n"
] | 1
|
stdio
|
We consider a positive integer perfect, if and only if the sum of its digits is exactly $10$. Given a positive integer $k$, your task is to find the $k$-th smallest perfect positive integer.
-----Input-----
A single line with a positive integer $k$ ($1 \leq k \leq 10\,000$).
-----Output-----
A single number, denoting the $k$-th smallest perfect integer.
-----Examples-----
Input
1
Output
19
Input
2
Output
28
-----Note-----
The first perfect integer is $19$ and the second one is $28$.
|
[
"1\n",
"2\n",
"13\n",
"101\n",
"1023\n",
"9999\n",
"10000\n",
"2333\n",
"9139\n",
"9859\n"
] |
[
"19\n",
"28\n",
"136\n",
"1432\n",
"100270\n",
"10800010\n",
"10800100\n",
"310060\n",
"10134010\n",
"10422001\n"
] | 1
|
stdio
|
International Abbreviation Olympiad takes place annually starting from 1989. Each year the competition receives an abbreviation of form IAO'y, where y stands for some number of consequent last digits of the current year. Organizers always pick an abbreviation with non-empty string y that has never been used before. Among all such valid abbreviations they choose the shortest one and announce it to be the abbreviation of this year's competition.
For example, the first three Olympiads (years 1989, 1990 and 1991, respectively) received the abbreviations IAO'9, IAO'0 and IAO'1, while the competition in 2015 received an abbreviation IAO'15, as IAO'5 has been already used in 1995.
You are given a list of abbreviations. For each of them determine the year it stands for.
-----Input-----
The first line of the input contains a single integer n (1 ≤ n ≤ 1000) — the number of abbreviations to process.
Then n lines follow, each containing a single abbreviation. It's guaranteed that each abbreviation contains at most nine digits.
-----Output-----
For each abbreviation given in the input, find the year of the corresponding Olympiad.
-----Examples-----
Input
5
IAO'15
IAO'2015
IAO'1
IAO'9
IAO'0
Output
2015
12015
1991
1989
1990
Input
4
IAO'9
IAO'99
IAO'999
IAO'9999
Output
1989
1999
2999
9999
|
[
"5\nIAO'15\nIAO'2015\nIAO'1\nIAO'9\nIAO'0\n",
"4\nIAO'9\nIAO'99\nIAO'999\nIAO'9999\n",
"1\nIAO'111110\n",
"2\nIAO'0\nIAO'00\n",
"1\nIAO'111111\n",
"1\nIAO'111111111\n",
"1\nIAO'001\n",
"1\nIAO'2000\n",
"1\nIAO'11109999\n",
"1\nIAO'11111\n"
] |
[
"2015\n12015\n1991\n1989\n1990\n",
"1989\n1999\n2999\n9999\n",
"1111110\n",
"1990\n2000\n",
"1111111\n",
"1111111111\n",
"3001\n",
"12000\n",
"111109999\n",
"111111\n"
] | 1
|
stdio
|
You are given a string $s$, consisting of $n$ lowercase Latin letters.
A substring of string $s$ is a continuous segment of letters from $s$. For example, "defor" is a substring of "codeforces" and "fors" is not.
The length of the substring is the number of letters in it.
Let's call some string of length $n$ diverse if and only if there is no letter to appear strictly more than $\frac n 2$ times. For example, strings "abc" and "iltlml" are diverse and strings "aab" and "zz" are not.
Your task is to find any diverse substring of string $s$ or report that there is none. Note that it is not required to maximize or minimize the length of the resulting substring.
-----Input-----
The first line contains a single integer $n$ ($1 \le n \le 1000$) — the length of string $s$.
The second line is the string $s$, consisting of exactly $n$ lowercase Latin letters.
-----Output-----
Print "NO" if there is no diverse substring in the string $s$.
Otherwise the first line should contain "YES". The second line should contain any diverse substring of string $s$.
-----Examples-----
Input
10
codeforces
Output
YES
code
Input
5
aaaaa
Output
NO
-----Note-----
The first example has lots of correct answers.
Please, restrain yourself from asking if some specific answer is correct for some specific test or not, these questions always lead to "No comments" answer.
|
[
"10\ncodeforces\n",
"5\naaaaa\n",
"5\noomph\n",
"1\ng\n",
"2\nab\n",
"3\naab\n",
"3\nabb\n",
"7\naaabaaa\n",
"9\naabbccaab\n",
"2\naz\n"
] |
[
"YES\nco\n",
"NO\n",
"YES\nom\n",
"NO\n",
"YES\nab\n",
"YES\nab\n",
"YES\nab\n",
"YES\nab\n",
"YES\nab\n",
"YES\naz\n"
] | 1
|
stdio
|
Polycarpus loves lucky numbers. Everybody knows that lucky numbers are positive integers, whose decimal representation (without leading zeroes) contain only the lucky digits x and y. For example, if x = 4, and y = 7, then numbers 47, 744, 4 are lucky.
Let's call a positive integer a undoubtedly lucky, if there are such digits x and y (0 ≤ x, y ≤ 9), that the decimal representation of number a (without leading zeroes) contains only digits x and y.
Polycarpus has integer n. He wants to know how many positive integers that do not exceed n, are undoubtedly lucky. Help him, count this number.
-----Input-----
The first line contains a single integer n (1 ≤ n ≤ 10^9) — Polycarpus's number.
-----Output-----
Print a single integer that says, how many positive integers that do not exceed n are undoubtedly lucky.
-----Examples-----
Input
10
Output
10
Input
123
Output
113
-----Note-----
In the first test sample all numbers that do not exceed 10 are undoubtedly lucky.
In the second sample numbers 102, 103, 104, 105, 106, 107, 108, 109, 120, 123 are not undoubtedly lucky.
|
[
"10\n",
"123\n",
"1\n",
"2\n",
"1000\n",
"1000000000\n",
"999999999\n",
"999999998\n",
"999999997\n",
"909090901\n"
] |
[
"10\n",
"113\n",
"1\n",
"2\n",
"352\n",
"40744\n",
"40743\n",
"40742\n",
"40741\n",
"38532\n"
] | 1
|
stdio
|
Your security guard friend recently got a new job at a new security company. The company requires him to patrol an area of the city encompassing exactly N city blocks, but they let him choose which blocks. That is, your friend must walk the perimeter of a region whose area is exactly N blocks. Your friend is quite lazy and would like your help to find the shortest possible route that meets the requirements. The city is laid out in a square grid pattern, and is large enough that for the sake of the problem it can be considered infinite.
-----Input-----
Input will consist of a single integer N (1 ≤ N ≤ 10^6), the number of city blocks that must be enclosed by the route.
-----Output-----
Print the minimum perimeter that can be achieved.
-----Examples-----
Input
4
Output
8
Input
11
Output
14
Input
22
Output
20
-----Note-----
Here are some possible shapes for the examples:
[Image]
|
[
"4\n",
"11\n",
"22\n",
"3\n",
"1024\n",
"101\n",
"30\n",
"1000000\n",
"1\n",
"2\n"
] |
[
"8\n",
"14\n",
"20\n",
"8\n",
"128\n",
"42\n",
"22\n",
"4000\n",
"4\n",
"6\n"
] | 1
|
stdio
|
You are given <var>Q</var> tuples of integers <var>(L_i, A_i, B_i, M_i)</var>. For each tuple, answer the following question.
There is an arithmetic progression with L terms: s_0, s_1, s_2, ... , s_{L-1}.
The initial term is A, and the common difference is B. That is, s_i = A + B \times i holds.
Consider the integer obtained by concatenating the terms written in base ten without leading zeros. For example, the sequence 3, 7, 11, 15, 19 would be concatenated into 37111519. What is the remainder when that integer is divided by M?
-----Constraints-----
- All values in input are integers.
- 1 \leq L, A, B < 10^{18}
- 2 \leq M \leq 10^9
- All terms in the arithmetic progression are less than 10^{18}.
-----Input-----
Input is given from Standard Input in the following format:
L A B M
-----Output-----
Print the remainder when the integer obtained by concatenating the terms is divided by M.
-----Sample Input-----
5 3 4 10007
-----Sample Output-----
5563
Our arithmetic progression is 3, 7, 11, 15, 19, so the answer is 37111519 mod 10007, that is, 5563.
|
[
"5 3 4 10007\n",
"4 8 1 1000000\n",
"107 10000000000007 1000000000000007 998244353\n",
"2500000000000 4 4 998244353\n",
"99982444353 100 4 998244353\n",
"333333333333333333 3 3 998244353\n",
"1 999999999999999999 999999999999999999 998244353\n",
"998244353 629149506971940504 319836804 14876851\n",
"999918203 4248 723308865 998244353\n",
"100000000000 6 231 25200\n"
] |
[
"5563\n",
"891011\n",
"39122908\n",
"900161126\n",
"658481246\n",
"521296277\n",
"716070897\n",
"9086340\n",
"822961451\n",
"12975\n"
] | 1
|
stdio
|
You are given a sequence $b_1, b_2, \ldots, b_n$. Find the lexicographically minimal permutation $a_1, a_2, \ldots, a_{2n}$ such that $b_i = \min(a_{2i-1}, a_{2i})$, or determine that it is impossible.
-----Input-----
Each test contains one or more test cases. The first line contains the number of test cases $t$ ($1 \le t \le 100$).
The first line of each test case consists of one integer $n$ — the number of elements in the sequence $b$ ($1 \le n \le 100$).
The second line of each test case consists of $n$ different integers $b_1, \ldots, b_n$ — elements of the sequence $b$ ($1 \le b_i \le 2n$).
It is guaranteed that the sum of $n$ by all test cases doesn't exceed $100$.
-----Output-----
For each test case, if there is no appropriate permutation, print one number $-1$.
Otherwise, print $2n$ integers $a_1, \ldots, a_{2n}$ — required lexicographically minimal permutation of numbers from $1$ to $2n$.
-----Example-----
Input
5
1
1
2
4 1
3
4 1 3
4
2 3 4 5
5
1 5 7 2 8
Output
1 2
-1
4 5 1 2 3 6
-1
1 3 5 6 7 9 2 4 8 10
|
[
"5\n1\n1\n2\n4 1\n3\n4 1 3\n4\n2 3 4 5\n5\n1 5 7 2 8\n",
"33\n3\n1 2 3\n3\n1 2 4\n3\n1 2 5\n3\n1 2 6\n3\n1 3 2\n3\n1 3 4\n3\n1 3 5\n3\n1 3 6\n3\n1 4 2\n3\n1 4 3\n3\n1 4 5\n3\n1 4 6\n3\n1 5 2\n3\n1 5 3\n3\n1 5 4\n3\n1 5 6\n3\n1 6 2\n3\n1 6 3\n3\n1 6 4\n3\n1 6 5\n3\n2 1 3\n3\n2 1 4\n3\n2 1 5\n3\n2 1 6\n3\n2 3 1\n3\n2 3 4\n3\n2 3 5\n3\n2 3 6\n3\n2 4 1\n3\n2 4 3\n3\n2 4 5\n3\n2 4 6\n3\n2 5 1\n",
"33\n3\n2 5 3\n3\n2 5 4\n3\n2 5 6\n3\n2 6 1\n3\n2 6 3\n3\n2 6 4\n3\n2 6 5\n3\n3 1 2\n3\n3 1 4\n3\n3 1 5\n3\n3 1 6\n3\n3 2 1\n3\n3 2 4\n3\n3 2 5\n3\n3 2 6\n3\n3 4 1\n3\n3 4 2\n3\n3 4 5\n3\n3 4 6\n3\n3 5 1\n3\n3 5 2\n3\n3 5 4\n3\n3 5 6\n3\n3 6 1\n3\n3 6 2\n3\n3 6 4\n3\n3 6 5\n3\n4 1 2\n3\n4 1 3\n3\n4 1 5\n3\n4 1 6\n3\n4 2 1\n3\n4 2 3\n",
"33\n3\n4 2 5\n3\n4 2 6\n3\n4 3 1\n3\n4 3 2\n3\n4 3 5\n3\n4 3 6\n3\n4 5 1\n3\n4 5 2\n3\n4 5 3\n3\n4 5 6\n3\n4 6 1\n3\n4 6 2\n3\n4 6 3\n3\n4 6 5\n3\n5 1 2\n3\n5 1 3\n3\n5 1 4\n3\n5 1 6\n3\n5 2 1\n3\n5 2 3\n3\n5 2 4\n3\n5 2 6\n3\n5 3 1\n3\n5 3 2\n3\n5 3 4\n3\n5 3 6\n3\n5 4 1\n3\n5 4 2\n3\n5 4 3\n3\n5 4 6\n3\n5 6 1\n3\n5 6 2\n3\n5 6 3\n",
"21\n3\n5 6 4\n3\n6 1 2\n3\n6 1 3\n3\n6 1 4\n3\n6 1 5\n3\n6 2 1\n3\n6 2 3\n3\n6 2 4\n3\n6 2 5\n3\n6 3 1\n3\n6 3 2\n3\n6 3 4\n3\n6 3 5\n3\n6 4 1\n3\n6 4 2\n3\n6 4 3\n3\n6 4 5\n3\n6 5 1\n3\n6 5 2\n3\n6 5 3\n3\n6 5 4\n",
"9\n11\n1 12 17 18 21 13 4 6 22 15 5\n11\n20 18 14 10 12 8 1 17 13 22 7\n11\n18 9 22 16 11 5 2 6 15 20 14\n11\n22 4 2 5 9 6 17 7 21 13 1\n11\n1 15 13 8 22 5 4 18 9 19 2\n11\n21 2 8 13 1 19 20 18 7 5 12\n11\n12 9 14 20 8 15 1 11 5 4 7\n11\n12 6 16 2 7 1 15 9 18 11 17\n11\n10 1 7 6 13 18 20 14 21 8 22\n",
"2\n1\n1\n1\n2\n",
"12\n2\n1 2\n2\n1 3\n2\n1 4\n2\n2 1\n2\n2 3\n2\n2 4\n2\n3 1\n2\n3 2\n2\n3 4\n2\n4 1\n2\n4 2\n2\n4 3\n",
"50\n2\n4 1\n2\n1 4\n2\n3 1\n2\n3 1\n2\n1 2\n2\n4 1\n2\n4 3\n2\n1 2\n2\n1 2\n2\n1 2\n2\n2 3\n2\n1 2\n2\n4 2\n2\n1 2\n2\n1 4\n2\n4 3\n2\n1 4\n2\n1 4\n2\n2 1\n2\n3 1\n2\n3 1\n2\n1 2\n2\n2 4\n2\n1 4\n2\n1 4\n2\n1 4\n2\n1 3\n2\n4 3\n2\n2 1\n2\n4 2\n2\n4 2\n2\n4 1\n2\n1 3\n2\n3 1\n2\n2 3\n2\n2 3\n2\n1 3\n2\n3 4\n2\n4 3\n2\n2 4\n2\n4 3\n2\n4 3\n2\n4 2\n2\n3 4\n2\n1 4\n2\n4 1\n2\n1 4\n2\n2 3\n2\n4 1\n2\n3 4\n",
"50\n2\n2 1\n2\n1 2\n2\n1 2\n2\n2 1\n2\n1 3\n2\n2 1\n2\n1 2\n2\n2 1\n2\n3 1\n2\n1 2\n2\n1 2\n2\n2 1\n2\n1 3\n2\n1 2\n2\n3 1\n2\n1 2\n2\n1 3\n2\n1 3\n2\n2 1\n2\n1 3\n2\n1 2\n2\n1 3\n2\n1 3\n2\n3 1\n2\n2 1\n2\n1 2\n2\n1 2\n2\n1 3\n2\n2 1\n2\n2 1\n2\n3 1\n2\n1 2\n2\n3 1\n2\n3 1\n2\n1 3\n2\n3 1\n2\n1 3\n2\n1 3\n2\n1 2\n2\n2 1\n2\n2 1\n2\n2 1\n2\n1 2\n2\n1 2\n2\n2 1\n2\n3 1\n2\n2 1\n2\n1 2\n2\n3 1\n2\n2 1\n"
] |
[
"1 2 \n-1\n4 5 1 2 3 6 \n-1\n1 3 5 6 7 9 2 4 8 10 \n",
"1 4 2 5 3 6 \n1 3 2 5 4 6 \n1 3 2 4 5 6 \n-1\n1 4 3 5 2 6 \n1 2 3 5 4 6 \n1 2 3 4 5 6 \n-1\n1 3 4 5 2 6 \n1 2 4 5 3 6 \n-1\n-1\n1 3 5 6 2 4 \n1 2 5 6 3 4 \n-1\n-1\n-1\n-1\n-1\n-1\n2 4 1 5 3 6 \n2 3 1 5 4 6 \n2 3 1 4 5 6 \n-1\n2 4 3 5 1 6 \n-1\n-1\n-1\n2 3 4 5 1 6 \n-1\n-1\n-1\n2 3 5 6 1 4 \n",
"-1\n-1\n-1\n-1\n-1\n-1\n-1\n3 4 1 5 2 6 \n3 5 1 2 4 6 \n3 4 1 2 5 6 \n-1\n3 4 2 5 1 6 \n-1\n-1\n-1\n3 5 4 6 1 2 \n-1\n-1\n-1\n3 4 5 6 1 2 \n-1\n-1\n-1\n-1\n-1\n-1\n-1\n4 5 1 3 2 6 \n4 5 1 2 3 6 \n-1\n-1\n4 5 2 3 1 6 \n-1\n",
"-1\n-1\n4 5 3 6 1 2 \n-1\n-1\n-1\n-1\n-1\n-1\n-1\n-1\n-1\n-1\n-1\n5 6 1 3 2 4 \n5 6 1 2 3 4 \n-1\n-1\n5 6 2 3 1 4 \n-1\n-1\n-1\n5 6 3 4 1 2 \n-1\n-1\n-1\n-1\n-1\n-1\n-1\n-1\n-1\n-1\n",
"-1\n-1\n-1\n-1\n-1\n-1\n-1\n-1\n-1\n-1\n-1\n-1\n-1\n-1\n-1\n-1\n-1\n-1\n-1\n-1\n-1\n",
"-1\n-1\n-1\n-1\n-1\n-1\n-1\n-1\n-1\n",
"1 2 \n-1\n",
"1 3 2 4 \n1 2 3 4 \n-1\n2 3 1 4 \n-1\n-1\n3 4 1 2 \n-1\n-1\n-1\n-1\n-1\n",
"-1\n-1\n3 4 1 2 \n3 4 1 2 \n1 3 2 4 \n-1\n-1\n1 3 2 4 \n1 3 2 4 \n1 3 2 4 \n-1\n1 3 2 4 \n-1\n1 3 2 4 \n-1\n-1\n-1\n-1\n2 3 1 4 \n3 4 1 2 \n3 4 1 2 \n1 3 2 4 \n-1\n-1\n-1\n-1\n1 2 3 4 \n-1\n2 3 1 4 \n-1\n-1\n-1\n1 2 3 4 \n3 4 1 2 \n-1\n-1\n1 2 3 4 \n-1\n-1\n-1\n-1\n-1\n-1\n-1\n-1\n-1\n-1\n-1\n-1\n-1\n",
"2 3 1 4 \n1 3 2 4 \n1 3 2 4 \n2 3 1 4 \n1 2 3 4 \n2 3 1 4 \n1 3 2 4 \n2 3 1 4 \n3 4 1 2 \n1 3 2 4 \n1 3 2 4 \n2 3 1 4 \n1 2 3 4 \n1 3 2 4 \n3 4 1 2 \n1 3 2 4 \n1 2 3 4 \n1 2 3 4 \n2 3 1 4 \n1 2 3 4 \n1 3 2 4 \n1 2 3 4 \n1 2 3 4 \n3 4 1 2 \n2 3 1 4 \n1 3 2 4 \n1 3 2 4 \n1 2 3 4 \n2 3 1 4 \n2 3 1 4 \n3 4 1 2 \n1 3 2 4 \n3 4 1 2 \n3 4 1 2 \n1 2 3 4 \n3 4 1 2 \n1 2 3 4 \n1 2 3 4 \n1 3 2 4 \n2 3 1 4 \n2 3 1 4 \n2 3 1 4 \n1 3 2 4 \n1 3 2 4 \n2 3 1 4 \n3 4 1 2 \n2 3 1 4 \n1 3 2 4 \n3 4 1 2 \n2 3 1 4 \n"
] | 1
|
stdio
|
Calculate the number of ways to place $n$ rooks on $n \times n$ chessboard so that both following conditions are met:
each empty cell is under attack; exactly $k$ pairs of rooks attack each other.
An empty cell is under attack if there is at least one rook in the same row or at least one rook in the same column. Two rooks attack each other if they share the same row or column, and there are no other rooks between them. For example, there are only two pairs of rooks that attack each other in the following picture:
[Image] One of the ways to place the rooks for $n = 3$ and $k = 2$
Two ways to place the rooks are considered different if there exists at least one cell which is empty in one of the ways but contains a rook in another way.
The answer might be large, so print it modulo $998244353$.
-----Input-----
The only line of the input contains two integers $n$ and $k$ ($1 \le n \le 200000$; $0 \le k \le \frac{n(n - 1)}{2}$).
-----Output-----
Print one integer — the number of ways to place the rooks, taken modulo $998244353$.
-----Examples-----
Input
3 2
Output
6
Input
3 3
Output
0
Input
4 0
Output
24
Input
1337 42
Output
807905441
|
[
"3 2\n",
"3 3\n",
"4 0\n",
"1337 42\n",
"1 0\n",
"2 0\n",
"2 1\n",
"3 0\n",
"3 1\n",
"4 1\n"
] |
[
"6\n",
"0\n",
"24\n",
"807905441\n",
"1\n",
"2\n",
"4\n",
"6\n",
"36\n",
"288\n"
] | 1
|
stdio
|
Xenia the mathematician has a sequence consisting of n (n is divisible by 3) positive integers, each of them is at most 7. She wants to split the sequence into groups of three so that for each group of three a, b, c the following conditions held: a < b < c; a divides b, b divides c.
Naturally, Xenia wants each element of the sequence to belong to exactly one group of three. Thus, if the required partition exists, then it has $\frac{n}{3}$ groups of three.
Help Xenia, find the required partition or else say that it doesn't exist.
-----Input-----
The first line contains integer n (3 ≤ n ≤ 99999) — the number of elements in the sequence. The next line contains n positive integers, each of them is at most 7.
It is guaranteed that n is divisible by 3.
-----Output-----
If the required partition exists, print $\frac{n}{3}$ groups of three. Print each group as values of the elements it contains. You should print values in increasing order. Separate the groups and integers in groups by whitespaces. If there are multiple solutions, you can print any of them.
If there is no solution, print -1.
-----Examples-----
Input
6
1 1 1 2 2 2
Output
-1
Input
6
2 2 1 1 4 6
Output
1 2 4
1 2 6
|
[
"6\n1 1 1 2 2 2\n",
"6\n2 2 1 1 4 6\n",
"3\n1 2 3\n",
"3\n7 5 7\n",
"3\n1 3 4\n",
"3\n1 1 1\n",
"9\n1 3 6 6 3 1 3 1 6\n",
"6\n1 2 4 1 3 5\n",
"3\n1 3 7\n",
"3\n1 1 1\n"
] |
[
"-1\n",
"1 2 4\n1 2 6\n",
"-1\n",
"-1\n",
"-1\n",
"-1\n",
"1 3 6\n1 3 6\n1 3 6\n",
"-1\n",
"-1\n",
"-1\n"
] | 1
|
stdio
|
You are given a string s consisting of lowercase Latin letters. Character c is called k-dominant iff each substring of s with length at least k contains this character c.
You have to find minimum k such that there exists at least one k-dominant character.
-----Input-----
The first line contains string s consisting of lowercase Latin letters (1 ≤ |s| ≤ 100000).
-----Output-----
Print one number — the minimum value of k such that there exists at least one k-dominant character.
-----Examples-----
Input
abacaba
Output
2
Input
zzzzz
Output
1
Input
abcde
Output
3
|
[
"abacaba\n",
"zzzzz\n",
"abcde\n",
"bcaccacaaabaacaabaaabcbbcbcaacacbcbaaaacccacbbcbaabcbacaacbabacacacaccbbccbcbacbbbbccccabcabaaab\n",
"daabcdabbabbacacbaacabacbcaabaacac\n",
"abghim\n",
"gfliflgfhhdkceacdljgkegmdlhcgkcmlelmbbbmdddgdeeljjhgbbffmemmmkhebgkhadkdajabcjkcgbkgbaeacdedlkklfech\n",
"a\n",
"aaabbb\n",
"ab\n"
] |
[
"2\n",
"1\n",
"3\n",
"8\n",
"4\n",
"4\n",
"17\n",
"1\n",
"4\n",
"2\n"
] | 1
|
stdio
|
There are n stones on the table in a row, each of them can be red, green or blue. Count the minimum number of stones to take from the table so that any two neighboring stones had different colors. Stones in a row are considered neighboring if there are no other stones between them.
-----Input-----
The first line contains integer n (1 ≤ n ≤ 50) — the number of stones on the table.
The next line contains string s, which represents the colors of the stones. We'll consider the stones in the row numbered from 1 to n from left to right. Then the i-th character s equals "R", if the i-th stone is red, "G", if it's green and "B", if it's blue.
-----Output-----
Print a single integer — the answer to the problem.
-----Examples-----
Input
3
RRG
Output
1
Input
5
RRRRR
Output
4
Input
4
BRBG
Output
0
|
[
"3\nRRG\n",
"5\nRRRRR\n",
"4\nBRBG\n",
"1\nB\n",
"2\nBG\n",
"3\nBGB\n",
"4\nRBBR\n",
"5\nRGGBG\n",
"10\nGGBRBRGGRB\n",
"50\nGRBGGRBRGRBGGBBBBBGGGBBBBRBRGBRRBRGBBBRBBRRGBGGGRB\n"
] |
[
"1\n",
"4\n",
"0\n",
"0\n",
"0\n",
"0\n",
"1\n",
"1\n",
"2\n",
"18\n"
] | 1
|
stdio
|
Bear Limak likes watching sports on TV. He is going to watch a game today. The game lasts 90 minutes and there are no breaks.
Each minute can be either interesting or boring. If 15 consecutive minutes are boring then Limak immediately turns TV off.
You know that there will be n interesting minutes t_1, t_2, ..., t_{n}. Your task is to calculate for how many minutes Limak will watch the game.
-----Input-----
The first line of the input contains one integer n (1 ≤ n ≤ 90) — the number of interesting minutes.
The second line contains n integers t_1, t_2, ..., t_{n} (1 ≤ t_1 < t_2 < ... t_{n} ≤ 90), given in the increasing order.
-----Output-----
Print the number of minutes Limak will watch the game.
-----Examples-----
Input
3
7 20 88
Output
35
Input
9
16 20 30 40 50 60 70 80 90
Output
15
Input
9
15 20 30 40 50 60 70 80 90
Output
90
-----Note-----
In the first sample, minutes 21, 22, ..., 35 are all boring and thus Limak will turn TV off immediately after the 35-th minute. So, he would watch the game for 35 minutes.
In the second sample, the first 15 minutes are boring.
In the third sample, there are no consecutive 15 boring minutes. So, Limak will watch the whole game.
|
[
"3\n7 20 88\n",
"9\n16 20 30 40 50 60 70 80 90\n",
"9\n15 20 30 40 50 60 70 80 90\n",
"30\n6 11 12 15 22 24 30 31 32 33 34 35 40 42 44 45 47 50 53 54 57 58 63 67 75 77 79 81 83 88\n",
"60\n1 2 4 5 6 7 11 14 16 18 20 21 22 23 24 25 26 33 34 35 36 37 38 39 41 42 43 44 46 47 48 49 52 55 56 57 58 59 60 61 63 64 65 67 68 70 71 72 73 74 75 77 78 80 82 83 84 85 86 88\n",
"90\n1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90\n",
"1\n1\n",
"5\n15 30 45 60 75\n",
"6\n14 29 43 59 70 74\n",
"1\n15\n"
] |
[
"35\n",
"15\n",
"90\n",
"90\n",
"90\n",
"90\n",
"16\n",
"90\n",
"58\n",
"30\n"
] | 1
|
stdio
|
Kolya got string s for his birthday, the string consists of small English letters. He immediately added k more characters to the right of the string.
Then Borya came and said that the new string contained a tandem repeat of length l as a substring. How large could l be?
See notes for definition of a tandem repeat.
-----Input-----
The first line contains s (1 ≤ |s| ≤ 200). This string contains only small English letters. The second line contains number k (1 ≤ k ≤ 200) — the number of the added characters.
-----Output-----
Print a single number — the maximum length of the tandem repeat that could have occurred in the new string.
-----Examples-----
Input
aaba
2
Output
6
Input
aaabbbb
2
Output
6
Input
abracadabra
10
Output
20
-----Note-----
A tandem repeat of length 2n is string s, where for any position i (1 ≤ i ≤ n) the following condition fulfills: s_{i} = s_{i} + n.
In the first sample Kolya could obtain a string aabaab, in the second — aaabbbbbb, in the third — abracadabrabracadabra.
|
[
"aaba\n2\n",
"aaabbbb\n2\n",
"abracadabra\n10\n",
"zwvrx\n3\n",
"ayi\n10\n",
"eexlzphiay\n1\n",
"zumtumtlitf\n2\n",
"xbmrxbmrkzovhb\n3\n",
"ijtvifbuajod\n5\n",
"jhfwjyyzwrjiyrrgveiqkoltivghgkontrqragikttxxuwszjwqhwxindyrdqhucnbwgwrppgqmsasrzohezjlfmkzsqptwpratprcrxyxecnlsaiqrvimihmhjfgzwdtvmfhgbuonpsblphyoxzclkrwbwrkasahiirzqlfjdoomlosltldbpomyyhmdwfchzxnmwlh\n200\n"
] |
[
"6\n",
"6\n",
"20\n",
"6\n",
"12\n",
"2\n",
"6\n",
"8\n",
"10\n",
"400\n"
] | 1
|
stdio
|
There are $n$ slimes in a row. Each slime has an integer value (possibly negative or zero) associated with it.
Any slime can eat its adjacent slime (the closest slime to its left or to its right, assuming that this slime exists).
When a slime with a value $x$ eats a slime with a value $y$, the eaten slime disappears, and the value of the remaining slime changes to $x - y$.
The slimes will eat each other until there is only one slime left.
Find the maximum possible value of the last slime.
-----Input-----
The first line of the input contains an integer $n$ ($1 \le n \le 500\,000$) denoting the number of slimes.
The next line contains $n$ integers $a_i$ ($-10^9 \le a_i \le 10^9$), where $a_i$ is the value of $i$-th slime.
-----Output-----
Print an only integer — the maximum possible value of the last slime.
-----Examples-----
Input
4
2 1 2 1
Output
4
Input
5
0 -1 -1 -1 -1
Output
4
-----Note-----
In the first example, a possible way of getting the last slime with value $4$ is:
Second slime eats the third slime, the row now contains slimes $2, -1, 1$
Second slime eats the third slime, the row now contains slimes $2, -2$
First slime eats the second slime, the row now contains $4$
In the second example, the first slime can keep eating slimes to its right to end up with a value of $4$.
|
[
"4\n2 1 2 1\n",
"5\n0 -1 -1 -1 -1\n",
"2\n10 8\n",
"5\n-14 -2 0 -19 -12\n",
"6\n-15 2 -19 20 0 9\n",
"3\n17 4 -1\n",
"4\n20 3 -15 7\n",
"1\n11\n",
"1\n-10\n",
"7\n-8 9 0 -10 -20 -8 3\n"
] |
[
"4",
"4",
"2",
"47",
"65",
"22",
"45",
"11",
"-10",
"58"
] | 1
|
stdio
|
Let's call a string adorable if its letters can be realigned in such a way that they form two consequent groups of equal symbols (note that different groups must contain different symbols). For example, ababa is adorable (you can transform it to aaabb, where the first three letters form a group of a-s and others — a group of b-s), but cccc is not since in each possible consequent partition letters in these two groups coincide.
You're given a string s. Check whether it can be split into two non-empty subsequences such that the strings formed by these subsequences are adorable. Here a subsequence is an arbitrary set of indexes of the string.
-----Input-----
The only line contains s (1 ≤ |s| ≤ 10^5) consisting of lowercase latin letters.
-----Output-----
Print «Yes» if the string can be split according to the criteria above or «No» otherwise.
Each letter can be printed in arbitrary case.
-----Examples-----
Input
ababa
Output
Yes
Input
zzcxx
Output
Yes
Input
yeee
Output
No
-----Note-----
In sample case two zzcxx can be split into subsequences zc and zxx each of which is adorable.
There's no suitable partition in sample case three.
|
[
"ababa\n",
"zzcxx\n",
"yeee\n",
"a\n",
"bbab\n",
"abcd\n",
"abc\n",
"abcdaaaa\n",
"aaaaaaaaaaaaaaa\n",
"adb\n"
] |
[
"Yes\n",
"Yes\n",
"No\n",
"No\n",
"No\n",
"Yes\n",
"No\n",
"Yes\n",
"No\n",
"No\n"
] | 1
|
stdio
|
You are given a set of points $x_1$, $x_2$, ..., $x_n$ on the number line.
Two points $i$ and $j$ can be matched with each other if the following conditions hold: neither $i$ nor $j$ is matched with any other point; $|x_i - x_j| \ge z$.
What is the maximum number of pairs of points you can match with each other?
-----Input-----
The first line contains two integers $n$ and $z$ ($2 \le n \le 2 \cdot 10^5$, $1 \le z \le 10^9$) — the number of points and the constraint on the distance between matched points, respectively.
The second line contains $n$ integers $x_1$, $x_2$, ..., $x_n$ ($1 \le x_i \le 10^9$).
-----Output-----
Print one integer — the maximum number of pairs of points you can match with each other.
-----Examples-----
Input
4 2
1 3 3 7
Output
2
Input
5 5
10 9 5 8 7
Output
1
-----Note-----
In the first example, you may match point $1$ with point $2$ ($|3 - 1| \ge 2$), and point $3$ with point $4$ ($|7 - 3| \ge 2$).
In the second example, you may match point $1$ with point $3$ ($|5 - 10| \ge 5$).
|
[
"4 2\n1 3 3 7\n",
"5 5\n10 9 5 8 7\n",
"3 2\n1 4 7\n",
"6 4\n17 13 16 12 15 11\n",
"6 5\n17 13 16 12 15 11\n",
"2 1\n2 2\n",
"14 16\n27 37 50 11 16 42 45 43 31 42 40 29 42 32\n",
"10 1\n3 1 3 4 5 3 2 4 1 4\n",
"12 15\n12 17 28 14 32 40 33 18 28 10 40 50\n",
"5 1\n5 4 3 2 4\n"
] |
[
"2\n",
"1\n",
"1\n",
"3\n",
"2\n",
"0\n",
"5\n",
"5\n",
"6\n",
"2\n"
] | 1
|
stdio
|
You have a fraction $\frac{a}{b}$. You need to find the first occurrence of digit c into decimal notation of the fraction after decimal point.
-----Input-----
The first contains three single positive integers a, b, c (1 ≤ a < b ≤ 10^5, 0 ≤ c ≤ 9).
-----Output-----
Print position of the first occurrence of digit c into the fraction. Positions are numbered from 1 after decimal point. It there is no such position, print -1.
-----Examples-----
Input
1 2 0
Output
2
Input
2 3 7
Output
-1
-----Note-----
The fraction in the first example has the following decimal notation: $\frac{1}{2} = 0.500(0)$. The first zero stands on second position.
The fraction in the second example has the following decimal notation: $\frac{2}{3} = 0.666(6)$. There is no digit 7 in decimal notation of the fraction.
|
[
"1 2 0\n",
"2 3 7\n",
"1 100000 1\n",
"1 7 7\n",
"99999 100000 8\n",
"44102 73848 2\n",
"7 31 3\n",
"8880 81608 9\n",
"4942 62768 5\n",
"69168 84860 4\n"
] |
[
"2",
"-1",
"5",
"6",
"-1",
"132",
"15",
"161",
"122",
"107"
] | 1
|
stdio
|
Kyoya Ootori is selling photobooks of the Ouran High School Host Club. He has 26 photos, labeled "a" to "z", and he has compiled them into a photo booklet with some photos in some order (possibly with some photos being duplicated). A photo booklet can be described as a string of lowercase letters, consisting of the photos in the booklet in order. He now wants to sell some "special edition" photobooks, each with one extra photo inserted anywhere in the book. He wants to make as many distinct photobooks as possible, so he can make more money. He asks Haruhi, how many distinct photobooks can he make by inserting one extra photo into the photobook he already has?
Please help Haruhi solve this problem.
-----Input-----
The first line of input will be a single string s (1 ≤ |s| ≤ 20). String s consists only of lowercase English letters.
-----Output-----
Output a single integer equal to the number of distinct photobooks Kyoya Ootori can make.
-----Examples-----
Input
a
Output
51
Input
hi
Output
76
-----Note-----
In the first case, we can make 'ab','ac',...,'az','ba','ca',...,'za', and 'aa', producing a total of 51 distinct photo booklets.
|
[
"a\n",
"hi\n",
"y\n",
"kgan\n",
"zoabkyuvus\n",
"spyemhyznjieyhhbk\n",
"xulsyfkuizjauadjjopu\n",
"e\n",
"zv\n",
"jgv\n"
] |
[
"51\n",
"76\n",
"51\n",
"126\n",
"276\n",
"451\n",
"526\n",
"51\n",
"76\n",
"101\n"
] | 1
|
stdio
|
Fafa owns a company that works on huge projects. There are n employees in Fafa's company. Whenever the company has a new project to start working on, Fafa has to divide the tasks of this project among all the employees.
Fafa finds doing this every time is very tiring for him. So, he decided to choose the best l employees in his company as team leaders. Whenever there is a new project, Fafa will divide the tasks among only the team leaders and each team leader will be responsible of some positive number of employees to give them the tasks. To make this process fair for the team leaders, each one of them should be responsible for the same number of employees. Moreover, every employee, who is not a team leader, has to be under the responsibility of exactly one team leader, and no team leader is responsible for another team leader.
Given the number of employees n, find in how many ways Fafa could choose the number of team leaders l in such a way that it is possible to divide employees between them evenly.
-----Input-----
The input consists of a single line containing a positive integer n (2 ≤ n ≤ 10^5) — the number of employees in Fafa's company.
-----Output-----
Print a single integer representing the answer to the problem.
-----Examples-----
Input
2
Output
1
Input
10
Output
3
-----Note-----
In the second sample Fafa has 3 ways: choose only 1 employee as a team leader with 9 employees under his responsibility. choose 2 employees as team leaders with 4 employees under the responsibility of each of them. choose 5 employees as team leaders with 1 employee under the responsibility of each of them.
|
[
"2\n",
"10\n",
"3\n",
"4\n",
"6\n",
"13\n",
"100000\n",
"1024\n",
"99999\n",
"10007\n"
] |
[
"1\n",
"3\n",
"1\n",
"2\n",
"3\n",
"1\n",
"35\n",
"10\n",
"11\n",
"1\n"
] | 1
|
stdio
|
The start of the new academic year brought about the problem of accommodation students into dormitories. One of such dormitories has a a × b square meter wonder room. The caretaker wants to accommodate exactly n students there. But the law says that there must be at least 6 square meters per student in a room (that is, the room for n students must have the area of at least 6n square meters). The caretaker can enlarge any (possibly both) side of the room by an arbitrary positive integer of meters. Help him change the room so as all n students could live in it and the total area of the room was as small as possible.
-----Input-----
The first line contains three space-separated integers n, a and b (1 ≤ n, a, b ≤ 10^9) — the number of students and the sizes of the room.
-----Output-----
Print three integers s, a_1 and b_1 (a ≤ a_1; b ≤ b_1) — the final area of the room and its sizes. If there are multiple optimal solutions, print any of them.
-----Examples-----
Input
3 3 5
Output
18
3 6
Input
2 4 4
Output
16
4 4
|
[
"3 3 5\n",
"2 4 4\n",
"1 1 1\n",
"1 1000000000 1000000000\n",
"8 7 5\n",
"1000000000 1 1\n",
"1000000000 1000000000 1000000000\n",
"800000003 7 7\n",
"11 7 7\n",
"1000000000 1 1\n"
] |
[
"18\n3 6\n",
"16\n4 4\n",
"6\n1 6\n",
"1000000000000000000\n1000000000 1000000000\n",
"48\n8 6\n",
"6000000000\n1 6000000000\n",
"1000000000000000000\n1000000000 1000000000\n",
"4800000018\n11 436363638\n",
"70\n7 10\n",
"6000000000\n1 6000000000\n"
] | 1
|
stdio
|
-----Input-----
The only line of the input is a string of 7 characters. The first character is letter A, followed by 6 digits. The input is guaranteed to be valid (for certain definition of "valid").
-----Output-----
Output a single integer.
-----Examples-----
Input
A221033
Output
21
Input
A223635
Output
22
Input
A232726
Output
23
|
[
"A221033\n",
"A223635\n",
"A232726\n",
"A102210\n",
"A231010\n",
"A222222\n",
"A555555\n",
"A102222\n",
"A234567\n",
"A987654\n"
] |
[
"21\n",
"22\n",
"23\n",
"25\n",
"26\n",
"13\n",
"31\n",
"19\n",
"28\n",
"40\n"
] | 1
|
stdio
|
Once again Tavas started eating coffee mix without water! Keione told him that it smells awful, but he didn't stop doing that. That's why Keione told his smart friend, SaDDas to punish him! SaDDas took Tavas' headphones and told him: "If you solve the following problem, I'll return it to you." [Image]
The problem is:
You are given a lucky number n. Lucky numbers are the positive integers whose decimal representations contain only the lucky digits 4 and 7. For example, numbers 47, 744, 4 are lucky and 5, 17, 467 are not.
If we sort all lucky numbers in increasing order, what's the 1-based index of n?
Tavas is not as smart as SaDDas, so he asked you to do him a favor and solve this problem so he can have his headphones back.
-----Input-----
The first and only line of input contains a lucky number n (1 ≤ n ≤ 10^9).
-----Output-----
Print the index of n among all lucky numbers.
-----Examples-----
Input
4
Output
1
Input
7
Output
2
Input
77
Output
6
|
[
"4\n",
"7\n",
"77\n",
"4\n",
"474744\n",
"777774\n",
"447\n",
"774\n",
"4\n",
"4447747\n"
] |
[
"1\n",
"2\n",
"6\n",
"1\n",
"83\n",
"125\n",
"8\n",
"13\n",
"1\n",
"140\n"
] | 1
|
stdio
|
Sergey is testing a next-generation processor. Instead of bytes the processor works with memory cells consisting of n bits. These bits are numbered from 1 to n. An integer is stored in the cell in the following way: the least significant bit is stored in the first bit of the cell, the next significant bit is stored in the second bit, and so on; the most significant bit is stored in the n-th bit.
Now Sergey wants to test the following instruction: "add 1 to the value of the cell". As a result of the instruction, the integer that is written in the cell must be increased by one; if some of the most significant bits of the resulting number do not fit into the cell, they must be discarded.
Sergey wrote certain values of the bits in the cell and is going to add one to its value. How many bits of the cell will change after the operation?
-----Input-----
The first line contains a single integer n (1 ≤ n ≤ 100) — the number of bits in the cell.
The second line contains a string consisting of n characters — the initial state of the cell. The first character denotes the state of the first bit of the cell. The second character denotes the second least significant bit and so on. The last character denotes the state of the most significant bit.
-----Output-----
Print a single integer — the number of bits in the cell which change their state after we add 1 to the cell.
-----Examples-----
Input
4
1100
Output
3
Input
4
1111
Output
4
-----Note-----
In the first sample the cell ends up with value 0010, in the second sample — with 0000.
|
[
"4\n1100\n",
"4\n1111\n",
"1\n0\n",
"1\n1\n",
"2\n00\n",
"2\n01\n",
"2\n10\n",
"2\n11\n",
"10\n0000000000\n",
"20\n11111111110110001100\n"
] |
[
"3\n",
"4\n",
"1\n",
"1\n",
"1\n",
"1\n",
"2\n",
"2\n",
"1\n",
"11\n"
] | 1
|
stdio
|
You're given an array $a$ of length $2n$. Is it possible to reorder it in such way so that the sum of the first $n$ elements isn't equal to the sum of the last $n$ elements?
-----Input-----
The first line contains an integer $n$ ($1 \le n \le 1000$), where $2n$ is the number of elements in the array $a$.
The second line contains $2n$ space-separated integers $a_1$, $a_2$, $\ldots$, $a_{2n}$ ($1 \le a_i \le 10^6$) — the elements of the array $a$.
-----Output-----
If there's no solution, print "-1" (without quotes). Otherwise, print a single line containing $2n$ space-separated integers. They must form a reordering of $a$. You are allowed to not change the order.
-----Examples-----
Input
3
1 2 2 1 3 1
Output
2 1 3 1 1 2
Input
1
1 1
Output
-1
-----Note-----
In the first example, the first $n$ elements have sum $2+1+3=6$ while the last $n$ elements have sum $1+1+2=4$. The sums aren't equal.
In the second example, there's no solution.
|
[
"3\n1 2 2 1 3 1\n",
"1\n1 1\n",
"10\n3 10 5 5 8 6 6 9 9 3 1 7 10 2 4 9 3 8 2 2\n",
"2\n1 4 2 3\n",
"2\n1 1 2 2\n",
"1\n79808 79808\n",
"4\n56 14 77 12 87 55 31 46\n",
"10\n859983 998985 909455 4688 549610 325108 492856 2751 734117 162579 97740 703983 356830 17839 881224 458713 233429 269974 351504 595389\n",
"97\n7 8 5 4 7 4 10 3 8 10 2 10 9 9 8 1 9 1 8 8 5 6 4 8 7 1 9 10 6 3 9 5 8 3 3 8 9 8 4 2 10 8 5 4 1 10 8 4 2 3 2 10 6 1 4 5 1 2 9 5 4 9 1 5 5 8 10 1 10 6 5 8 8 8 5 4 5 7 8 8 6 2 7 10 4 2 1 6 5 9 1 8 6 7 5 2 3 4 1 10 4 5 4 3 10 8 9 9 9 8 6 5 8 7 8 10 4 4 7 5 8 8 1 10 6 9 5 9 8 4 9 1 10 1 4 7 7 1 8 5 7 1 4 4 9 2 4 8 9 10 8 5 1 2 10 4 8 10 6 4 3 2 2 5 1 8 7 4 6 2 1 4 6 5 7 2 6 3 10 3 3 8 6 9 10 10 6 2 1 10 3 1 8 5\n",
"3\n1 2 3 3 2 1\n"
] |
[
"2 1 3 1 1 2",
"-1",
"1 2 2 2 3 3 3 4 5 5 6 6 7 8 8 9 9 9 10 10 ",
"1 2 3 4 ",
"1 1 2 2 ",
"-1",
"12 14 31 46 55 56 77 87 ",
"2751 4688 17839 97740 162579 233429 269974 325108 351504 356830 458713 492856 549610 595389 703983 734117 859983 881224 909455 998985 ",
"1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3 3 3 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 7 7 7 7 7 7 7 7 7 7 7 7 7 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 ",
"1 1 2 2 3 3 "
] | 1
|
stdio
|
In mathematics, the Pythagorean theorem — is a relation in Euclidean geometry among the three sides of a right-angled triangle. In terms of areas, it states:
In any right-angled triangle, the area of the square whose side is the hypotenuse (the side opposite the right angle) is equal to the sum of the areas of the squares whose sides are the two legs (the two sides that meet at a right angle).
The theorem can be written as an equation relating the lengths of the sides a, b and c, often called the Pythagorean equation:
a^2 + b^2 = c^2
where c represents the length of the hypotenuse, and a and b represent the lengths of the other two sides.
[Image]
Given n, your task is to count how many right-angled triangles with side-lengths a, b and c that satisfied an inequality 1 ≤ a ≤ b ≤ c ≤ n.
-----Input-----
The only line contains one integer n (1 ≤ n ≤ 10^4) as we mentioned above.
-----Output-----
Print a single integer — the answer to the problem.
-----Examples-----
Input
5
Output
1
Input
74
Output
35
|
[
"5\n",
"74\n",
"1000\n",
"586\n",
"2\n",
"362\n",
"778\n",
"194\n",
"906\n",
"659\n"
] |
[
"1\n",
"35\n",
"881\n",
"472\n",
"0\n",
"258\n",
"653\n",
"120\n",
"786\n",
"535\n"
] | 1
|
stdio
|
You have $n \times n$ square grid and an integer $k$. Put an integer in each cell while satisfying the conditions below. All numbers in the grid should be between $1$ and $k$ inclusive. Minimum number of the $i$-th row is $1$ ($1 \le i \le n$). Minimum number of the $j$-th column is $1$ ($1 \le j \le n$).
Find the number of ways to put integers in the grid. Since the answer can be very large, find the answer modulo $(10^{9} + 7)$. [Image] These are the examples of valid and invalid grid when $n=k=2$.
-----Input-----
The only line contains two integers $n$ and $k$ ($1 \le n \le 250$, $1 \le k \le 10^{9}$).
-----Output-----
Print the answer modulo $(10^{9} + 7)$.
-----Examples-----
Input
2 2
Output
7
Input
123 456789
Output
689974806
-----Note-----
In the first example, following $7$ cases are possible. [Image]
In the second example, make sure you print the answer modulo $(10^{9} + 7)$.
|
[
"2 2\n",
"123 456789\n",
"250 1000000000\n",
"250 1\n",
"1 3\n",
"3 497285769\n",
"3 212096267\n",
"4 221874066\n",
"244 315404017\n",
"218 325181815\n"
] |
[
"7\n",
"689974806\n",
"770503193\n",
"1\n",
"1\n",
"790515254\n",
"501206544\n",
"274467242\n",
"868949606\n",
"230476135\n"
] | 1
|
stdio
|
In this problem MEX of a certain array is the smallest positive integer not contained in this array.
Everyone knows this definition, including Lesha. But Lesha loves MEX, so he comes up with a new problem involving MEX every day, including today.
You are given an array $a$ of length $n$. Lesha considers all the non-empty subarrays of the initial array and computes MEX for each of them. Then Lesha computes MEX of the obtained numbers.
An array $b$ is a subarray of an array $a$, if $b$ can be obtained from $a$ by deletion of several (possible none or all) elements from the beginning and several (possibly none or all) elements from the end. In particular, an array is a subarray of itself.
Lesha understands that the problem is very interesting this time, but he doesn't know how to solve it. Help him and find the MEX of MEXes of all the subarrays!
-----Input-----
The first line contains a single integer $n$ ($1 \le n \le 10^5$) — the length of the array.
The next line contains $n$ integers $a_1, a_2, \ldots, a_n$ ($1 \le a_i \le n$) — the elements of the array.
-----Output-----
Print a single integer — the MEX of MEXes of all subarrays.
-----Examples-----
Input
3
1 3 2
Output
3
Input
5
1 4 3 1 2
Output
6
|
[
"3\n1 3 2\n",
"5\n1 4 3 1 2\n",
"51\n45 37 1 8 4 41 35 15 17 2 7 48 20 42 41 5 26 25 37 1 19 43 3 49 33 2 45 43 39 14 1 21 22 17 18 8 49 24 35 26 22 43 45 1 3 17 1 16 35 33 5\n",
"100\n1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100\n",
"100\n100 2 3 99 5 6 7 8 9 10 65 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 48 32 83 79 35 36 37 38 39 40 41 42 43 44 45 46 47 31 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 11 66 67 68 69 70 71 72 73 80 75 76 77 78 34 74 81 82 33 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 4 1\n",
"100\n1 2 3 4 5 6 7 8 9 10 11 12 13 14 76 16 17 18 19 20 21 22 23 47 25 26 27 28 29 30 31 32 44 34 33 36 37 38 39 40 41 42 43 35 45 46 24 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 80 65 66 67 68 69 70 71 72 73 74 75 15 77 78 79 97 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 64 98 99 100\n",
"1\n1\n",
"56\n42 33 13 55 38 6 25 10 25 53 8 52 40 15 54 6 16 23 19 38 7 2 8 53 23 21 39 44 50 29 55 1 51 43 5 8 44 55 14 8 51 18 13 21 52 45 48 9 37 7 31 37 34 14 44 21\n",
"84\n60 20 43 2 59 10 25 82 84 41 39 35 33 48 21 67 79 81 16 56 27 31 6 23 3 74 56 39 41 54 15 21 9 54 13 15 79 55 34 7 42 68 22 50 47 83 16 76 62 8 58 84 83 60 83 24 79 9 68 10 52 17 21 30 1 58 15 81 24 68 34 53 38 10 74 5 65 78 27 40 11 75 5 44\n",
"58\n5 11 38 39 29 31 3 42 10 38 52 52 15 20 57 32 45 28 34 58 29 34 36 29 53 47 2 37 47 46 19 18 10 45 23 53 18 29 21 35 30 55 26 42 43 54 37 3 28 10 22 11 11 50 34 17 33 47\n"
] |
[
"3\n",
"6\n",
"5\n",
"102\n",
"3\n",
"16\n",
"1\n",
"4\n",
"3\n",
"2\n"
] | 1
|
stdio
|
Pasha has many hamsters and he makes them work out. Today, n hamsters (n is even) came to work out. The hamsters lined up and each hamster either sat down or stood up.
For another exercise, Pasha needs exactly $\frac{n}{2}$ hamsters to stand up and the other hamsters to sit down. In one minute, Pasha can make some hamster ether sit down or stand up. How many minutes will he need to get what he wants if he acts optimally well?
-----Input-----
The first line contains integer n (2 ≤ n ≤ 200; n is even). The next line contains n characters without spaces. These characters describe the hamsters' position: the i-th character equals 'X', if the i-th hamster in the row is standing, and 'x', if he is sitting.
-----Output-----
In the first line, print a single integer — the minimum required number of minutes. In the second line, print a string that describes the hamsters' position after Pasha makes the required changes. If there are multiple optimal positions, print any of them.
-----Examples-----
Input
4
xxXx
Output
1
XxXx
Input
2
XX
Output
1
xX
Input
6
xXXxXx
Output
0
xXXxXx
|
[
"4\nxxXx\n",
"2\nXX\n",
"6\nxXXxXx\n",
"4\nxXXX\n",
"2\nXx\n",
"22\nXXxXXxxXxXxXXXXXXXXXxx\n",
"30\nXXxXxxXXXXxxXXxxXXxxxxXxxXXXxx\n",
"104\nxxXxXxxXXXxxXxXxxXXXxxxXxxXXXxxXXXxXxXxXXxxXxxxxxXXXXxXXXXxXXXxxxXxxxxxxxXxxXxXXxxXXXXxXXXxxXXXXXXXXXxXX\n",
"78\nxxxXxxXxXxxXxxxxxXxXXXxXXXXxxxxxXxXXXxxXxXXXxxxxXxxXXXxxxxxxxxXXXXxXxXXxXXXxXX\n",
"200\nxxXXxxXXxXxxXxxXxXxxXxXxXxXxxxxxXXxXXxxXXXXxXXXxXXxXxXxxxxXxxXXXxxxXxXxxxXxxXXxXxXxxxxxxxXxxXxXxxXxXXXxxXxXXXXxxXxxxXxXXXXXXxXxXXxxxxXxxxXxxxXxXXXxXxXXXXxXXxxxXxXXxxXXxxxXxXxXXxXXXxXxXxxxXXxxxxXXxXXXX\n"
] |
[
"1\nXxXx\n",
"1\nxX\n",
"0\nxXXxXx\n",
"1\nxxXX\n",
"0\nXx\n",
"4\nxxxxxxxXxXxXXXXXXXXXxx\n",
"0\nXXxXxxXXXXxxXXxxXXxxxxXxxXXXxx\n",
"4\nxxxxxxxxxXxxXxXxxXXXxxxXxxXXXxxXXXxXxXxXXxxXxxxxxXXXXxXXXXxXXXxxxXxxxxxxxXxxXxXXxxXXXXxXXXxxXXXXXXXXXxXX\n",
"3\nXXXXxxXxXxxXxxxxxXxXXXxXXXXxxxxxXxXXXxxXxXXXxxxxXxxXXXxxxxxxxxXXXXxXxXXxXXXxXX\n",
"4\nXXXXXXXXxXxxXxxXxXxxXxXxXxXxxxxxXXxXXxxXXXXxXXXxXXxXxXxxxxXxxXXXxxxXxXxxxXxxXXxXxXxxxxxxxXxxXxXxxXxXXXxxXxXXXXxxXxxxXxXXXXXXxXxXXxxxxXxxxXxxxXxXXXxXxXXXXxXXxxxXxXXxxXXxxxXxXxXXxXXXxXxXxxxXXxxxxXXxXXXX\n"
] | 1
|
stdio
|
Calculate the minimum number of characters you need to change in the string s, so that it contains at least k different letters, or print that it is impossible.
String s consists only of lowercase Latin letters, and it is allowed to change characters only to lowercase Latin letters too.
-----Input-----
First line of input contains string s, consisting only of lowercase Latin letters (1 ≤ |s| ≤ 1000, |s| denotes the length of s).
Second line of input contains integer k (1 ≤ k ≤ 26).
-----Output-----
Print single line with a minimum number of necessary changes, or the word «impossible» (without quotes) if it is impossible.
-----Examples-----
Input
yandex
6
Output
0
Input
yahoo
5
Output
1
Input
google
7
Output
impossible
-----Note-----
In the first test case string contains 6 different letters, so we don't need to change anything.
In the second test case string contains 4 different letters: {'a', 'h', 'o', 'y'}. To get 5 different letters it is necessary to change one occurrence of 'o' to some letter, which doesn't occur in the string, for example, {'b'}.
In the third test case, it is impossible to make 7 different letters because the length of the string is 6.
|
[
"yandex\n6\n",
"yahoo\n5\n",
"google\n7\n",
"a\n1\n",
"z\n2\n",
"fwgfrwgkuwghfiruhewgirueguhergiqrbvgrgf\n26\n",
"nfevghreuoghrueighoqghbnebvnejbvnbgneluqe\n26\n",
"a\n3\n",
"smaxpqplaqqbxuqxalqmbmmgubbpspxhawbxsuqhhegpmmpebqmqpbbeplwaepxmsahuepuhuhwxeqmmlgqubuaxehwuwasgxpqmugbmuawuhwqlswllssueglbxepbmwgs\n1\n",
"cuguccgcugcugucgggggcgcgucgucugcuuuccccuugccg\n4\n"
] |
[
"0\n",
"1\n",
"impossible\n",
"0\n",
"impossible\n",
"14\n",
"12\n",
"impossible\n",
"0\n",
"1\n"
] | 1
|
stdio
|
Ayoub had an array $a$ of integers of size $n$ and this array had two interesting properties: All the integers in the array were between $l$ and $r$ (inclusive). The sum of all the elements was divisible by $3$.
Unfortunately, Ayoub has lost his array, but he remembers the size of the array $n$ and the numbers $l$ and $r$, so he asked you to find the number of ways to restore the array.
Since the answer could be very large, print it modulo $10^9 + 7$ (i.e. the remainder when dividing by $10^9 + 7$). In case there are no satisfying arrays (Ayoub has a wrong memory), print $0$.
-----Input-----
The first and only line contains three integers $n$, $l$ and $r$ ($1 \le n \le 2 \cdot 10^5 , 1 \le l \le r \le 10^9$) — the size of the lost array and the range of numbers in the array.
-----Output-----
Print the remainder when dividing by $10^9 + 7$ the number of ways to restore the array.
-----Examples-----
Input
2 1 3
Output
3
Input
3 2 2
Output
1
Input
9 9 99
Output
711426616
-----Note-----
In the first example, the possible arrays are : $[1,2], [2,1], [3, 3]$.
In the second example, the only possible array is $[2, 2, 2]$.
|
[
"2 1 3\n",
"3 2 2\n",
"9 9 99\n",
"1000 562 6782363\n",
"200000 1 1000000000\n",
"1 1 1\n",
"3 1000000000 1000000000\n",
"120881 536336525 585696606\n",
"7884 43814 254290\n",
"3895 1 564243401\n"
] |
[
"3\n",
"1\n",
"711426616\n",
"710038164\n",
"69063912\n",
"0\n",
"1\n",
"915864703\n",
"104223746\n",
"169725536\n"
] | 1
|
stdio
|
Innokentiy likes tea very much and today he wants to drink exactly n cups of tea. He would be happy to drink more but he had exactly n tea bags, a of them are green and b are black.
Innokentiy doesn't like to drink the same tea (green or black) more than k times in a row. Your task is to determine the order of brewing tea bags so that Innokentiy will be able to drink n cups of tea, without drinking the same tea more than k times in a row, or to inform that it is impossible. Each tea bag has to be used exactly once.
-----Input-----
The first line contains four integers n, k, a and b (1 ≤ k ≤ n ≤ 10^5, 0 ≤ a, b ≤ n) — the number of cups of tea Innokentiy wants to drink, the maximum number of cups of same tea he can drink in a row, the number of tea bags of green and black tea. It is guaranteed that a + b = n.
-----Output-----
If it is impossible to drink n cups of tea, print "NO" (without quotes).
Otherwise, print the string of the length n, which consists of characters 'G' and 'B'. If some character equals 'G', then the corresponding cup of tea should be green. If some character equals 'B', then the corresponding cup of tea should be black.
If there are multiple answers, print any of them.
-----Examples-----
Input
5 1 3 2
Output
GBGBG
Input
7 2 2 5
Output
BBGBGBB
Input
4 3 4 0
Output
NO
|
[
"5 1 3 2\n",
"7 2 2 5\n",
"4 3 4 0\n",
"2 2 0 2\n",
"3 2 0 3\n",
"1 1 0 1\n",
"1 1 1 0\n",
"11 2 3 8\n",
"2 2 2 0\n",
"2 2 1 1\n"
] |
[
"GBGBG\n",
"BBGBBGB\n",
"NO\n",
"BB\n",
"NO\n",
"B\n",
"G\n",
"BBGBBGBBGBB\n",
"GG\n",
"GB\n"
] | 1
|
stdio
|
Vitaly is a very weird man. He's got two favorite digits a and b. Vitaly calls a positive integer good, if the decimal representation of this integer only contains digits a and b. Vitaly calls a good number excellent, if the sum of its digits is a good number.
For example, let's say that Vitaly's favourite digits are 1 and 3, then number 12 isn't good and numbers 13 or 311 are. Also, number 111 is excellent and number 11 isn't.
Now Vitaly is wondering, how many excellent numbers of length exactly n are there. As this number can be rather large, he asks you to count the remainder after dividing it by 1000000007 (10^9 + 7).
A number's length is the number of digits in its decimal representation without leading zeroes.
-----Input-----
The first line contains three integers: a, b, n (1 ≤ a < b ≤ 9, 1 ≤ n ≤ 10^6).
-----Output-----
Print a single integer — the answer to the problem modulo 1000000007 (10^9 + 7).
-----Examples-----
Input
1 3 3
Output
1
Input
2 3 10
Output
165
|
[
"1 3 3\n",
"2 3 10\n",
"6 8 14215\n",
"4 9 104671\n",
"6 7 78755\n",
"1 8 265\n",
"3 9 37413\n",
"1 7 49055\n",
"3 4 11028\n",
"2 6 32377\n"
] |
[
"1\n",
"165\n",
"651581472\n",
"329390901\n",
"0\n",
"461320265\n",
"461358757\n",
"461364774\n",
"461668105\n",
"887598327\n"
] | 1
|
stdio
|
Vasily the Programmer loves romance, so this year he decided to illuminate his room with candles.
Vasily has a candles.When Vasily lights up a new candle, it first burns for an hour and then it goes out. Vasily is smart, so he can make b went out candles into a new candle. As a result, this new candle can be used like any other new candle.
Now Vasily wonders: for how many hours can his candles light up the room if he acts optimally well? Help him find this number.
-----Input-----
The single line contains two integers, a and b (1 ≤ a ≤ 1000; 2 ≤ b ≤ 1000).
-----Output-----
Print a single integer — the number of hours Vasily can light up the room for.
-----Examples-----
Input
4 2
Output
7
Input
6 3
Output
8
-----Note-----
Consider the first sample. For the first four hours Vasily lights up new candles, then he uses four burned out candles to make two new ones and lights them up. When these candles go out (stop burning), Vasily can make another candle. Overall, Vasily can light up the room for 7 hours.
|
[
"4 2\n",
"6 3\n",
"1000 1000\n",
"123 5\n",
"1000 2\n",
"1 2\n",
"1 3\n",
"1 4\n",
"2 2\n",
"3 2\n"
] |
[
"7\n",
"8\n",
"1001\n",
"153\n",
"1999\n",
"1\n",
"1\n",
"1\n",
"3\n",
"5\n"
] | 1
|
stdio
|
Little Chris is bored during his physics lessons (too easy), so he has built a toy box to keep himself occupied. The box is special, since it has the ability to change gravity.
There are n columns of toy cubes in the box arranged in a line. The i-th column contains a_{i} cubes. At first, the gravity in the box is pulling the cubes downwards. When Chris switches the gravity, it begins to pull all the cubes to the right side of the box. The figure shows the initial and final configurations of the cubes in the box: the cubes that have changed their position are highlighted with orange. [Image]
Given the initial configuration of the toy cubes in the box, find the amounts of cubes in each of the n columns after the gravity switch!
-----Input-----
The first line of input contains an integer n (1 ≤ n ≤ 100), the number of the columns in the box. The next line contains n space-separated integer numbers. The i-th number a_{i} (1 ≤ a_{i} ≤ 100) denotes the number of cubes in the i-th column.
-----Output-----
Output n integer numbers separated by spaces, where the i-th number is the amount of cubes in the i-th column after the gravity switch.
-----Examples-----
Input
4
3 2 1 2
Output
1 2 2 3
Input
3
2 3 8
Output
2 3 8
-----Note-----
The first example case is shown on the figure. The top cube of the first column falls to the top of the last column; the top cube of the second column falls to the top of the third column; the middle cube of the first column falls to the top of the second column.
In the second example case the gravity switch does not change the heights of the columns.
|
[
"4\n3 2 1 2\n",
"3\n2 3 8\n",
"5\n2 1 2 1 2\n",
"1\n1\n",
"2\n4 3\n",
"6\n100 40 60 20 1 80\n",
"10\n10 8 6 7 5 3 4 2 9 1\n",
"10\n1 2 3 4 5 6 7 8 9 10\n",
"100\n82 51 81 14 37 17 78 92 64 15 8 86 89 8 87 77 66 10 15 12 100 25 92 47 21 78 20 63 13 49 41 36 41 79 16 87 87 69 3 76 80 60 100 49 70 59 72 8 38 71 45 97 71 14 76 54 81 4 59 46 39 29 92 3 49 22 53 99 59 52 74 31 92 43 42 23 44 9 82 47 7 40 12 9 3 55 37 85 46 22 84 52 98 41 21 77 63 17 62 91\n",
"100\n100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100\n"
] |
[
"1 2 2 3 \n",
"2 3 8 \n",
"1 1 2 2 2 \n",
"1 \n",
"3 4 \n",
"1 20 40 60 80 100 \n",
"1 2 3 4 5 6 7 8 9 10 \n",
"1 2 3 4 5 6 7 8 9 10 \n",
"3 3 3 4 7 8 8 8 9 9 10 12 12 13 14 14 15 15 16 17 17 20 21 21 22 22 23 25 29 31 36 37 37 38 39 40 41 41 41 42 43 44 45 46 46 47 47 49 49 49 51 52 52 53 54 55 59 59 59 60 62 63 63 64 66 69 70 71 71 72 74 76 76 77 77 78 78 79 80 81 81 82 82 84 85 86 87 87 87 89 91 92 92 92 92 97 98 99 100 100 \n",
"100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 \n"
] | 1
|
stdio
|
Chilly Willy loves playing with numbers. He only knows prime numbers that are digits yet. These numbers are 2, 3, 5 and 7. But Willy grew rather bored of such numbers, so he came up with a few games that were connected with them.
Chilly Willy wants to find the minimum number of length n, such that it is simultaneously divisible by all numbers Willy already knows (2, 3, 5 and 7). Help him with that.
A number's length is the number of digits in its decimal representation without leading zeros.
-----Input-----
A single input line contains a single integer n (1 ≤ n ≤ 10^5).
-----Output-----
Print a single integer — the answer to the problem without leading zeroes, or "-1" (without the quotes), if the number that meet the problem condition does not exist.
-----Examples-----
Input
1
Output
-1
Input
5
Output
10080
|
[
"1\n",
"5\n",
"6\n",
"4\n",
"15\n",
"16\n",
"17\n",
"7\n",
"120\n",
"8\n"
] |
[
"-1\n",
"10080",
"100170",
"1050",
"100000000000110",
"1000000000000050",
"10000000000000080",
"1000020",
"100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000170",
"10000200"
] | 1
|
stdio
|
Comrade Dujikov is busy choosing artists for Timofey's birthday and is recieving calls from Taymyr from Ilia-alpinist.
Ilia-alpinist calls every n minutes, i.e. in minutes n, 2n, 3n and so on. Artists come to the comrade every m minutes, i.e. in minutes m, 2m, 3m and so on. The day is z minutes long, i.e. the day consists of minutes 1, 2, ..., z. How many artists should be killed so that there are no artists in the room when Ilia calls? Consider that a call and a talk with an artist take exactly one minute.
-----Input-----
The only string contains three integers — n, m and z (1 ≤ n, m, z ≤ 10^4).
-----Output-----
Print single integer — the minimum number of artists that should be killed so that there are no artists in the room when Ilia calls.
-----Examples-----
Input
1 1 10
Output
10
Input
1 2 5
Output
2
Input
2 3 9
Output
1
-----Note-----
Taymyr is a place in the north of Russia.
In the first test the artists come each minute, as well as the calls, so we need to kill all of them.
In the second test we need to kill artists which come on the second and the fourth minutes.
In the third test — only the artist which comes on the sixth minute.
|
[
"1 1 10\n",
"1 2 5\n",
"2 3 9\n",
"4 8 9\n",
"7 9 2\n",
"10000 10000 10000\n",
"24 22 9235\n",
"74 8 417\n",
"972 1 203\n",
"550 1 754\n"
] |
[
"10\n",
"2\n",
"1\n",
"1\n",
"0\n",
"1\n",
"34\n",
"1\n",
"0\n",
"1\n"
] | 1
|
stdio
|
Valera the horse lives on a plane. The Cartesian coordinate system is defined on this plane. Also an infinite spiral is painted on the plane. The spiral consists of segments: [(0, 0), (1, 0)], [(1, 0), (1, 1)], [(1, 1), ( - 1, 1)], [( - 1, 1), ( - 1, - 1)], [( - 1, - 1), (2, - 1)], [(2, - 1), (2, 2)] and so on. Thus, this infinite spiral passes through each integer point of the plane.
Valera the horse lives on the plane at coordinates (0, 0). He wants to walk along the spiral to point (x, y). Valera the horse has four legs, so he finds turning very difficult. Count how many times he will have to turn if he goes along a spiral from point (0, 0) to point (x, y).
-----Input-----
The first line contains two space-separated integers x and y (|x|, |y| ≤ 100).
-----Output-----
Print a single integer, showing how many times Valera has to turn.
-----Examples-----
Input
0 0
Output
0
Input
1 0
Output
0
Input
0 1
Output
2
Input
-1 -1
Output
3
|
[
"0 0\n",
"1 0\n",
"0 1\n",
"-1 -1\n",
"10 10\n",
"0 6\n",
"-7 -13\n",
"37 -100\n",
"99 100\n",
"16 -32\n"
] |
[
"0\n",
"0\n",
"2\n",
"3\n",
"37\n",
"22\n",
"52\n",
"400\n",
"398\n",
"128\n"
] | 1
|
stdio
|
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