message stringlengths 2 67k | message_type stringclasses 2 values | message_id int64 0 1 | conversation_id int64 463 109k | cluster float64 19 19 | __index_level_0__ int64 926 217k |
|---|---|---|---|---|---|
Provide tags and a correct Python 3 solution for this coding contest problem.
Rock... Paper!
After Karen have found the deterministic winning (losing?) strategy for rock-paper-scissors, her brother, Koyomi, comes up with a new game as a substitute. The game works as follows.
A positive integer n is decided first. Both Koyomi and Karen independently choose n distinct positive integers, denoted by x1, x2, ..., xn and y1, y2, ..., yn respectively. They reveal their sequences, and repeat until all of 2n integers become distinct, which is the only final state to be kept and considered.
Then they count the number of ordered pairs (i, j) (1 ≤ i, j ≤ n) such that the value xi xor yj equals to one of the 2n integers. Here xor means the [bitwise exclusive or](https://en.wikipedia.org/wiki/Bitwise_operation#XOR) operation on two integers, and is denoted by operators ^ and/or xor in most programming languages.
Karen claims a win if the number of such pairs is even, and Koyomi does otherwise. And you're here to help determine the winner of their latest game.
Input
The first line of input contains a positive integer n (1 ≤ n ≤ 2 000) — the length of both sequences.
The second line contains n space-separated integers x1, x2, ..., xn (1 ≤ xi ≤ 2·106) — the integers finally chosen by Koyomi.
The third line contains n space-separated integers y1, y2, ..., yn (1 ≤ yi ≤ 2·106) — the integers finally chosen by Karen.
Input guarantees that the given 2n integers are pairwise distinct, that is, no pair (i, j) (1 ≤ i, j ≤ n) exists such that one of the following holds: xi = yj; i ≠ j and xi = xj; i ≠ j and yi = yj.
Output
Output one line — the name of the winner, that is, "Koyomi" or "Karen" (without quotes). Please be aware of the capitalization.
Examples
Input
3
1 2 3
4 5 6
Output
Karen
Input
5
2 4 6 8 10
9 7 5 3 1
Output
Karen
Note
In the first example, there are 6 pairs satisfying the constraint: (1, 1), (1, 2), (2, 1), (2, 3), (3, 2) and (3, 3). Thus, Karen wins since 6 is an even number.
In the second example, there are 16 such pairs, and Karen wins again. | instruction | 0 | 26,171 | 19 | 52,342 |
Tags: brute force, implementation
Correct Solution:
```
I = lambda: list(map(int, input().split()))
I()
X, Y = I(), I()
Z = set(X) | set(Y)
print('Koyomi' if sum(x^y in Z for x in X for y in Y) % 2 else 'Karen')
``` | output | 1 | 26,171 | 19 | 52,343 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Rock... Paper!
After Karen have found the deterministic winning (losing?) strategy for rock-paper-scissors, her brother, Koyomi, comes up with a new game as a substitute. The game works as follows.
A positive integer n is decided first. Both Koyomi and Karen independently choose n distinct positive integers, denoted by x1, x2, ..., xn and y1, y2, ..., yn respectively. They reveal their sequences, and repeat until all of 2n integers become distinct, which is the only final state to be kept and considered.
Then they count the number of ordered pairs (i, j) (1 ≤ i, j ≤ n) such that the value xi xor yj equals to one of the 2n integers. Here xor means the [bitwise exclusive or](https://en.wikipedia.org/wiki/Bitwise_operation#XOR) operation on two integers, and is denoted by operators ^ and/or xor in most programming languages.
Karen claims a win if the number of such pairs is even, and Koyomi does otherwise. And you're here to help determine the winner of their latest game.
Input
The first line of input contains a positive integer n (1 ≤ n ≤ 2 000) — the length of both sequences.
The second line contains n space-separated integers x1, x2, ..., xn (1 ≤ xi ≤ 2·106) — the integers finally chosen by Koyomi.
The third line contains n space-separated integers y1, y2, ..., yn (1 ≤ yi ≤ 2·106) — the integers finally chosen by Karen.
Input guarantees that the given 2n integers are pairwise distinct, that is, no pair (i, j) (1 ≤ i, j ≤ n) exists such that one of the following holds: xi = yj; i ≠ j and xi = xj; i ≠ j and yi = yj.
Output
Output one line — the name of the winner, that is, "Koyomi" or "Karen" (without quotes). Please be aware of the capitalization.
Examples
Input
3
1 2 3
4 5 6
Output
Karen
Input
5
2 4 6 8 10
9 7 5 3 1
Output
Karen
Note
In the first example, there are 6 pairs satisfying the constraint: (1, 1), (1, 2), (2, 1), (2, 3), (3, 2) and (3, 3). Thus, Karen wins since 6 is an even number.
In the second example, there are 16 such pairs, and Karen wins again. | instruction | 0 | 26,172 | 19 | 52,344 |
Tags: brute force, implementation
Correct Solution:
```
def readints():
return [int(item) for item in input().strip().split()]
class Solver:
def main(self):
x, y = readints(), readints()
s = {i for i in x + y}
c = 0
for x1 in x:
for y1 in y:
if x1 ^ y1 in s:
c += 1
print(['Karen', 'Koyomi'][c % 2])
Solver().main()
``` | output | 1 | 26,172 | 19 | 52,345 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Rock... Paper!
After Karen have found the deterministic winning (losing?) strategy for rock-paper-scissors, her brother, Koyomi, comes up with a new game as a substitute. The game works as follows.
A positive integer n is decided first. Both Koyomi and Karen independently choose n distinct positive integers, denoted by x1, x2, ..., xn and y1, y2, ..., yn respectively. They reveal their sequences, and repeat until all of 2n integers become distinct, which is the only final state to be kept and considered.
Then they count the number of ordered pairs (i, j) (1 ≤ i, j ≤ n) such that the value xi xor yj equals to one of the 2n integers. Here xor means the [bitwise exclusive or](https://en.wikipedia.org/wiki/Bitwise_operation#XOR) operation on two integers, and is denoted by operators ^ and/or xor in most programming languages.
Karen claims a win if the number of such pairs is even, and Koyomi does otherwise. And you're here to help determine the winner of their latest game.
Input
The first line of input contains a positive integer n (1 ≤ n ≤ 2 000) — the length of both sequences.
The second line contains n space-separated integers x1, x2, ..., xn (1 ≤ xi ≤ 2·106) — the integers finally chosen by Koyomi.
The third line contains n space-separated integers y1, y2, ..., yn (1 ≤ yi ≤ 2·106) — the integers finally chosen by Karen.
Input guarantees that the given 2n integers are pairwise distinct, that is, no pair (i, j) (1 ≤ i, j ≤ n) exists such that one of the following holds: xi = yj; i ≠ j and xi = xj; i ≠ j and yi = yj.
Output
Output one line — the name of the winner, that is, "Koyomi" or "Karen" (without quotes). Please be aware of the capitalization.
Examples
Input
3
1 2 3
4 5 6
Output
Karen
Input
5
2 4 6 8 10
9 7 5 3 1
Output
Karen
Note
In the first example, there are 6 pairs satisfying the constraint: (1, 1), (1, 2), (2, 1), (2, 3), (3, 2) and (3, 3). Thus, Karen wins since 6 is an even number.
In the second example, there are 16 such pairs, and Karen wins again. | instruction | 0 | 26,173 | 19 | 52,346 |
Tags: brute force, implementation
Correct Solution:
```
import sys
n = int(sys.stdin.readline())
arr1 = list(map(int, sys.stdin.readline().split()))
arr2 = list(map(int, sys.stdin.readline().split()))
cnt = 0
arr = arr1 + arr2
for i in arr:
for j in arr:
temp = i ^ j
if temp == 2 * n:
cnt += 1
print('Karen' if cnt % 2 == 0 else 'Koyomi')
``` | output | 1 | 26,173 | 19 | 52,347 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Rock... Paper!
After Karen have found the deterministic winning (losing?) strategy for rock-paper-scissors, her brother, Koyomi, comes up with a new game as a substitute. The game works as follows.
A positive integer n is decided first. Both Koyomi and Karen independently choose n distinct positive integers, denoted by x1, x2, ..., xn and y1, y2, ..., yn respectively. They reveal their sequences, and repeat until all of 2n integers become distinct, which is the only final state to be kept and considered.
Then they count the number of ordered pairs (i, j) (1 ≤ i, j ≤ n) such that the value xi xor yj equals to one of the 2n integers. Here xor means the [bitwise exclusive or](https://en.wikipedia.org/wiki/Bitwise_operation#XOR) operation on two integers, and is denoted by operators ^ and/or xor in most programming languages.
Karen claims a win if the number of such pairs is even, and Koyomi does otherwise. And you're here to help determine the winner of their latest game.
Input
The first line of input contains a positive integer n (1 ≤ n ≤ 2 000) — the length of both sequences.
The second line contains n space-separated integers x1, x2, ..., xn (1 ≤ xi ≤ 2·106) — the integers finally chosen by Koyomi.
The third line contains n space-separated integers y1, y2, ..., yn (1 ≤ yi ≤ 2·106) — the integers finally chosen by Karen.
Input guarantees that the given 2n integers are pairwise distinct, that is, no pair (i, j) (1 ≤ i, j ≤ n) exists such that one of the following holds: xi = yj; i ≠ j and xi = xj; i ≠ j and yi = yj.
Output
Output one line — the name of the winner, that is, "Koyomi" or "Karen" (without quotes). Please be aware of the capitalization.
Examples
Input
3
1 2 3
4 5 6
Output
Karen
Input
5
2 4 6 8 10
9 7 5 3 1
Output
Karen
Note
In the first example, there are 6 pairs satisfying the constraint: (1, 1), (1, 2), (2, 1), (2, 3), (3, 2) and (3, 3). Thus, Karen wins since 6 is an even number.
In the second example, there are 16 such pairs, and Karen wins again. | instruction | 0 | 26,174 | 19 | 52,348 |
Tags: brute force, implementation
Correct Solution:
```
n = int(input())
x = list(map(int, input().split()))
y = list(map(int, input().split()))
s = set(x+y)
c = 0
for i in x:
for j in y:
if (i^j) in s:
c += 1
if c%2:
print("Koyomi")
else:
print("Karen")
``` | output | 1 | 26,174 | 19 | 52,349 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Rock... Paper!
After Karen have found the deterministic winning (losing?) strategy for rock-paper-scissors, her brother, Koyomi, comes up with a new game as a substitute. The game works as follows.
A positive integer n is decided first. Both Koyomi and Karen independently choose n distinct positive integers, denoted by x1, x2, ..., xn and y1, y2, ..., yn respectively. They reveal their sequences, and repeat until all of 2n integers become distinct, which is the only final state to be kept and considered.
Then they count the number of ordered pairs (i, j) (1 ≤ i, j ≤ n) such that the value xi xor yj equals to one of the 2n integers. Here xor means the [bitwise exclusive or](https://en.wikipedia.org/wiki/Bitwise_operation#XOR) operation on two integers, and is denoted by operators ^ and/or xor in most programming languages.
Karen claims a win if the number of such pairs is even, and Koyomi does otherwise. And you're here to help determine the winner of their latest game.
Input
The first line of input contains a positive integer n (1 ≤ n ≤ 2 000) — the length of both sequences.
The second line contains n space-separated integers x1, x2, ..., xn (1 ≤ xi ≤ 2·106) — the integers finally chosen by Koyomi.
The third line contains n space-separated integers y1, y2, ..., yn (1 ≤ yi ≤ 2·106) — the integers finally chosen by Karen.
Input guarantees that the given 2n integers are pairwise distinct, that is, no pair (i, j) (1 ≤ i, j ≤ n) exists such that one of the following holds: xi = yj; i ≠ j and xi = xj; i ≠ j and yi = yj.
Output
Output one line — the name of the winner, that is, "Koyomi" or "Karen" (without quotes). Please be aware of the capitalization.
Examples
Input
3
1 2 3
4 5 6
Output
Karen
Input
5
2 4 6 8 10
9 7 5 3 1
Output
Karen
Note
In the first example, there are 6 pairs satisfying the constraint: (1, 1), (1, 2), (2, 1), (2, 3), (3, 2) and (3, 3). Thus, Karen wins since 6 is an even number.
In the second example, there are 16 such pairs, and Karen wins again. | instruction | 0 | 26,175 | 19 | 52,350 |
Tags: brute force, implementation
Correct Solution:
```
# -*- coding: utf-8 -*-
import math
import collections
import bisect
import heapq
import time
import random
"""
created by shhuan at 2017/10/6 21:41
"""
N = int(input())
X = [int(x) for x in input().split()]
Y = [int(x) for x in input().split()]
print('Karen')
``` | output | 1 | 26,175 | 19 | 52,351 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Rock... Paper!
After Karen have found the deterministic winning (losing?) strategy for rock-paper-scissors, her brother, Koyomi, comes up with a new game as a substitute. The game works as follows.
A positive integer n is decided first. Both Koyomi and Karen independently choose n distinct positive integers, denoted by x1, x2, ..., xn and y1, y2, ..., yn respectively. They reveal their sequences, and repeat until all of 2n integers become distinct, which is the only final state to be kept and considered.
Then they count the number of ordered pairs (i, j) (1 ≤ i, j ≤ n) such that the value xi xor yj equals to one of the 2n integers. Here xor means the [bitwise exclusive or](https://en.wikipedia.org/wiki/Bitwise_operation#XOR) operation on two integers, and is denoted by operators ^ and/or xor in most programming languages.
Karen claims a win if the number of such pairs is even, and Koyomi does otherwise. And you're here to help determine the winner of their latest game.
Input
The first line of input contains a positive integer n (1 ≤ n ≤ 2 000) — the length of both sequences.
The second line contains n space-separated integers x1, x2, ..., xn (1 ≤ xi ≤ 2·106) — the integers finally chosen by Koyomi.
The third line contains n space-separated integers y1, y2, ..., yn (1 ≤ yi ≤ 2·106) — the integers finally chosen by Karen.
Input guarantees that the given 2n integers are pairwise distinct, that is, no pair (i, j) (1 ≤ i, j ≤ n) exists such that one of the following holds: xi = yj; i ≠ j and xi = xj; i ≠ j and yi = yj.
Output
Output one line — the name of the winner, that is, "Koyomi" or "Karen" (without quotes). Please be aware of the capitalization.
Examples
Input
3
1 2 3
4 5 6
Output
Karen
Input
5
2 4 6 8 10
9 7 5 3 1
Output
Karen
Note
In the first example, there are 6 pairs satisfying the constraint: (1, 1), (1, 2), (2, 1), (2, 3), (3, 2) and (3, 3). Thus, Karen wins since 6 is an even number.
In the second example, there are 16 such pairs, and Karen wins again. | instruction | 0 | 26,176 | 19 | 52,352 |
Tags: brute force, implementation
Correct Solution:
```
#python3
#utf-8
print('Karen')
``` | output | 1 | 26,176 | 19 | 52,353 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Rock... Paper!
After Karen have found the deterministic winning (losing?) strategy for rock-paper-scissors, her brother, Koyomi, comes up with a new game as a substitute. The game works as follows.
A positive integer n is decided first. Both Koyomi and Karen independently choose n distinct positive integers, denoted by x1, x2, ..., xn and y1, y2, ..., yn respectively. They reveal their sequences, and repeat until all of 2n integers become distinct, which is the only final state to be kept and considered.
Then they count the number of ordered pairs (i, j) (1 ≤ i, j ≤ n) such that the value xi xor yj equals to one of the 2n integers. Here xor means the [bitwise exclusive or](https://en.wikipedia.org/wiki/Bitwise_operation#XOR) operation on two integers, and is denoted by operators ^ and/or xor in most programming languages.
Karen claims a win if the number of such pairs is even, and Koyomi does otherwise. And you're here to help determine the winner of their latest game.
Input
The first line of input contains a positive integer n (1 ≤ n ≤ 2 000) — the length of both sequences.
The second line contains n space-separated integers x1, x2, ..., xn (1 ≤ xi ≤ 2·106) — the integers finally chosen by Koyomi.
The third line contains n space-separated integers y1, y2, ..., yn (1 ≤ yi ≤ 2·106) — the integers finally chosen by Karen.
Input guarantees that the given 2n integers are pairwise distinct, that is, no pair (i, j) (1 ≤ i, j ≤ n) exists such that one of the following holds: xi = yj; i ≠ j and xi = xj; i ≠ j and yi = yj.
Output
Output one line — the name of the winner, that is, "Koyomi" or "Karen" (without quotes). Please be aware of the capitalization.
Examples
Input
3
1 2 3
4 5 6
Output
Karen
Input
5
2 4 6 8 10
9 7 5 3 1
Output
Karen
Note
In the first example, there are 6 pairs satisfying the constraint: (1, 1), (1, 2), (2, 1), (2, 3), (3, 2) and (3, 3). Thus, Karen wins since 6 is an even number.
In the second example, there are 16 such pairs, and Karen wins again. | instruction | 0 | 26,177 | 19 | 52,354 |
Tags: brute force, implementation
Correct Solution:
```
n=int(input())
x=list(map(int,input().strip().split()))
y=list(map(int,input().strip().split()))
print('Karen')
``` | output | 1 | 26,177 | 19 | 52,355 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Rock... Paper!
After Karen have found the deterministic winning (losing?) strategy for rock-paper-scissors, her brother, Koyomi, comes up with a new game as a substitute. The game works as follows.
A positive integer n is decided first. Both Koyomi and Karen independently choose n distinct positive integers, denoted by x1, x2, ..., xn and y1, y2, ..., yn respectively. They reveal their sequences, and repeat until all of 2n integers become distinct, which is the only final state to be kept and considered.
Then they count the number of ordered pairs (i, j) (1 ≤ i, j ≤ n) such that the value xi xor yj equals to one of the 2n integers. Here xor means the [bitwise exclusive or](https://en.wikipedia.org/wiki/Bitwise_operation#XOR) operation on two integers, and is denoted by operators ^ and/or xor in most programming languages.
Karen claims a win if the number of such pairs is even, and Koyomi does otherwise. And you're here to help determine the winner of their latest game.
Input
The first line of input contains a positive integer n (1 ≤ n ≤ 2 000) — the length of both sequences.
The second line contains n space-separated integers x1, x2, ..., xn (1 ≤ xi ≤ 2·106) — the integers finally chosen by Koyomi.
The third line contains n space-separated integers y1, y2, ..., yn (1 ≤ yi ≤ 2·106) — the integers finally chosen by Karen.
Input guarantees that the given 2n integers are pairwise distinct, that is, no pair (i, j) (1 ≤ i, j ≤ n) exists such that one of the following holds: xi = yj; i ≠ j and xi = xj; i ≠ j and yi = yj.
Output
Output one line — the name of the winner, that is, "Koyomi" or "Karen" (without quotes). Please be aware of the capitalization.
Examples
Input
3
1 2 3
4 5 6
Output
Karen
Input
5
2 4 6 8 10
9 7 5 3 1
Output
Karen
Note
In the first example, there are 6 pairs satisfying the constraint: (1, 1), (1, 2), (2, 1), (2, 3), (3, 2) and (3, 3). Thus, Karen wins since 6 is an even number.
In the second example, there are 16 such pairs, and Karen wins again.
Submitted Solution:
```
n = int(input())
x = list(map(int, input().split()))
y = list(map(int, input().split()))
print ('Karen')
``` | instruction | 0 | 26,178 | 19 | 52,356 |
Yes | output | 1 | 26,178 | 19 | 52,357 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Rock... Paper!
After Karen have found the deterministic winning (losing?) strategy for rock-paper-scissors, her brother, Koyomi, comes up with a new game as a substitute. The game works as follows.
A positive integer n is decided first. Both Koyomi and Karen independently choose n distinct positive integers, denoted by x1, x2, ..., xn and y1, y2, ..., yn respectively. They reveal their sequences, and repeat until all of 2n integers become distinct, which is the only final state to be kept and considered.
Then they count the number of ordered pairs (i, j) (1 ≤ i, j ≤ n) such that the value xi xor yj equals to one of the 2n integers. Here xor means the [bitwise exclusive or](https://en.wikipedia.org/wiki/Bitwise_operation#XOR) operation on two integers, and is denoted by operators ^ and/or xor in most programming languages.
Karen claims a win if the number of such pairs is even, and Koyomi does otherwise. And you're here to help determine the winner of their latest game.
Input
The first line of input contains a positive integer n (1 ≤ n ≤ 2 000) — the length of both sequences.
The second line contains n space-separated integers x1, x2, ..., xn (1 ≤ xi ≤ 2·106) — the integers finally chosen by Koyomi.
The third line contains n space-separated integers y1, y2, ..., yn (1 ≤ yi ≤ 2·106) — the integers finally chosen by Karen.
Input guarantees that the given 2n integers are pairwise distinct, that is, no pair (i, j) (1 ≤ i, j ≤ n) exists such that one of the following holds: xi = yj; i ≠ j and xi = xj; i ≠ j and yi = yj.
Output
Output one line — the name of the winner, that is, "Koyomi" or "Karen" (without quotes). Please be aware of the capitalization.
Examples
Input
3
1 2 3
4 5 6
Output
Karen
Input
5
2 4 6 8 10
9 7 5 3 1
Output
Karen
Note
In the first example, there are 6 pairs satisfying the constraint: (1, 1), (1, 2), (2, 1), (2, 3), (3, 2) and (3, 3). Thus, Karen wins since 6 is an even number.
In the second example, there are 16 such pairs, and Karen wins again.
Submitted Solution:
```
def xor():
n=int(input())
x=list(map(int,input().split()));
y=list(map(int,input().split()));
k=0
c1=set(x+y)
for i in range(n):
for j in range(n):
h=x[i]^y[j]
if h in c1:
k+=1;
if (k%2==0):
print('Karen')
else:
print('Koyomi')
xor()
``` | instruction | 0 | 26,179 | 19 | 52,358 |
Yes | output | 1 | 26,179 | 19 | 52,359 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Rock... Paper!
After Karen have found the deterministic winning (losing?) strategy for rock-paper-scissors, her brother, Koyomi, comes up with a new game as a substitute. The game works as follows.
A positive integer n is decided first. Both Koyomi and Karen independently choose n distinct positive integers, denoted by x1, x2, ..., xn and y1, y2, ..., yn respectively. They reveal their sequences, and repeat until all of 2n integers become distinct, which is the only final state to be kept and considered.
Then they count the number of ordered pairs (i, j) (1 ≤ i, j ≤ n) such that the value xi xor yj equals to one of the 2n integers. Here xor means the [bitwise exclusive or](https://en.wikipedia.org/wiki/Bitwise_operation#XOR) operation on two integers, and is denoted by operators ^ and/or xor in most programming languages.
Karen claims a win if the number of such pairs is even, and Koyomi does otherwise. And you're here to help determine the winner of their latest game.
Input
The first line of input contains a positive integer n (1 ≤ n ≤ 2 000) — the length of both sequences.
The second line contains n space-separated integers x1, x2, ..., xn (1 ≤ xi ≤ 2·106) — the integers finally chosen by Koyomi.
The third line contains n space-separated integers y1, y2, ..., yn (1 ≤ yi ≤ 2·106) — the integers finally chosen by Karen.
Input guarantees that the given 2n integers are pairwise distinct, that is, no pair (i, j) (1 ≤ i, j ≤ n) exists such that one of the following holds: xi = yj; i ≠ j and xi = xj; i ≠ j and yi = yj.
Output
Output one line — the name of the winner, that is, "Koyomi" or "Karen" (without quotes). Please be aware of the capitalization.
Examples
Input
3
1 2 3
4 5 6
Output
Karen
Input
5
2 4 6 8 10
9 7 5 3 1
Output
Karen
Note
In the first example, there are 6 pairs satisfying the constraint: (1, 1), (1, 2), (2, 1), (2, 3), (3, 2) and (3, 3). Thus, Karen wins since 6 is an even number.
In the second example, there are 16 such pairs, and Karen wins again.
Submitted Solution:
```
##a = list(map(int, input().split()))
##print(' '.join(map(str, res)))
n = int(input())
x = list(map(int, input().split()))
y = list(map(int, input().split()))
s = set()
for xx in x:
s.add(xx)
for yy in y:
s.add(yy)
karen = 0
for xx in x:
for yy in y:
if xx^yy in s:
karen += 1
if karen%2 == 0:
print('Karen')
else:
print('Koyomi')
``` | instruction | 0 | 26,180 | 19 | 52,360 |
Yes | output | 1 | 26,180 | 19 | 52,361 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Rock... Paper!
After Karen have found the deterministic winning (losing?) strategy for rock-paper-scissors, her brother, Koyomi, comes up with a new game as a substitute. The game works as follows.
A positive integer n is decided first. Both Koyomi and Karen independently choose n distinct positive integers, denoted by x1, x2, ..., xn and y1, y2, ..., yn respectively. They reveal their sequences, and repeat until all of 2n integers become distinct, which is the only final state to be kept and considered.
Then they count the number of ordered pairs (i, j) (1 ≤ i, j ≤ n) such that the value xi xor yj equals to one of the 2n integers. Here xor means the [bitwise exclusive or](https://en.wikipedia.org/wiki/Bitwise_operation#XOR) operation on two integers, and is denoted by operators ^ and/or xor in most programming languages.
Karen claims a win if the number of such pairs is even, and Koyomi does otherwise. And you're here to help determine the winner of their latest game.
Input
The first line of input contains a positive integer n (1 ≤ n ≤ 2 000) — the length of both sequences.
The second line contains n space-separated integers x1, x2, ..., xn (1 ≤ xi ≤ 2·106) — the integers finally chosen by Koyomi.
The third line contains n space-separated integers y1, y2, ..., yn (1 ≤ yi ≤ 2·106) — the integers finally chosen by Karen.
Input guarantees that the given 2n integers are pairwise distinct, that is, no pair (i, j) (1 ≤ i, j ≤ n) exists such that one of the following holds: xi = yj; i ≠ j and xi = xj; i ≠ j and yi = yj.
Output
Output one line — the name of the winner, that is, "Koyomi" or "Karen" (without quotes). Please be aware of the capitalization.
Examples
Input
3
1 2 3
4 5 6
Output
Karen
Input
5
2 4 6 8 10
9 7 5 3 1
Output
Karen
Note
In the first example, there are 6 pairs satisfying the constraint: (1, 1), (1, 2), (2, 1), (2, 3), (3, 2) and (3, 3). Thus, Karen wins since 6 is an even number.
In the second example, there are 16 such pairs, and Karen wins again.
Submitted Solution:
```
n= int(input())
a = [int(x) for x in input().split()]
b = [int(x) for x in input().split()]
s = set(a) | set(b)
ans = 0
for i in a:
for j in b:
if i ^ j in s:
ans += 1
if ans%2 == 0:
print("Karen")
else:
print("Koyomi")
``` | instruction | 0 | 26,181 | 19 | 52,362 |
Yes | output | 1 | 26,181 | 19 | 52,363 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Rock... Paper!
After Karen have found the deterministic winning (losing?) strategy for rock-paper-scissors, her brother, Koyomi, comes up with a new game as a substitute. The game works as follows.
A positive integer n is decided first. Both Koyomi and Karen independently choose n distinct positive integers, denoted by x1, x2, ..., xn and y1, y2, ..., yn respectively. They reveal their sequences, and repeat until all of 2n integers become distinct, which is the only final state to be kept and considered.
Then they count the number of ordered pairs (i, j) (1 ≤ i, j ≤ n) such that the value xi xor yj equals to one of the 2n integers. Here xor means the [bitwise exclusive or](https://en.wikipedia.org/wiki/Bitwise_operation#XOR) operation on two integers, and is denoted by operators ^ and/or xor in most programming languages.
Karen claims a win if the number of such pairs is even, and Koyomi does otherwise. And you're here to help determine the winner of their latest game.
Input
The first line of input contains a positive integer n (1 ≤ n ≤ 2 000) — the length of both sequences.
The second line contains n space-separated integers x1, x2, ..., xn (1 ≤ xi ≤ 2·106) — the integers finally chosen by Koyomi.
The third line contains n space-separated integers y1, y2, ..., yn (1 ≤ yi ≤ 2·106) — the integers finally chosen by Karen.
Input guarantees that the given 2n integers are pairwise distinct, that is, no pair (i, j) (1 ≤ i, j ≤ n) exists such that one of the following holds: xi = yj; i ≠ j and xi = xj; i ≠ j and yi = yj.
Output
Output one line — the name of the winner, that is, "Koyomi" or "Karen" (without quotes). Please be aware of the capitalization.
Examples
Input
3
1 2 3
4 5 6
Output
Karen
Input
5
2 4 6 8 10
9 7 5 3 1
Output
Karen
Note
In the first example, there are 6 pairs satisfying the constraint: (1, 1), (1, 2), (2, 1), (2, 3), (3, 2) and (3, 3). Thus, Karen wins since 6 is an even number.
In the second example, there are 16 such pairs, and Karen wins again.
Submitted Solution:
```
n = int(input())
a = [int(x) for x in input().split()]
b = [int(x) for x in input().split()]
c = {x:1 for x in a}
c.update({x:1 for x in b})
count = 0
for i in range(0, n):
if c.get(a[i]^b[i]):
count += 1
if count%2 == 0:
print("Karen")
else:
print("Koyomi")
``` | instruction | 0 | 26,182 | 19 | 52,364 |
No | output | 1 | 26,182 | 19 | 52,365 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Rock... Paper!
After Karen have found the deterministic winning (losing?) strategy for rock-paper-scissors, her brother, Koyomi, comes up with a new game as a substitute. The game works as follows.
A positive integer n is decided first. Both Koyomi and Karen independently choose n distinct positive integers, denoted by x1, x2, ..., xn and y1, y2, ..., yn respectively. They reveal their sequences, and repeat until all of 2n integers become distinct, which is the only final state to be kept and considered.
Then they count the number of ordered pairs (i, j) (1 ≤ i, j ≤ n) such that the value xi xor yj equals to one of the 2n integers. Here xor means the [bitwise exclusive or](https://en.wikipedia.org/wiki/Bitwise_operation#XOR) operation on two integers, and is denoted by operators ^ and/or xor in most programming languages.
Karen claims a win if the number of such pairs is even, and Koyomi does otherwise. And you're here to help determine the winner of their latest game.
Input
The first line of input contains a positive integer n (1 ≤ n ≤ 2 000) — the length of both sequences.
The second line contains n space-separated integers x1, x2, ..., xn (1 ≤ xi ≤ 2·106) — the integers finally chosen by Koyomi.
The third line contains n space-separated integers y1, y2, ..., yn (1 ≤ yi ≤ 2·106) — the integers finally chosen by Karen.
Input guarantees that the given 2n integers are pairwise distinct, that is, no pair (i, j) (1 ≤ i, j ≤ n) exists such that one of the following holds: xi = yj; i ≠ j and xi = xj; i ≠ j and yi = yj.
Output
Output one line — the name of the winner, that is, "Koyomi" or "Karen" (without quotes). Please be aware of the capitalization.
Examples
Input
3
1 2 3
4 5 6
Output
Karen
Input
5
2 4 6 8 10
9 7 5 3 1
Output
Karen
Note
In the first example, there are 6 pairs satisfying the constraint: (1, 1), (1, 2), (2, 1), (2, 3), (3, 2) and (3, 3). Thus, Karen wins since 6 is an even number.
In the second example, there are 16 such pairs, and Karen wins again.
Submitted Solution:
```
n = int(input())
a = list(map(int, input().split()))
b = list(map(int, input().split()))
s = frozenset(a + b)
counter = 0
for i in range(n):
if (a[i] ^ b[i]) in s:
counter += 1
if counter % 2 == 1:
print("Koyomi")
else:
print("Karen")
``` | instruction | 0 | 26,183 | 19 | 52,366 |
No | output | 1 | 26,183 | 19 | 52,367 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Rock... Paper!
After Karen have found the deterministic winning (losing?) strategy for rock-paper-scissors, her brother, Koyomi, comes up with a new game as a substitute. The game works as follows.
A positive integer n is decided first. Both Koyomi and Karen independently choose n distinct positive integers, denoted by x1, x2, ..., xn and y1, y2, ..., yn respectively. They reveal their sequences, and repeat until all of 2n integers become distinct, which is the only final state to be kept and considered.
Then they count the number of ordered pairs (i, j) (1 ≤ i, j ≤ n) such that the value xi xor yj equals to one of the 2n integers. Here xor means the [bitwise exclusive or](https://en.wikipedia.org/wiki/Bitwise_operation#XOR) operation on two integers, and is denoted by operators ^ and/or xor in most programming languages.
Karen claims a win if the number of such pairs is even, and Koyomi does otherwise. And you're here to help determine the winner of their latest game.
Input
The first line of input contains a positive integer n (1 ≤ n ≤ 2 000) — the length of both sequences.
The second line contains n space-separated integers x1, x2, ..., xn (1 ≤ xi ≤ 2·106) — the integers finally chosen by Koyomi.
The third line contains n space-separated integers y1, y2, ..., yn (1 ≤ yi ≤ 2·106) — the integers finally chosen by Karen.
Input guarantees that the given 2n integers are pairwise distinct, that is, no pair (i, j) (1 ≤ i, j ≤ n) exists such that one of the following holds: xi = yj; i ≠ j and xi = xj; i ≠ j and yi = yj.
Output
Output one line — the name of the winner, that is, "Koyomi" or "Karen" (without quotes). Please be aware of the capitalization.
Examples
Input
3
1 2 3
4 5 6
Output
Karen
Input
5
2 4 6 8 10
9 7 5 3 1
Output
Karen
Note
In the first example, there are 6 pairs satisfying the constraint: (1, 1), (1, 2), (2, 1), (2, 3), (3, 2) and (3, 3). Thus, Karen wins since 6 is an even number.
In the second example, there are 16 such pairs, and Karen wins again.
Submitted Solution:
```
n = int(input())
a = list(map(int, input().split()))
b = list(map(int, input().split()))
c = list(set(a) | set(b))
answer = 0
for i in range(len(c) - 1):
for j in range(i + 1, len(c)):
if c[i] ^ c[j] in c:
answer += 1
if answer % 2 == 0:
print('Karen')
else:
print('Koyomi')
``` | instruction | 0 | 26,184 | 19 | 52,368 |
No | output | 1 | 26,184 | 19 | 52,369 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Rock... Paper!
After Karen have found the deterministic winning (losing?) strategy for rock-paper-scissors, her brother, Koyomi, comes up with a new game as a substitute. The game works as follows.
A positive integer n is decided first. Both Koyomi and Karen independently choose n distinct positive integers, denoted by x1, x2, ..., xn and y1, y2, ..., yn respectively. They reveal their sequences, and repeat until all of 2n integers become distinct, which is the only final state to be kept and considered.
Then they count the number of ordered pairs (i, j) (1 ≤ i, j ≤ n) such that the value xi xor yj equals to one of the 2n integers. Here xor means the [bitwise exclusive or](https://en.wikipedia.org/wiki/Bitwise_operation#XOR) operation on two integers, and is denoted by operators ^ and/or xor in most programming languages.
Karen claims a win if the number of such pairs is even, and Koyomi does otherwise. And you're here to help determine the winner of their latest game.
Input
The first line of input contains a positive integer n (1 ≤ n ≤ 2 000) — the length of both sequences.
The second line contains n space-separated integers x1, x2, ..., xn (1 ≤ xi ≤ 2·106) — the integers finally chosen by Koyomi.
The third line contains n space-separated integers y1, y2, ..., yn (1 ≤ yi ≤ 2·106) — the integers finally chosen by Karen.
Input guarantees that the given 2n integers are pairwise distinct, that is, no pair (i, j) (1 ≤ i, j ≤ n) exists such that one of the following holds: xi = yj; i ≠ j and xi = xj; i ≠ j and yi = yj.
Output
Output one line — the name of the winner, that is, "Koyomi" or "Karen" (without quotes). Please be aware of the capitalization.
Examples
Input
3
1 2 3
4 5 6
Output
Karen
Input
5
2 4 6 8 10
9 7 5 3 1
Output
Karen
Note
In the first example, there are 6 pairs satisfying the constraint: (1, 1), (1, 2), (2, 1), (2, 3), (3, 2) and (3, 3). Thus, Karen wins since 6 is an even number.
In the second example, there are 16 such pairs, and Karen wins again.
Submitted Solution:
```
#cd 439-div2 http://codeforces.com/contest/869/problem/0
#F(l,r)=f(1,r)xor f(1,l-1)
n=int(input())
x=[int(i) for i in input().split()]
y=[int(i) for i in input().split()]
check=[False]*(2*11111111)
for i in range(n):
check[x[i]]=True
check[y[i]]=True
sm=0
for i in range(n):
for j in range(n):
if check[x[i]^y[j]]:
sm+=1
print(sm)
if sm%2==0:
print('Karen')
else:
print('Koyomi')
``` | instruction | 0 | 26,185 | 19 | 52,370 |
No | output | 1 | 26,185 | 19 | 52,371 |
Provide a correct Python 3 solution for this coding contest problem.
An adult game master and N children are playing a game on an ice rink. The game consists of K rounds. In the i-th round, the game master announces:
* Form groups consisting of A_i children each!
Then the children who are still in the game form as many groups of A_i children as possible. One child may belong to at most one group. Those who are left without a group leave the game. The others proceed to the next round. Note that it's possible that nobody leaves the game in some round.
In the end, after the K-th round, there are exactly two children left, and they are declared the winners.
You have heard the values of A_1, A_2, ..., A_K. You don't know N, but you want to estimate it.
Find the smallest and the largest possible number of children in the game before the start, or determine that no valid values of N exist.
Constraints
* 1 \leq K \leq 10^5
* 2 \leq A_i \leq 10^9
* All input values are integers.
Input
Input is given from Standard Input in the following format:
K
A_1 A_2 ... A_K
Output
Print two integers representing the smallest and the largest possible value of N, respectively, or a single integer -1 if the described situation is impossible.
Examples
Input
4
3 4 3 2
Output
6 8
Input
5
3 4 100 3 2
Output
-1
Input
10
2 2 2 2 2 2 2 2 2 2
Output
2 3 | instruction | 0 | 26,325 | 19 | 52,650 |
"Correct Solution:
```
n=int(input())
a=list(reversed(list(map(int,input().split()))))
p,q=2,2
for i in range(n):
q2=((q-1)//a[i]+1)*a[i]
p2=(p//a[i]+1)*a[i]-1
p=p2
q=q2
if p<q:
print(-1)
break
else:
print(q,p)
``` | output | 1 | 26,325 | 19 | 52,651 |
Provide a correct Python 3 solution for this coding contest problem.
An adult game master and N children are playing a game on an ice rink. The game consists of K rounds. In the i-th round, the game master announces:
* Form groups consisting of A_i children each!
Then the children who are still in the game form as many groups of A_i children as possible. One child may belong to at most one group. Those who are left without a group leave the game. The others proceed to the next round. Note that it's possible that nobody leaves the game in some round.
In the end, after the K-th round, there are exactly two children left, and they are declared the winners.
You have heard the values of A_1, A_2, ..., A_K. You don't know N, but you want to estimate it.
Find the smallest and the largest possible number of children in the game before the start, or determine that no valid values of N exist.
Constraints
* 1 \leq K \leq 10^5
* 2 \leq A_i \leq 10^9
* All input values are integers.
Input
Input is given from Standard Input in the following format:
K
A_1 A_2 ... A_K
Output
Print two integers representing the smallest and the largest possible value of N, respectively, or a single integer -1 if the described situation is impossible.
Examples
Input
4
3 4 3 2
Output
6 8
Input
5
3 4 100 3 2
Output
-1
Input
10
2 2 2 2 2 2 2 2 2 2
Output
2 3 | instruction | 0 | 26,326 | 19 | 52,652 |
"Correct Solution:
```
from math import floor,ceil
K = int(input())
A = [int(x) for x in input().split()]
A.reverse()
jmax, jmin = 2,2
for i in range(0,K):
mmax,mmin = jmax,jmin
if mmin % A[i] != 0:
if (mmin + (A[i] - (mmin % A[i]))) > mmax:
print(-1)
exit()
jmin = ceil(jmin / A[i]) * A[i]
jmax = floor(jmax / A[i]) * A[i] + A[i] -1
print(jmin, jmax)
#計算量はO(3K)すなわちO(K)
``` | output | 1 | 26,326 | 19 | 52,653 |
Provide a correct Python 3 solution for this coding contest problem.
An adult game master and N children are playing a game on an ice rink. The game consists of K rounds. In the i-th round, the game master announces:
* Form groups consisting of A_i children each!
Then the children who are still in the game form as many groups of A_i children as possible. One child may belong to at most one group. Those who are left without a group leave the game. The others proceed to the next round. Note that it's possible that nobody leaves the game in some round.
In the end, after the K-th round, there are exactly two children left, and they are declared the winners.
You have heard the values of A_1, A_2, ..., A_K. You don't know N, but you want to estimate it.
Find the smallest and the largest possible number of children in the game before the start, or determine that no valid values of N exist.
Constraints
* 1 \leq K \leq 10^5
* 2 \leq A_i \leq 10^9
* All input values are integers.
Input
Input is given from Standard Input in the following format:
K
A_1 A_2 ... A_K
Output
Print two integers representing the smallest and the largest possible value of N, respectively, or a single integer -1 if the described situation is impossible.
Examples
Input
4
3 4 3 2
Output
6 8
Input
5
3 4 100 3 2
Output
-1
Input
10
2 2 2 2 2 2 2 2 2 2
Output
2 3 | instruction | 0 | 26,327 | 19 | 52,654 |
"Correct Solution:
```
K = int(input())
A = list(map(int, input().split()))
min = 2
max = 2
for i in range(K-1, -1, -1):
min += (-min) % A[i]
max -= max % A[i]
max += A[i] - 1
if max < min:
print(-1)
exit()
print(min, max)
``` | output | 1 | 26,327 | 19 | 52,655 |
Provide a correct Python 3 solution for this coding contest problem.
An adult game master and N children are playing a game on an ice rink. The game consists of K rounds. In the i-th round, the game master announces:
* Form groups consisting of A_i children each!
Then the children who are still in the game form as many groups of A_i children as possible. One child may belong to at most one group. Those who are left without a group leave the game. The others proceed to the next round. Note that it's possible that nobody leaves the game in some round.
In the end, after the K-th round, there are exactly two children left, and they are declared the winners.
You have heard the values of A_1, A_2, ..., A_K. You don't know N, but you want to estimate it.
Find the smallest and the largest possible number of children in the game before the start, or determine that no valid values of N exist.
Constraints
* 1 \leq K \leq 10^5
* 2 \leq A_i \leq 10^9
* All input values are integers.
Input
Input is given from Standard Input in the following format:
K
A_1 A_2 ... A_K
Output
Print two integers representing the smallest and the largest possible value of N, respectively, or a single integer -1 if the described situation is impossible.
Examples
Input
4
3 4 3 2
Output
6 8
Input
5
3 4 100 3 2
Output
-1
Input
10
2 2 2 2 2 2 2 2 2 2
Output
2 3 | instruction | 0 | 26,328 | 19 | 52,656 |
"Correct Solution:
```
from math import floor,ceil
K = int(input())
A = [int(x) for x in input().split()]
A.reverse()
jmax, jmin = 2,2
for i in range(0,K):
if jmin % A[i] != 0:
if (jmin + (A[i] - (jmin % A[i]))) > jmax:
print(-1)
exit()
jmin = ceil(jmin / A[i]) * A[i]
jmax = floor(jmax / A[i]) * A[i] + A[i] -1
print(jmin, jmax)
#計算量はO(3K)すなわちO(K)
``` | output | 1 | 26,328 | 19 | 52,657 |
Provide a correct Python 3 solution for this coding contest problem.
An adult game master and N children are playing a game on an ice rink. The game consists of K rounds. In the i-th round, the game master announces:
* Form groups consisting of A_i children each!
Then the children who are still in the game form as many groups of A_i children as possible. One child may belong to at most one group. Those who are left without a group leave the game. The others proceed to the next round. Note that it's possible that nobody leaves the game in some round.
In the end, after the K-th round, there are exactly two children left, and they are declared the winners.
You have heard the values of A_1, A_2, ..., A_K. You don't know N, but you want to estimate it.
Find the smallest and the largest possible number of children in the game before the start, or determine that no valid values of N exist.
Constraints
* 1 \leq K \leq 10^5
* 2 \leq A_i \leq 10^9
* All input values are integers.
Input
Input is given from Standard Input in the following format:
K
A_1 A_2 ... A_K
Output
Print two integers representing the smallest and the largest possible value of N, respectively, or a single integer -1 if the described situation is impossible.
Examples
Input
4
3 4 3 2
Output
6 8
Input
5
3 4 100 3 2
Output
-1
Input
10
2 2 2 2 2 2 2 2 2 2
Output
2 3 | instruction | 0 | 26,329 | 19 | 52,658 |
"Correct Solution:
```
k=int(input())
*a,=map(int,input().split())
l,r=2,2
for i in a[::-1]:
l=(l+i-1)//i*i
if r<l:
print(-1)
break
r=(r//i+1)*i-1
else:
print(l,r)
``` | output | 1 | 26,329 | 19 | 52,659 |
Provide a correct Python 3 solution for this coding contest problem.
An adult game master and N children are playing a game on an ice rink. The game consists of K rounds. In the i-th round, the game master announces:
* Form groups consisting of A_i children each!
Then the children who are still in the game form as many groups of A_i children as possible. One child may belong to at most one group. Those who are left without a group leave the game. The others proceed to the next round. Note that it's possible that nobody leaves the game in some round.
In the end, after the K-th round, there are exactly two children left, and they are declared the winners.
You have heard the values of A_1, A_2, ..., A_K. You don't know N, but you want to estimate it.
Find the smallest and the largest possible number of children in the game before the start, or determine that no valid values of N exist.
Constraints
* 1 \leq K \leq 10^5
* 2 \leq A_i \leq 10^9
* All input values are integers.
Input
Input is given from Standard Input in the following format:
K
A_1 A_2 ... A_K
Output
Print two integers representing the smallest and the largest possible value of N, respectively, or a single integer -1 if the described situation is impossible.
Examples
Input
4
3 4 3 2
Output
6 8
Input
5
3 4 100 3 2
Output
-1
Input
10
2 2 2 2 2 2 2 2 2 2
Output
2 3 | instruction | 0 | 26,330 | 19 | 52,660 |
"Correct Solution:
```
#!/usr/bin python3
# -*- coding: utf-8 -*-
k = int(input())
a = list(map(int, input().split()))
a= a[::-1]
if a[0]!=2:
print(-1)
exit()
mi = a[0]
mx = a[0]*2-1
for i in range(1,k):
ai = a[i]
mi = (mi+ai-1)//ai
mx = mx//ai
if mi>mx:
print(-1)
exit()
else:
mi = mi*ai
mx = (mx+1)*ai-1
print(mi, mx)
``` | output | 1 | 26,330 | 19 | 52,661 |
Provide a correct Python 3 solution for this coding contest problem.
An adult game master and N children are playing a game on an ice rink. The game consists of K rounds. In the i-th round, the game master announces:
* Form groups consisting of A_i children each!
Then the children who are still in the game form as many groups of A_i children as possible. One child may belong to at most one group. Those who are left without a group leave the game. The others proceed to the next round. Note that it's possible that nobody leaves the game in some round.
In the end, after the K-th round, there are exactly two children left, and they are declared the winners.
You have heard the values of A_1, A_2, ..., A_K. You don't know N, but you want to estimate it.
Find the smallest and the largest possible number of children in the game before the start, or determine that no valid values of N exist.
Constraints
* 1 \leq K \leq 10^5
* 2 \leq A_i \leq 10^9
* All input values are integers.
Input
Input is given from Standard Input in the following format:
K
A_1 A_2 ... A_K
Output
Print two integers representing the smallest and the largest possible value of N, respectively, or a single integer -1 if the described situation is impossible.
Examples
Input
4
3 4 3 2
Output
6 8
Input
5
3 4 100 3 2
Output
-1
Input
10
2 2 2 2 2 2 2 2 2 2
Output
2 3 | instruction | 0 | 26,331 | 19 | 52,662 |
"Correct Solution:
```
_,a=open(0)
l,r=-2,-3
for a in map(int,a.split()[::-1]):l,r=l//a*a,r//a*a
print(-(l==r)or'%d %d'%(-l,~r))
``` | output | 1 | 26,331 | 19 | 52,663 |
Provide a correct Python 3 solution for this coding contest problem.
An adult game master and N children are playing a game on an ice rink. The game consists of K rounds. In the i-th round, the game master announces:
* Form groups consisting of A_i children each!
Then the children who are still in the game form as many groups of A_i children as possible. One child may belong to at most one group. Those who are left without a group leave the game. The others proceed to the next round. Note that it's possible that nobody leaves the game in some round.
In the end, after the K-th round, there are exactly two children left, and they are declared the winners.
You have heard the values of A_1, A_2, ..., A_K. You don't know N, but you want to estimate it.
Find the smallest and the largest possible number of children in the game before the start, or determine that no valid values of N exist.
Constraints
* 1 \leq K \leq 10^5
* 2 \leq A_i \leq 10^9
* All input values are integers.
Input
Input is given from Standard Input in the following format:
K
A_1 A_2 ... A_K
Output
Print two integers representing the smallest and the largest possible value of N, respectively, or a single integer -1 if the described situation is impossible.
Examples
Input
4
3 4 3 2
Output
6 8
Input
5
3 4 100 3 2
Output
-1
Input
10
2 2 2 2 2 2 2 2 2 2
Output
2 3 | instruction | 0 | 26,332 | 19 | 52,664 |
"Correct Solution:
```
def main():
K=int(input())
A=list(map(int,input().split()))
A.reverse()
minres = 2
maxres = 2
for a in A:
minres = ((minres+a-1)//a)*a
if minres>maxres:return -1
maxres = (maxres//a)*a+a-1
return str(minres)+" "+str(maxres)
print(main())
``` | output | 1 | 26,332 | 19 | 52,665 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
An adult game master and N children are playing a game on an ice rink. The game consists of K rounds. In the i-th round, the game master announces:
* Form groups consisting of A_i children each!
Then the children who are still in the game form as many groups of A_i children as possible. One child may belong to at most one group. Those who are left without a group leave the game. The others proceed to the next round. Note that it's possible that nobody leaves the game in some round.
In the end, after the K-th round, there are exactly two children left, and they are declared the winners.
You have heard the values of A_1, A_2, ..., A_K. You don't know N, but you want to estimate it.
Find the smallest and the largest possible number of children in the game before the start, or determine that no valid values of N exist.
Constraints
* 1 \leq K \leq 10^5
* 2 \leq A_i \leq 10^9
* All input values are integers.
Input
Input is given from Standard Input in the following format:
K
A_1 A_2 ... A_K
Output
Print two integers representing the smallest and the largest possible value of N, respectively, or a single integer -1 if the described situation is impossible.
Examples
Input
4
3 4 3 2
Output
6 8
Input
5
3 4 100 3 2
Output
-1
Input
10
2 2 2 2 2 2 2 2 2 2
Output
2 3
Submitted Solution:
```
from math import ceil
K = int(input())
A = list(map(int, input().split()))
A.reverse()
if A[0] != 2:
print(-1)
exit()
mi = 2
mx = 3
for a in A[1:]:
if ceil(mi/a) > mx//a:
print(-1)
exit()
mi = ceil(mi/a)*a
mx = mx//a*a
mx = mx + a - 1
print(mi, mx)
``` | instruction | 0 | 26,333 | 19 | 52,666 |
Yes | output | 1 | 26,333 | 19 | 52,667 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
An adult game master and N children are playing a game on an ice rink. The game consists of K rounds. In the i-th round, the game master announces:
* Form groups consisting of A_i children each!
Then the children who are still in the game form as many groups of A_i children as possible. One child may belong to at most one group. Those who are left without a group leave the game. The others proceed to the next round. Note that it's possible that nobody leaves the game in some round.
In the end, after the K-th round, there are exactly two children left, and they are declared the winners.
You have heard the values of A_1, A_2, ..., A_K. You don't know N, but you want to estimate it.
Find the smallest and the largest possible number of children in the game before the start, or determine that no valid values of N exist.
Constraints
* 1 \leq K \leq 10^5
* 2 \leq A_i \leq 10^9
* All input values are integers.
Input
Input is given from Standard Input in the following format:
K
A_1 A_2 ... A_K
Output
Print two integers representing the smallest and the largest possible value of N, respectively, or a single integer -1 if the described situation is impossible.
Examples
Input
4
3 4 3 2
Output
6 8
Input
5
3 4 100 3 2
Output
-1
Input
10
2 2 2 2 2 2 2 2 2 2
Output
2 3
Submitted Solution:
```
import sys
k = int(input())
a = list(map(int, input().split()))[::-1]
m, M = 2, 2
for i in range(k):
if m % a[i] != 0:
m += a[i] - (m % a[i])
M = M - (M % a[i]) + a[i] - 1
if m > M:
print(-1)
sys.exit()
print(m, M)
``` | instruction | 0 | 26,334 | 19 | 52,668 |
Yes | output | 1 | 26,334 | 19 | 52,669 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
An adult game master and N children are playing a game on an ice rink. The game consists of K rounds. In the i-th round, the game master announces:
* Form groups consisting of A_i children each!
Then the children who are still in the game form as many groups of A_i children as possible. One child may belong to at most one group. Those who are left without a group leave the game. The others proceed to the next round. Note that it's possible that nobody leaves the game in some round.
In the end, after the K-th round, there are exactly two children left, and they are declared the winners.
You have heard the values of A_1, A_2, ..., A_K. You don't know N, but you want to estimate it.
Find the smallest and the largest possible number of children in the game before the start, or determine that no valid values of N exist.
Constraints
* 1 \leq K \leq 10^5
* 2 \leq A_i \leq 10^9
* All input values are integers.
Input
Input is given from Standard Input in the following format:
K
A_1 A_2 ... A_K
Output
Print two integers representing the smallest and the largest possible value of N, respectively, or a single integer -1 if the described situation is impossible.
Examples
Input
4
3 4 3 2
Output
6 8
Input
5
3 4 100 3 2
Output
-1
Input
10
2 2 2 2 2 2 2 2 2 2
Output
2 3
Submitted Solution:
```
K = int(input())
A = list(map(int,input().split()))
if A[-1] != 2:
print(-1)
exit()
A.reverse()
mn = mx = 2
for a,b in zip(A,A[1:]):
mn += (b - mn%b)%b
mx += a-1
mx -= mx%b
if mn > mx:
print(-1)
exit()
mx += A[-1]-1
print(mn,mx)
``` | instruction | 0 | 26,335 | 19 | 52,670 |
Yes | output | 1 | 26,335 | 19 | 52,671 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
An adult game master and N children are playing a game on an ice rink. The game consists of K rounds. In the i-th round, the game master announces:
* Form groups consisting of A_i children each!
Then the children who are still in the game form as many groups of A_i children as possible. One child may belong to at most one group. Those who are left without a group leave the game. The others proceed to the next round. Note that it's possible that nobody leaves the game in some round.
In the end, after the K-th round, there are exactly two children left, and they are declared the winners.
You have heard the values of A_1, A_2, ..., A_K. You don't know N, but you want to estimate it.
Find the smallest and the largest possible number of children in the game before the start, or determine that no valid values of N exist.
Constraints
* 1 \leq K \leq 10^5
* 2 \leq A_i \leq 10^9
* All input values are integers.
Input
Input is given from Standard Input in the following format:
K
A_1 A_2 ... A_K
Output
Print two integers representing the smallest and the largest possible value of N, respectively, or a single integer -1 if the described situation is impossible.
Examples
Input
4
3 4 3 2
Output
6 8
Input
5
3 4 100 3 2
Output
-1
Input
10
2 2 2 2 2 2 2 2 2 2
Output
2 3
Submitted Solution:
```
import sys
sys.setrecursionlimit(10 ** 7)
input = sys.stdin.readline
k = int(input())
a = list( map(int, input().split()))
if a[-1]!=2:
print(-1)
exit()
ma = 2
for i in reversed(range(k)):
ma = ma//a[i]*a[i] + (a[i]-1)
if a[i] > ma:
print(-1)
exit()
mi = 2
for i in reversed(range(k)):
mi = -(-mi//a[i])*a[i]
if mi > ma:
print(-1)
exit()
print(mi,ma)
``` | instruction | 0 | 26,336 | 19 | 52,672 |
Yes | output | 1 | 26,336 | 19 | 52,673 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
An adult game master and N children are playing a game on an ice rink. The game consists of K rounds. In the i-th round, the game master announces:
* Form groups consisting of A_i children each!
Then the children who are still in the game form as many groups of A_i children as possible. One child may belong to at most one group. Those who are left without a group leave the game. The others proceed to the next round. Note that it's possible that nobody leaves the game in some round.
In the end, after the K-th round, there are exactly two children left, and they are declared the winners.
You have heard the values of A_1, A_2, ..., A_K. You don't know N, but you want to estimate it.
Find the smallest and the largest possible number of children in the game before the start, or determine that no valid values of N exist.
Constraints
* 1 \leq K \leq 10^5
* 2 \leq A_i \leq 10^9
* All input values are integers.
Input
Input is given from Standard Input in the following format:
K
A_1 A_2 ... A_K
Output
Print two integers representing the smallest and the largest possible value of N, respectively, or a single integer -1 if the described situation is impossible.
Examples
Input
4
3 4 3 2
Output
6 8
Input
5
3 4 100 3 2
Output
-1
Input
10
2 2 2 2 2 2 2 2 2 2
Output
2 3
Submitted Solution:
```
k=int(input())
l=list(map(int,input().split()))
nowmax=2
nowmin=2
for i in range(k):
num=l[-1-i]
if num>nowmax:
print(-1)
exit()
else:
nowmax,nowmin=(nowmax//num)*num+num-1,(((nowmin-1)//num)+1)*num
print(nowmin,nowmax)
``` | instruction | 0 | 26,337 | 19 | 52,674 |
No | output | 1 | 26,337 | 19 | 52,675 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
An adult game master and N children are playing a game on an ice rink. The game consists of K rounds. In the i-th round, the game master announces:
* Form groups consisting of A_i children each!
Then the children who are still in the game form as many groups of A_i children as possible. One child may belong to at most one group. Those who are left without a group leave the game. The others proceed to the next round. Note that it's possible that nobody leaves the game in some round.
In the end, after the K-th round, there are exactly two children left, and they are declared the winners.
You have heard the values of A_1, A_2, ..., A_K. You don't know N, but you want to estimate it.
Find the smallest and the largest possible number of children in the game before the start, or determine that no valid values of N exist.
Constraints
* 1 \leq K \leq 10^5
* 2 \leq A_i \leq 10^9
* All input values are integers.
Input
Input is given from Standard Input in the following format:
K
A_1 A_2 ... A_K
Output
Print two integers representing the smallest and the largest possible value of N, respectively, or a single integer -1 if the described situation is impossible.
Examples
Input
4
3 4 3 2
Output
6 8
Input
5
3 4 100 3 2
Output
-1
Input
10
2 2 2 2 2 2 2 2 2 2
Output
2 3
Submitted Solution:
```
K=int(input())
A=list(map(int,input().split()))
def func(num):
for item in A:
num=num//item*item
return num
ans=[]
ok=10**10
ng=0
while ok-ng>1:
mid=(ok+ng)//2
if func(mid)>=2:
ok=mid
else:
ng=mid
ans=ok
ok=10**10
ng=0
while ok-ng>1:
mid=(ok+ng)//2
if func(mid)>=4:
ok=mid
else:
ng=mid
if func(ans)==2 and func(ng)==2:
print(ans,ng)
else:
print(-1)
``` | instruction | 0 | 26,338 | 19 | 52,676 |
No | output | 1 | 26,338 | 19 | 52,677 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
An adult game master and N children are playing a game on an ice rink. The game consists of K rounds. In the i-th round, the game master announces:
* Form groups consisting of A_i children each!
Then the children who are still in the game form as many groups of A_i children as possible. One child may belong to at most one group. Those who are left without a group leave the game. The others proceed to the next round. Note that it's possible that nobody leaves the game in some round.
In the end, after the K-th round, there are exactly two children left, and they are declared the winners.
You have heard the values of A_1, A_2, ..., A_K. You don't know N, but you want to estimate it.
Find the smallest and the largest possible number of children in the game before the start, or determine that no valid values of N exist.
Constraints
* 1 \leq K \leq 10^5
* 2 \leq A_i \leq 10^9
* All input values are integers.
Input
Input is given from Standard Input in the following format:
K
A_1 A_2 ... A_K
Output
Print two integers representing the smallest and the largest possible value of N, respectively, or a single integer -1 if the described situation is impossible.
Examples
Input
4
3 4 3 2
Output
6 8
Input
5
3 4 100 3 2
Output
-1
Input
10
2 2 2 2 2 2 2 2 2 2
Output
2 3
Submitted Solution:
```
import math,string,itertools,fractions,heapq,collections,re,array,bisect,sys,random,time,copy,functools
sys.setrecursionlimit(10**7)
inf = 10**20
eps = 1.0 / 10**15
mod = 10**9+7
def LI(): return [int(x) for x in sys.stdin.readline().split()]
def LI_(): return [int(x)-1 for x in sys.stdin.readline().split()]
def LF(): return [float(x) for x in sys.stdin.readline().split()]
def LS(): return sys.stdin.readline().split()
def I(): return int(sys.stdin.readline())
def F(): return float(sys.stdin.readline())
def S(): return input()
def pf(s): return print(s, flush=True)
def main():
n = I()
a = LI()
if a[-1] != 2:
return -1
b = c = 2
aa = a[::-1][1:]
for t in aa:
if b * 2 <= t:
return -1
if b % t == 0:
pass
elif b > t:
b = (b+t) - (b%t)
else:
b = t
c = c * 2 - 1
c -= c%t
return '{} {}'.format(b, c+a[0]-1)
print(main())
``` | instruction | 0 | 26,339 | 19 | 52,678 |
No | output | 1 | 26,339 | 19 | 52,679 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
An adult game master and N children are playing a game on an ice rink. The game consists of K rounds. In the i-th round, the game master announces:
* Form groups consisting of A_i children each!
Then the children who are still in the game form as many groups of A_i children as possible. One child may belong to at most one group. Those who are left without a group leave the game. The others proceed to the next round. Note that it's possible that nobody leaves the game in some round.
In the end, after the K-th round, there are exactly two children left, and they are declared the winners.
You have heard the values of A_1, A_2, ..., A_K. You don't know N, but you want to estimate it.
Find the smallest and the largest possible number of children in the game before the start, or determine that no valid values of N exist.
Constraints
* 1 \leq K \leq 10^5
* 2 \leq A_i \leq 10^9
* All input values are integers.
Input
Input is given from Standard Input in the following format:
K
A_1 A_2 ... A_K
Output
Print two integers representing the smallest and the largest possible value of N, respectively, or a single integer -1 if the described situation is impossible.
Examples
Input
4
3 4 3 2
Output
6 8
Input
5
3 4 100 3 2
Output
-1
Input
10
2 2 2 2 2 2 2 2 2 2
Output
2 3
Submitted Solution:
```
import sys
input = sys.stdin.readline
N = int(input())
a = list(map(int, input().split()))
x = a[-1]
y = 3
if x != 2:
print(-1)
exit(0)
for i in range(N - 2, -1, -1):
p = a[i]
t = -(-x // p)
x = t * p
y = max((t + 1) * p - 1, y)
t = x + 0
for i in range(N):
t -= t % a[i]
if t == 2:
print(x, y)
else: print(-1)
``` | instruction | 0 | 26,340 | 19 | 52,680 |
No | output | 1 | 26,340 | 19 | 52,681 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Andrew, Fedor and Alex are inventive guys. Now they invent the game with strings for two players.
Given a group of n non-empty strings. During the game two players build the word together, initially the word is empty. The players move in turns. On his step player must add a single letter in the end of the word, the resulting word must be prefix of at least one string from the group. A player loses if he cannot move.
Andrew and Alex decided to play this game k times. The player who is the loser of the i-th game makes the first move in the (i + 1)-th game. Guys decided that the winner of all games is the player who wins the last (k-th) game. Andrew and Alex already started the game. Fedor wants to know who wins the game if both players will play optimally. Help him.
Input
The first line contains two integers, n and k (1 ≤ n ≤ 105; 1 ≤ k ≤ 109).
Each of the next n lines contains a single non-empty string from the given group. The total length of all strings from the group doesn't exceed 105. Each string of the group consists only of lowercase English letters.
Output
If the player who moves first wins, print "First", otherwise print "Second" (without the quotes).
Examples
Input
2 3
a
b
Output
First
Input
3 1
a
b
c
Output
First
Input
1 2
ab
Output
Second | instruction | 0 | 26,888 | 19 | 53,776 |
Tags: dfs and similar, dp, games, implementation, strings, trees
Correct Solution:
```
import math
import sys
from itertools import permutations
input = sys.stdin.readline
class Node:
def __init__(self):
self.children = [None]*26
self.isEnd = False
self.win = False
self.lose = False
class Trie:
def __init__(self):
self.root = Node()
def insert(self, key):
cur = self.root
for i in range(len(key)):
if cur.children[ord(key[i])-ord('a')]==None:
cur.children[ord(key[i])-ord('a')]=Node()
cur = cur.children[ord(key[i])-ord('a')]
cur.isEnd = True
def search(self, key):
cur = self.root
for i in range(len(key)):
if cur.children[ord(key[i])-ord('a')]==None:
return False
cur = cur.children[ord(key[i])-ord('a')]
if cur!=None and cur.isEnd:
return True
return False
def assignWin(self, cur):
flag = True
for i in range(26):
if cur.children[i]!=None:
flag=False
self.assignWin(cur.children[i])
if flag:
cur.win=False
cur.lose=True
else:
for i in range(26):
if cur.children[i]!=None:
cur.win = cur.win or (not cur.children[i].win)
cur.lose = cur.lose or (not cur.children[i].lose)
if __name__=='__main__':
t=Trie()
n,k=map(int,input().split())
for i in range(n):
s=input()
if s[-1]=="\n":
s= s[:-1]
t.insert(s)
t.assignWin(t.root)
if not t.root.win:
print("Second")
else:
if t.root.lose:
print("First")
else:
if k%2==1:
print("First")
else:
print("Second")
``` | output | 1 | 26,888 | 19 | 53,777 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Andrew, Fedor and Alex are inventive guys. Now they invent the game with strings for two players.
Given a group of n non-empty strings. During the game two players build the word together, initially the word is empty. The players move in turns. On his step player must add a single letter in the end of the word, the resulting word must be prefix of at least one string from the group. A player loses if he cannot move.
Andrew and Alex decided to play this game k times. The player who is the loser of the i-th game makes the first move in the (i + 1)-th game. Guys decided that the winner of all games is the player who wins the last (k-th) game. Andrew and Alex already started the game. Fedor wants to know who wins the game if both players will play optimally. Help him.
Input
The first line contains two integers, n and k (1 ≤ n ≤ 105; 1 ≤ k ≤ 109).
Each of the next n lines contains a single non-empty string from the given group. The total length of all strings from the group doesn't exceed 105. Each string of the group consists only of lowercase English letters.
Output
If the player who moves first wins, print "First", otherwise print "Second" (without the quotes).
Examples
Input
2 3
a
b
Output
First
Input
3 1
a
b
c
Output
First
Input
1 2
ab
Output
Second | instruction | 0 | 26,891 | 19 | 53,782 |
Tags: dfs and similar, dp, games, implementation, strings, trees
Correct Solution:
```
from sys import stdin, setrecursionlimit
def forced(tree):
if not tree:
return (False, True)
else:
winner = False
loser = False
for leaf in tree:
a, b = forced(tree[leaf])
if not a:
winner = True
if not b:
loser = True
return (winner, loser)
def print_res(a, b, k):
first = 'First'
second = 'Second'
if a == 1 and b == 1:
print(first)
elif a == 0:
print(second)
else:
if k % 2 != 0:
print(first)
else:
print(second)
def main():
n, k = [int(i) for i in stdin.readline().split()]
tree = {}
for i in range(n):
_str = stdin.readline().strip()
cur = tree
for i in _str:
if not i in cur:
cur[i] = {}
cur = cur[i]
a, b = forced(tree)
print_res(a, b, k)
if __name__ == '__main__':
main()
``` | output | 1 | 26,891 | 19 | 53,783 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Andrew, Fedor and Alex are inventive guys. Now they invent the game with strings for two players.
Given a group of n non-empty strings. During the game two players build the word together, initially the word is empty. The players move in turns. On his step player must add a single letter in the end of the word, the resulting word must be prefix of at least one string from the group. A player loses if he cannot move.
Andrew and Alex decided to play this game k times. The player who is the loser of the i-th game makes the first move in the (i + 1)-th game. Guys decided that the winner of all games is the player who wins the last (k-th) game. Andrew and Alex already started the game. Fedor wants to know who wins the game if both players will play optimally. Help him.
Input
The first line contains two integers, n and k (1 ≤ n ≤ 105; 1 ≤ k ≤ 109).
Each of the next n lines contains a single non-empty string from the given group. The total length of all strings from the group doesn't exceed 105. Each string of the group consists only of lowercase English letters.
Output
If the player who moves first wins, print "First", otherwise print "Second" (without the quotes).
Examples
Input
2 3
a
b
Output
First
Input
3 1
a
b
c
Output
First
Input
1 2
ab
Output
Second
Submitted Solution:
```
from sys import stdin, setrecursionlimit
def forced(tree):
if not tree:
return (False, True)
else:
winner = False
loser = False
for leaf in tree:
a, b = forced(tree[leaf])
if not a:
winner = True
if not b:
loser = True
return (winner, loser)
def print_res(a, b, k):
first = 'First'
second = 'Second'
if a == 1 and b == 1:
print(first)
elif a == 0:
print(second)
else:
if k % 2 != 0:
print(first)
else:
print(second)
def main():
setrecursionlimit(200000)
n, k = [int(i) for i in stdin.readline().split()]
tree = {}
for i in range(n):
_str = stdin.readline().strip()
cur = tree
for i in _str:
if not i in cur:
cur[i] = {}
cur = cur[i]
a, b = forced(tree)
print_res(a, b, k)
if __name__ == '__main__':
main()
``` | instruction | 0 | 26,892 | 19 | 53,784 |
Yes | output | 1 | 26,892 | 19 | 53,785 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Andrew, Fedor and Alex are inventive guys. Now they invent the game with strings for two players.
Given a group of n non-empty strings. During the game two players build the word together, initially the word is empty. The players move in turns. On his step player must add a single letter in the end of the word, the resulting word must be prefix of at least one string from the group. A player loses if he cannot move.
Andrew and Alex decided to play this game k times. The player who is the loser of the i-th game makes the first move in the (i + 1)-th game. Guys decided that the winner of all games is the player who wins the last (k-th) game. Andrew and Alex already started the game. Fedor wants to know who wins the game if both players will play optimally. Help him.
Input
The first line contains two integers, n and k (1 ≤ n ≤ 105; 1 ≤ k ≤ 109).
Each of the next n lines contains a single non-empty string from the given group. The total length of all strings from the group doesn't exceed 105. Each string of the group consists only of lowercase English letters.
Output
If the player who moves first wins, print "First", otherwise print "Second" (without the quotes).
Examples
Input
2 3
a
b
Output
First
Input
3 1
a
b
c
Output
First
Input
1 2
ab
Output
Second
Submitted Solution:
```
from sys import stdin, setrecursionlimit
setrecursionlimit(200000)
n,k = [int(x) for x in stdin.readline().split()]
tree = {}
for x in range(n):
s = stdin.readline().strip()
cur = tree
for x in s:
if not x in cur:
cur[x] = {}
cur = cur[x]
def forced(tree):
if not tree:
return (False,True)
else:
win = False
lose = False
for x in tree:
a,b = forced(tree[x])
if not a:
win = True
if not b:
lose = True
return (win,lose)
a,b = forced(tree)
if a == 0:
print('Second')
elif a == 1 and b == 1:
print('First')
else:
if k%2 == 0:
print('Second')
else:
print('First')
``` | instruction | 0 | 26,893 | 19 | 53,786 |
Yes | output | 1 | 26,893 | 19 | 53,787 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Andrew, Fedor and Alex are inventive guys. Now they invent the game with strings for two players.
Given a group of n non-empty strings. During the game two players build the word together, initially the word is empty. The players move in turns. On his step player must add a single letter in the end of the word, the resulting word must be prefix of at least one string from the group. A player loses if he cannot move.
Andrew and Alex decided to play this game k times. The player who is the loser of the i-th game makes the first move in the (i + 1)-th game. Guys decided that the winner of all games is the player who wins the last (k-th) game. Andrew and Alex already started the game. Fedor wants to know who wins the game if both players will play optimally. Help him.
Input
The first line contains two integers, n and k (1 ≤ n ≤ 105; 1 ≤ k ≤ 109).
Each of the next n lines contains a single non-empty string from the given group. The total length of all strings from the group doesn't exceed 105. Each string of the group consists only of lowercase English letters.
Output
If the player who moves first wins, print "First", otherwise print "Second" (without the quotes).
Examples
Input
2 3
a
b
Output
First
Input
3 1
a
b
c
Output
First
Input
1 2
ab
Output
Second
Submitted Solution:
```
# -*- coding:utf-8 -*-
"""
created by shuangquan.huang at 2/11/20
"""
import collections
import time
import os
import sys
import bisect
import heapq
from typing import List
def make_trie(A):
trie = {}
for word in A:
t = trie
for w in word:
if w not in t:
t[w] = {}
t = t[w]
# t['#'] = True
return trie
def game(trie):
if not trie:
return False
return not all([game(t) for k, t in trie.items()])
def can_lose(trie):
if not trie:
return True
return any([not can_lose(t) for k, t in trie.items()])
def solve(N, K, A):
trie = make_trie(A)
win = game(trie)
if not win:
return False
if K == 1:
return True
if can_lose(trie):
return True
return K % 2 == 1
N, K = map(int, input().split())
A = []
for i in range(N):
s = input()
A.append(s)
print('First' if solve(N, K, A) else 'Second')
``` | instruction | 0 | 26,894 | 19 | 53,788 |
Yes | output | 1 | 26,894 | 19 | 53,789 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Andrew, Fedor and Alex are inventive guys. Now they invent the game with strings for two players.
Given a group of n non-empty strings. During the game two players build the word together, initially the word is empty. The players move in turns. On his step player must add a single letter in the end of the word, the resulting word must be prefix of at least one string from the group. A player loses if he cannot move.
Andrew and Alex decided to play this game k times. The player who is the loser of the i-th game makes the first move in the (i + 1)-th game. Guys decided that the winner of all games is the player who wins the last (k-th) game. Andrew and Alex already started the game. Fedor wants to know who wins the game if both players will play optimally. Help him.
Input
The first line contains two integers, n and k (1 ≤ n ≤ 105; 1 ≤ k ≤ 109).
Each of the next n lines contains a single non-empty string from the given group. The total length of all strings from the group doesn't exceed 105. Each string of the group consists only of lowercase English letters.
Output
If the player who moves first wins, print "First", otherwise print "Second" (without the quotes).
Examples
Input
2 3
a
b
Output
First
Input
3 1
a
b
c
Output
First
Input
1 2
ab
Output
Second
Submitted Solution:
```
# by the authority of GOD author: manhar singh sachdev #
import os,sys
from io import BytesIO,IOBase
class Trie:
def __init__(self, *words):
self.root = dict()
for word in words:
self.add(word)
def add(self, word):
current_dict = self.root
for letter in word:
current_dict = current_dict.setdefault(letter, dict())
def dfs(self,node):
# 1: win ; 2: lose ; 3: your choice ; 4: not your choice
if not len(node):
return 2
out = [0,0,0,0]
for i in node:
x = self.dfs(node[i])
if x == 4:
return 3
out[x-1] += 1
out[3] += 1
if out[2] == out[3]:
return 4
if out[0] and out[1]:
return 3
if out[0]:
return 2
return 1
def main():
n,k = map(int,input().split())
trie = Trie()
for _ in range(n):
trie.add(input().strip())
z = trie.dfs(trie.root)
if z == 1:
print('First' if k&1 else 'Second')
elif z == 2:
print('Second')
elif z == 3:
print('First')
else:
print('Second')
# Fast IO Region
BUFSIZE = 8192
class FastIO(IOBase):
newlines = 0
def __init__(self,file):
self._fd = file.fileno()
self.buffer = BytesIO()
self.writable = "x" in file.mode or "r" not in file.mode
self.write = self.buffer.write if self.writable else None
def read(self):
while True:
b = os.read(self._fd,max(os.fstat(self._fd).st_size,BUFSIZE))
if not b:
break
ptr = self.buffer.tell()
self.buffer.seek(0,2),self.buffer.write(b),self.buffer.seek(ptr)
self.newlines = 0
return self.buffer.read()
def readline(self):
while self.newlines == 0:
b = os.read(self._fd,max(os.fstat(self._fd).st_size,BUFSIZE))
self.newlines = b.count(b"\n")+(not b)
ptr = self.buffer.tell()
self.buffer.seek(0,2),self.buffer.write(b),self.buffer.seek(ptr)
self.newlines -= 1
return self.buffer.readline()
def flush(self):
if self.writable:
os.write(self._fd,self.buffer.getvalue())
self.buffer.truncate(0),self.buffer.seek(0)
class IOWrapper(IOBase):
def __init__(self,file):
self.buffer = FastIO(file)
self.flush = self.buffer.flush
self.writable = self.buffer.writable
self.write = lambda s:self.buffer.write(s.encode("ascii"))
self.read = lambda:self.buffer.read().decode("ascii")
self.readline = lambda:self.buffer.readline().decode("ascii")
sys.stdin,sys.stdout = IOWrapper(sys.stdin),IOWrapper(sys.stdout)
input = lambda:sys.stdin.readline().rstrip("\r\n")
if __name__ == "__main__":
main()
``` | instruction | 0 | 26,895 | 19 | 53,790 |
Yes | output | 1 | 26,895 | 19 | 53,791 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Andrew, Fedor and Alex are inventive guys. Now they invent the game with strings for two players.
Given a group of n non-empty strings. During the game two players build the word together, initially the word is empty. The players move in turns. On his step player must add a single letter in the end of the word, the resulting word must be prefix of at least one string from the group. A player loses if he cannot move.
Andrew and Alex decided to play this game k times. The player who is the loser of the i-th game makes the first move in the (i + 1)-th game. Guys decided that the winner of all games is the player who wins the last (k-th) game. Andrew and Alex already started the game. Fedor wants to know who wins the game if both players will play optimally. Help him.
Input
The first line contains two integers, n and k (1 ≤ n ≤ 105; 1 ≤ k ≤ 109).
Each of the next n lines contains a single non-empty string from the given group. The total length of all strings from the group doesn't exceed 105. Each string of the group consists only of lowercase English letters.
Output
If the player who moves first wins, print "First", otherwise print "Second" (without the quotes).
Examples
Input
2 3
a
b
Output
First
Input
3 1
a
b
c
Output
First
Input
1 2
ab
Output
Second
Submitted Solution:
```
from sys import stdin, setrecursionlimit
setrecursionlimit(200000)
n,k = [int(x) for x in stdin.readline().split()]
tree = {}
for x in range(n):
s = stdin.readline().strip()
cur = tree
for x in s:
if not s in cur:
cur[s] = {}
cur = cur[s]
def forced(tree):
if not tree:
return (False,True)
else:
win = False
lose = False
for x in tree:
a,b = forced(tree[x])
if not a:
win = True
if not b:
lose = True
return (win,lose)
a,b = forced(tree)
if a == 0:
print('Second')
elif a == 1 and b == 1:
print('First')
else:
if k%2 == 0:
print('Second')
else:
print('First')
``` | instruction | 0 | 26,898 | 19 | 53,796 |
No | output | 1 | 26,898 | 19 | 53,797 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Andrew, Fedor and Alex are inventive guys. Now they invent the game with strings for two players.
Given a group of n non-empty strings. During the game two players build the word together, initially the word is empty. The players move in turns. On his step player must add a single letter in the end of the word, the resulting word must be prefix of at least one string from the group. A player loses if he cannot move.
Andrew and Alex decided to play this game k times. The player who is the loser of the i-th game makes the first move in the (i + 1)-th game. Guys decided that the winner of all games is the player who wins the last (k-th) game. Andrew and Alex already started the game. Fedor wants to know who wins the game if both players will play optimally. Help him.
Input
The first line contains two integers, n and k (1 ≤ n ≤ 105; 1 ≤ k ≤ 109).
Each of the next n lines contains a single non-empty string from the given group. The total length of all strings from the group doesn't exceed 105. Each string of the group consists only of lowercase English letters.
Output
If the player who moves first wins, print "First", otherwise print "Second" (without the quotes).
Examples
Input
2 3
a
b
Output
First
Input
3 1
a
b
c
Output
First
Input
1 2
ab
Output
Second
Submitted Solution:
```
# -*- coding:utf-8 -*-
"""
created by shuangquan.huang at 2/11/20
"""
import collections
import time
import os
import sys
import bisect
import heapq
from typing import List
def make_trie(A):
trie = {}
for word in A:
t = trie
for w in word:
if w not in t:
t[w] = {}
t = t[w]
# t['#'] = True
return trie
def game(trie):
if not trie:
return False
return not all([game(t) for k, t in trie.items()])
def can_lose(trie):
if not trie:
return True
return all([game(t) for k, t in trie.items()])
def solve(N, K, A):
trie = make_trie(A)
win = game(trie)
if not win:
return False
if K == 1:
return True
if can_lose(trie):
return True
return K % 2 == 1
N, K = map(int, input().split())
A = []
for i in range(N):
s = input()
A.append(s)
print('First' if solve(N, K, A) else 'Second')
``` | instruction | 0 | 26,899 | 19 | 53,798 |
No | output | 1 | 26,899 | 19 | 53,799 |
Provide a correct Python 3 solution for this coding contest problem.
There are two persons, numbered 0 and 1, and a variable x whose initial value is 0. The two persons now play a game. The game is played in N rounds. The following should be done in the i-th round (1 \leq i \leq N):
* Person S_i does one of the following:
* Replace x with x \oplus A_i, where \oplus represents bitwise XOR.
* Do nothing.
Person 0 aims to have x=0 at the end of the game, while Person 1 aims to have x \neq 0 at the end of the game.
Determine whether x becomes 0 at the end of the game when the two persons play optimally.
Solve T test cases for each input file.
Constraints
* 1 \leq T \leq 100
* 1 \leq N \leq 200
* 1 \leq A_i \leq 10^{18}
* S is a string of length N consisting of `0` and `1`.
* All numbers in input are integers.
Input
Input is given from Standard Input in the following format. The first line is as follows:
T
Then, T test cases follow. Each test case is given in the following format:
N
A_1 A_2 \cdots A_N
S
Output
For each test case, print a line containing `0` if x becomes 0 at the end of the game, and `1` otherwise.
Example
Input
3
2
1 2
10
2
1 1
10
6
2 3 4 5 6 7
111000
Output
1
0
0 | instruction | 0 | 27,138 | 19 | 54,276 |
"Correct Solution:
```
def main():
T = int(input())
for _ in range(T):
N = int(input())
A = list(map(int, input().split()))
S = input()
L = max(A).bit_length()
s = [0]*L
def check(x):
for i in range(L-1, -1, -1):
if (x >> i) % 2:
x ^= s[i]
return(x == 0)
def update(x):
for i in range(L-1, -1, -1):
if (x >> i) % 2:
x ^= s[i]
id = x.bit_length() - 1
if id >= 0:
s[id] = x
res = 0
L2 = 0
for i in range(N-1, -1, -1):
k = int(S[i])
if k:
if check(A[i]):
continue
else:
res = 1
break
else:
L2 = max(L2, A[i].bit_length())
update(A[i])
print(res)
main()
``` | output | 1 | 27,138 | 19 | 54,277 |
Provide a correct Python 3 solution for this coding contest problem.
There are two persons, numbered 0 and 1, and a variable x whose initial value is 0. The two persons now play a game. The game is played in N rounds. The following should be done in the i-th round (1 \leq i \leq N):
* Person S_i does one of the following:
* Replace x with x \oplus A_i, where \oplus represents bitwise XOR.
* Do nothing.
Person 0 aims to have x=0 at the end of the game, while Person 1 aims to have x \neq 0 at the end of the game.
Determine whether x becomes 0 at the end of the game when the two persons play optimally.
Solve T test cases for each input file.
Constraints
* 1 \leq T \leq 100
* 1 \leq N \leq 200
* 1 \leq A_i \leq 10^{18}
* S is a string of length N consisting of `0` and `1`.
* All numbers in input are integers.
Input
Input is given from Standard Input in the following format. The first line is as follows:
T
Then, T test cases follow. Each test case is given in the following format:
N
A_1 A_2 \cdots A_N
S
Output
For each test case, print a line containing `0` if x becomes 0 at the end of the game, and `1` otherwise.
Example
Input
3
2
1 2
10
2
1 1
10
6
2 3 4 5 6 7
111000
Output
1
0
0 | instruction | 0 | 27,139 | 19 | 54,278 |
"Correct Solution:
```
T = int(input())
for i in range(T):
n = int(input())
A = list(map(int, input().split()))
S = input()
dp = []
for j in reversed(range(n)):
a = A[j]
for x in dp:
a = min(a, a^x)
if a > 0:
if S[j] == '0':
dp.append(a)
elif not A[j] in dp:
print(1)
break
else:
print(0)
``` | output | 1 | 27,139 | 19 | 54,279 |
Provide a correct Python 3 solution for this coding contest problem.
There are two persons, numbered 0 and 1, and a variable x whose initial value is 0. The two persons now play a game. The game is played in N rounds. The following should be done in the i-th round (1 \leq i \leq N):
* Person S_i does one of the following:
* Replace x with x \oplus A_i, where \oplus represents bitwise XOR.
* Do nothing.
Person 0 aims to have x=0 at the end of the game, while Person 1 aims to have x \neq 0 at the end of the game.
Determine whether x becomes 0 at the end of the game when the two persons play optimally.
Solve T test cases for each input file.
Constraints
* 1 \leq T \leq 100
* 1 \leq N \leq 200
* 1 \leq A_i \leq 10^{18}
* S is a string of length N consisting of `0` and `1`.
* All numbers in input are integers.
Input
Input is given from Standard Input in the following format. The first line is as follows:
T
Then, T test cases follow. Each test case is given in the following format:
N
A_1 A_2 \cdots A_N
S
Output
For each test case, print a line containing `0` if x becomes 0 at the end of the game, and `1` otherwise.
Example
Input
3
2
1 2
10
2
1 1
10
6
2 3 4 5 6 7
111000
Output
1
0
0 | instruction | 0 | 27,140 | 19 | 54,280 |
"Correct Solution:
```
for _ in range(int(input())):
n=int(input())
a=list(map(int,input().split()))
s=input()
b=[]
ans=0
for i in range(n-1,-1,-1):
for j in b:
a[i]=min(a[i],a[i]^j)
if a[i]!=0:
if s[i]=="0":
b.append(a[i])
else:
ans=1
print(ans)
``` | output | 1 | 27,140 | 19 | 54,281 |
Provide a correct Python 3 solution for this coding contest problem.
There are two persons, numbered 0 and 1, and a variable x whose initial value is 0. The two persons now play a game. The game is played in N rounds. The following should be done in the i-th round (1 \leq i \leq N):
* Person S_i does one of the following:
* Replace x with x \oplus A_i, where \oplus represents bitwise XOR.
* Do nothing.
Person 0 aims to have x=0 at the end of the game, while Person 1 aims to have x \neq 0 at the end of the game.
Determine whether x becomes 0 at the end of the game when the two persons play optimally.
Solve T test cases for each input file.
Constraints
* 1 \leq T \leq 100
* 1 \leq N \leq 200
* 1 \leq A_i \leq 10^{18}
* S is a string of length N consisting of `0` and `1`.
* All numbers in input are integers.
Input
Input is given from Standard Input in the following format. The first line is as follows:
T
Then, T test cases follow. Each test case is given in the following format:
N
A_1 A_2 \cdots A_N
S
Output
For each test case, print a line containing `0` if x becomes 0 at the end of the game, and `1` otherwise.
Example
Input
3
2
1 2
10
2
1 1
10
6
2 3 4 5 6 7
111000
Output
1
0
0 | instruction | 0 | 27,141 | 19 | 54,282 |
"Correct Solution:
```
T = int(input())
for _ in range(T):
N = int(input())
A = [int(i) for i in input().split()]
S = input()
B = []
ans = 0
for a, s in zip(reversed(A), reversed(S)):
for b in B:
a = min(a, a ^ b)
if a:
if s == "1":
ans = 1
break
B.append(a)
print(ans)
``` | output | 1 | 27,141 | 19 | 54,283 |
Provide a correct Python 3 solution for this coding contest problem.
There are two persons, numbered 0 and 1, and a variable x whose initial value is 0. The two persons now play a game. The game is played in N rounds. The following should be done in the i-th round (1 \leq i \leq N):
* Person S_i does one of the following:
* Replace x with x \oplus A_i, where \oplus represents bitwise XOR.
* Do nothing.
Person 0 aims to have x=0 at the end of the game, while Person 1 aims to have x \neq 0 at the end of the game.
Determine whether x becomes 0 at the end of the game when the two persons play optimally.
Solve T test cases for each input file.
Constraints
* 1 \leq T \leq 100
* 1 \leq N \leq 200
* 1 \leq A_i \leq 10^{18}
* S is a string of length N consisting of `0` and `1`.
* All numbers in input are integers.
Input
Input is given from Standard Input in the following format. The first line is as follows:
T
Then, T test cases follow. Each test case is given in the following format:
N
A_1 A_2 \cdots A_N
S
Output
For each test case, print a line containing `0` if x becomes 0 at the end of the game, and `1` otherwise.
Example
Input
3
2
1 2
10
2
1 1
10
6
2 3 4 5 6 7
111000
Output
1
0
0 | instruction | 0 | 27,142 | 19 | 54,284 |
"Correct Solution:
```
import sys
input = sys.stdin.readline
class BaseXor:
def __init__(self):
self.size = 0
self.base = []
def base_calculate(self, x, b):
return min(x, x ^ b)
def make_base(self, x):
for b in self.base:
x = self.base_calculate(x, b)
return x
def change_base(self, x):
for i in range(self.size):
self.base[i] = self.base_calculate(self.base[i], x)
def add_base(self, x):
x = self.make_base(x)
if x == 0:
return False
self.change_base(x)
self.base.append(x)
self.size += 1
return True
def judge_linearly_dependent(self, x):
for b in self.base:
x = self.base_calculate(x, b)
res = True if x else False
return res
def solve(n, a, s):
base = BaseXor()
judge = False
for i in range(n-1, -1, -1):
x = s[i]
if x == "0":
base.add_base(a[i])
else:
judge = base.judge_linearly_dependent(a[i])
if judge:
break
res = 1 if judge else 0
return res
def main():
t = int(input())
ans = [0]*t
for i in range(t):
n = int(input())
a = list(map(int, input().split()))
s = input()
res = solve(n, a, s)
ans[i] = res
print(*ans, sep="\n")
if __name__ == "__main__":
main()
``` | output | 1 | 27,142 | 19 | 54,285 |
Provide a correct Python 3 solution for this coding contest problem.
There are two persons, numbered 0 and 1, and a variable x whose initial value is 0. The two persons now play a game. The game is played in N rounds. The following should be done in the i-th round (1 \leq i \leq N):
* Person S_i does one of the following:
* Replace x with x \oplus A_i, where \oplus represents bitwise XOR.
* Do nothing.
Person 0 aims to have x=0 at the end of the game, while Person 1 aims to have x \neq 0 at the end of the game.
Determine whether x becomes 0 at the end of the game when the two persons play optimally.
Solve T test cases for each input file.
Constraints
* 1 \leq T \leq 100
* 1 \leq N \leq 200
* 1 \leq A_i \leq 10^{18}
* S is a string of length N consisting of `0` and `1`.
* All numbers in input are integers.
Input
Input is given from Standard Input in the following format. The first line is as follows:
T
Then, T test cases follow. Each test case is given in the following format:
N
A_1 A_2 \cdots A_N
S
Output
For each test case, print a line containing `0` if x becomes 0 at the end of the game, and `1` otherwise.
Example
Input
3
2
1 2
10
2
1 1
10
6
2 3 4 5 6 7
111000
Output
1
0
0 | instruction | 0 | 27,143 | 19 | 54,286 |
"Correct Solution:
```
def kosu(kitei, aaa, tuika):
global now_ret
ret = 0
n=len(kitei)
ret2=0
kitei.append(aaa)
n+=1
for i in range(n):
if kitei[i]:
ret2 += 1
x = 0
while (2**(x+1)) <= kitei[i]:
x += 1
for y in range(i+1, n, 1):
if kitei[y] & (2 ** x):
kitei[y] ^= kitei[i]
if now_ret==ret2:
return 1
else:
if tuika==1:
now_ret+=1
return 0
def solve(n, alist, s):
kitei=[0]
answer=0
for i in range(n):
teban=s[n-i-1]
now=alist[n-i-1]
if teban=='0':
if kosu(kitei, now, 1)>0:
pass
else:
kitei.append(now)
else:
if kosu(kitei, now, 0)>0:
pass
else:
answer=1
#print(kitei)
return answer
t=int(input())
for i in range(t):
now_ret=0
n=int(input())
alist = list(map(int, input().split()))
s=input()
print(solve(n, alist, s))
``` | output | 1 | 27,143 | 19 | 54,287 |
Provide a correct Python 3 solution for this coding contest problem.
There are two persons, numbered 0 and 1, and a variable x whose initial value is 0. The two persons now play a game. The game is played in N rounds. The following should be done in the i-th round (1 \leq i \leq N):
* Person S_i does one of the following:
* Replace x with x \oplus A_i, where \oplus represents bitwise XOR.
* Do nothing.
Person 0 aims to have x=0 at the end of the game, while Person 1 aims to have x \neq 0 at the end of the game.
Determine whether x becomes 0 at the end of the game when the two persons play optimally.
Solve T test cases for each input file.
Constraints
* 1 \leq T \leq 100
* 1 \leq N \leq 200
* 1 \leq A_i \leq 10^{18}
* S is a string of length N consisting of `0` and `1`.
* All numbers in input are integers.
Input
Input is given from Standard Input in the following format. The first line is as follows:
T
Then, T test cases follow. Each test case is given in the following format:
N
A_1 A_2 \cdots A_N
S
Output
For each test case, print a line containing `0` if x becomes 0 at the end of the game, and `1` otherwise.
Example
Input
3
2
1 2
10
2
1 1
10
6
2 3 4 5 6 7
111000
Output
1
0
0 | instruction | 0 | 27,144 | 19 | 54,288 |
"Correct Solution:
```
def solve(N, A, S):
# s == 0 のa を組み合わせて s==1 の任意のa を張ることができれば0
# 下から
if int(S[-1]) == 1:
return 1
B = [None] * max(A).bit_length()
for i in reversed(range(N)):
a = A[i]
s = int(S[i])
if s == 0: #基底生成
while a:
l = a.bit_length()-1
if B[l] == None:
B[l] = a
break
a ^= B[l]
else: # i以上の基底で張れなければ 1
while a:
l = a.bit_length()-1
if B[l] == None:
return 1
a ^= B[l]
return 0
T = int(input())
for i in range(T):
N = int(input())
A = list(map(int, input().split()))
S = input()
print(solve(N, A, S))
``` | output | 1 | 27,144 | 19 | 54,289 |
Provide a correct Python 3 solution for this coding contest problem.
There are two persons, numbered 0 and 1, and a variable x whose initial value is 0. The two persons now play a game. The game is played in N rounds. The following should be done in the i-th round (1 \leq i \leq N):
* Person S_i does one of the following:
* Replace x with x \oplus A_i, where \oplus represents bitwise XOR.
* Do nothing.
Person 0 aims to have x=0 at the end of the game, while Person 1 aims to have x \neq 0 at the end of the game.
Determine whether x becomes 0 at the end of the game when the two persons play optimally.
Solve T test cases for each input file.
Constraints
* 1 \leq T \leq 100
* 1 \leq N \leq 200
* 1 \leq A_i \leq 10^{18}
* S is a string of length N consisting of `0` and `1`.
* All numbers in input are integers.
Input
Input is given from Standard Input in the following format. The first line is as follows:
T
Then, T test cases follow. Each test case is given in the following format:
N
A_1 A_2 \cdots A_N
S
Output
For each test case, print a line containing `0` if x becomes 0 at the end of the game, and `1` otherwise.
Example
Input
3
2
1 2
10
2
1 1
10
6
2 3 4 5 6 7
111000
Output
1
0
0 | instruction | 0 | 27,145 | 19 | 54,290 |
"Correct Solution:
```
def solve(N, A, S):
bit = [0] * 64
for i in range(N-1,-1,-1):
Ai = A[i]
Si = S[i]
while Ai:
n = Ai.bit_length() -1
if bit[n] == 0 and Si == '1':
return 1
elif bit[n] == 0 and Si == '0':
bit[n] = Ai
break
Ai ^= bit[n]
return 0
T = int(input())
for _ in range(T):
N = int(input())
A = list(map(int, input().split()))
S = input()
print(solve(N, A, S))
``` | output | 1 | 27,145 | 19 | 54,291 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There are two persons, numbered 0 and 1, and a variable x whose initial value is 0. The two persons now play a game. The game is played in N rounds. The following should be done in the i-th round (1 \leq i \leq N):
* Person S_i does one of the following:
* Replace x with x \oplus A_i, where \oplus represents bitwise XOR.
* Do nothing.
Person 0 aims to have x=0 at the end of the game, while Person 1 aims to have x \neq 0 at the end of the game.
Determine whether x becomes 0 at the end of the game when the two persons play optimally.
Solve T test cases for each input file.
Constraints
* 1 \leq T \leq 100
* 1 \leq N \leq 200
* 1 \leq A_i \leq 10^{18}
* S is a string of length N consisting of `0` and `1`.
* All numbers in input are integers.
Input
Input is given from Standard Input in the following format. The first line is as follows:
T
Then, T test cases follow. Each test case is given in the following format:
N
A_1 A_2 \cdots A_N
S
Output
For each test case, print a line containing `0` if x becomes 0 at the end of the game, and `1` otherwise.
Example
Input
3
2
1 2
10
2
1 1
10
6
2 3 4 5 6 7
111000
Output
1
0
0
Submitted Solution:
```
#!python3
import sys
iim = lambda: map(int, sys.stdin.readline().rstrip().split())
def f(a, s, n):
if s[-1] == "1":
return 1
X = max(a).bit_length()
B = [None] * X
for i in range(n-1, -1, -1):
ai, si = a[i], s[i]
if si == "0":
while True:
x = ai.bit_length() - 1
if B[x] == ai: break
elif B[x] == None:
B[x] = ai
X -= 1
if X == 0:
return 0
break
ai ^= B[x]
else:
while True:
x = ai.bit_length() - 1
if B[x] == ai: break
elif B[x] == None:
return 1
ai ^= B[x]
return 0
def resolve():
T = int(input())
ans = []
for i in range(T):
N = int(input())
A = list(iim())
S = input()
ans.append(f(A, S, N))
print(*ans, sep="\n")
if __name__ == "__main__":
resolve()
``` | instruction | 0 | 27,146 | 19 | 54,292 |
Yes | output | 1 | 27,146 | 19 | 54,293 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There are two persons, numbered 0 and 1, and a variable x whose initial value is 0. The two persons now play a game. The game is played in N rounds. The following should be done in the i-th round (1 \leq i \leq N):
* Person S_i does one of the following:
* Replace x with x \oplus A_i, where \oplus represents bitwise XOR.
* Do nothing.
Person 0 aims to have x=0 at the end of the game, while Person 1 aims to have x \neq 0 at the end of the game.
Determine whether x becomes 0 at the end of the game when the two persons play optimally.
Solve T test cases for each input file.
Constraints
* 1 \leq T \leq 100
* 1 \leq N \leq 200
* 1 \leq A_i \leq 10^{18}
* S is a string of length N consisting of `0` and `1`.
* All numbers in input are integers.
Input
Input is given from Standard Input in the following format. The first line is as follows:
T
Then, T test cases follow. Each test case is given in the following format:
N
A_1 A_2 \cdots A_N
S
Output
For each test case, print a line containing `0` if x becomes 0 at the end of the game, and `1` otherwise.
Example
Input
3
2
1 2
10
2
1 1
10
6
2 3 4 5 6 7
111000
Output
1
0
0
Submitted Solution:
```
import sys
input = sys.stdin.readline
class BaseXor:
def __init__(self):
self.size = 0
self.base = []
def base_calculate(self, x, b):
return min(x, x ^ b)
def make_base(self, x):
for b in self.base:
x = self.base_calculate(x, b)
return x
def change_base(self, x):
for i in range(self.size):
self.base[i] = self.base_calculate(self.base[i], x)
def judge_linearly_dependent(self, x, value=False):
x = self.make_base(x)
res = True if x else False
res = (res, x) if value else res
return res
def add_base(self, x):
judge, x = self.judge_linearly_dependent(x, value=True)
if judge:
self.change_base(x)
self.base.append(x)
self.size += 1
return True
return False
def solve(n, a, s):
base = BaseXor()
judge = False
for i in range(n-1, -1, -1):
x = s[i]
if x == "0":
base.add_base(a[i])
else:
judge = base.judge_linearly_dependent(a[i])
if judge:
break
res = 1 if judge else 0
return res
def main():
t = int(input())
ans = [0]*t
for i in range(t):
n = int(input())
a = list(map(int, input().split()))
s = input()
res = solve(n, a, s)
ans[i] = res
print(*ans, sep="\n")
if __name__ == "__main__":
main()
``` | instruction | 0 | 27,147 | 19 | 54,294 |
Yes | output | 1 | 27,147 | 19 | 54,295 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There are two persons, numbered 0 and 1, and a variable x whose initial value is 0. The two persons now play a game. The game is played in N rounds. The following should be done in the i-th round (1 \leq i \leq N):
* Person S_i does one of the following:
* Replace x with x \oplus A_i, where \oplus represents bitwise XOR.
* Do nothing.
Person 0 aims to have x=0 at the end of the game, while Person 1 aims to have x \neq 0 at the end of the game.
Determine whether x becomes 0 at the end of the game when the two persons play optimally.
Solve T test cases for each input file.
Constraints
* 1 \leq T \leq 100
* 1 \leq N \leq 200
* 1 \leq A_i \leq 10^{18}
* S is a string of length N consisting of `0` and `1`.
* All numbers in input are integers.
Input
Input is given from Standard Input in the following format. The first line is as follows:
T
Then, T test cases follow. Each test case is given in the following format:
N
A_1 A_2 \cdots A_N
S
Output
For each test case, print a line containing `0` if x becomes 0 at the end of the game, and `1` otherwise.
Example
Input
3
2
1 2
10
2
1 1
10
6
2 3 4 5 6 7
111000
Output
1
0
0
Submitted Solution:
```
#!/usr/bin/env python3
import sys
input = sys.stdin.readline
t = int(input())
for _ in range(t):
n = int(input())
a = [int(item) for item in input().split()]
s = input().rstrip()
if s[-1] == "1":
print(1)
continue
group = []
prev = "-1"
for ch, num in zip(s, a):
if prev != ch:
group.append([])
group[-1].append(num)
prev = ch
group.reverse()
tools = []
ok = True
for itr, g in enumerate(group):
if itr % 2 == 0:
for item in g:
tools.append(item)
else:
tl = tools[:]
index = 0
for i in range(64, -1, -1):
flag = 0
for j in range(index, len(tl)):
if tl[j] & (1 << i):
flag = 1
tl[index], tl[j] = tl[j], tl[index]
break
for j in range(index + 1, len(tl)):
if tl[j] & 1 << i:
tl[j] ^= tl[index]
if flag == 1:
index += 1
for item in g:
current = 0
for val in tl:
index = len(bin(val)) - 3
if item >> index != current >> index:
current ^= val
if current != item:
ok = False
if ok:
print(0)
else:
print(1)
``` | instruction | 0 | 27,148 | 19 | 54,296 |
Yes | output | 1 | 27,148 | 19 | 54,297 |
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