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 |
|---|---|---|---|---|---|
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Edogawa Conan got tired of solving cases, and invited his friend, Professor Agasa, over. They decided to play a game of cards. Conan has n cards, and the i-th card has a number ai written on it.
They take turns playing, starting with Conan. In each turn, the player chooses a card and removes it. Also, he removes all cards having a number strictly lesser than the number on the chosen card. Formally, if the player chooses the i-th card, he removes that card and removes the j-th card for all j such that aj < ai.
A player loses if he cannot make a move on his turn, that is, he loses if there are no cards left. Predict the outcome of the game, assuming both players play optimally.
Input
The first line contains an integer n (1 ≤ n ≤ 105) — the number of cards Conan has.
The next line contains n integers a1, a2, ..., an (1 ≤ ai ≤ 105), where ai is the number on the i-th card.
Output
If Conan wins, print "Conan" (without quotes), otherwise print "Agasa" (without quotes).
Examples
Input
3
4 5 7
Output
Conan
Input
2
1 1
Output
Agasa
Note
In the first example, Conan can just choose the card having number 7 on it and hence remove all the cards. After that, there are no cards left on Agasa's turn.
In the second example, no matter which card Conan chooses, there will be one one card left, which Agasa can choose. After that, there are no cards left when it becomes Conan's turn again.
Submitted Solution:
```
input()
from collections import Counter as c
print('Conan' if [i for i in c(map(int , input().split())).values() if i % 2 ] else 'Agasa')
``` | instruction | 0 | 2,194 | 19 | 4,388 |
Yes | output | 1 | 2,194 | 19 | 4,389 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Edogawa Conan got tired of solving cases, and invited his friend, Professor Agasa, over. They decided to play a game of cards. Conan has n cards, and the i-th card has a number ai written on it.
They take turns playing, starting with Conan. In each turn, the player chooses a card and removes it. Also, he removes all cards having a number strictly lesser than the number on the chosen card. Formally, if the player chooses the i-th card, he removes that card and removes the j-th card for all j such that aj < ai.
A player loses if he cannot make a move on his turn, that is, he loses if there are no cards left. Predict the outcome of the game, assuming both players play optimally.
Input
The first line contains an integer n (1 ≤ n ≤ 105) — the number of cards Conan has.
The next line contains n integers a1, a2, ..., an (1 ≤ ai ≤ 105), where ai is the number on the i-th card.
Output
If Conan wins, print "Conan" (without quotes), otherwise print "Agasa" (without quotes).
Examples
Input
3
4 5 7
Output
Conan
Input
2
1 1
Output
Agasa
Note
In the first example, Conan can just choose the card having number 7 on it and hence remove all the cards. After that, there are no cards left on Agasa's turn.
In the second example, no matter which card Conan chooses, there will be one one card left, which Agasa can choose. After that, there are no cards left when it becomes Conan's turn again.
Submitted Solution:
```
#import math
#t=int(input())
#for i in range(t):
n=int(input())
#n,k = map(int, input().strip().split(' '))
lst = list(map(int, input().strip().split(' ')))
c=lst.count(max(lst))
if c%2==0:
print('Agasa')
else:
print('Conan')
``` | instruction | 0 | 2,195 | 19 | 4,390 |
No | output | 1 | 2,195 | 19 | 4,391 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Edogawa Conan got tired of solving cases, and invited his friend, Professor Agasa, over. They decided to play a game of cards. Conan has n cards, and the i-th card has a number ai written on it.
They take turns playing, starting with Conan. In each turn, the player chooses a card and removes it. Also, he removes all cards having a number strictly lesser than the number on the chosen card. Formally, if the player chooses the i-th card, he removes that card and removes the j-th card for all j such that aj < ai.
A player loses if he cannot make a move on his turn, that is, he loses if there are no cards left. Predict the outcome of the game, assuming both players play optimally.
Input
The first line contains an integer n (1 ≤ n ≤ 105) — the number of cards Conan has.
The next line contains n integers a1, a2, ..., an (1 ≤ ai ≤ 105), where ai is the number on the i-th card.
Output
If Conan wins, print "Conan" (without quotes), otherwise print "Agasa" (without quotes).
Examples
Input
3
4 5 7
Output
Conan
Input
2
1 1
Output
Agasa
Note
In the first example, Conan can just choose the card having number 7 on it and hence remove all the cards. After that, there are no cards left on Agasa's turn.
In the second example, no matter which card Conan chooses, there will be one one card left, which Agasa can choose. After that, there are no cards left when it becomes Conan's turn again.
Submitted Solution:
```
n=int(input())
a=input().split()
for i in range(n):
a[i]=int(a[i])
a.sort()
print(a)
k=0
h=a[0]
for i in a:
if(i==h):
if(k==1):
k=0
else:
k=1
else:
if(k==1):
p=1
break
k=1
h=i
if(k==1):
print("Conan")
else:
print("Agasa")
``` | instruction | 0 | 2,196 | 19 | 4,392 |
No | output | 1 | 2,196 | 19 | 4,393 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Edogawa Conan got tired of solving cases, and invited his friend, Professor Agasa, over. They decided to play a game of cards. Conan has n cards, and the i-th card has a number ai written on it.
They take turns playing, starting with Conan. In each turn, the player chooses a card and removes it. Also, he removes all cards having a number strictly lesser than the number on the chosen card. Formally, if the player chooses the i-th card, he removes that card and removes the j-th card for all j such that aj < ai.
A player loses if he cannot make a move on his turn, that is, he loses if there are no cards left. Predict the outcome of the game, assuming both players play optimally.
Input
The first line contains an integer n (1 ≤ n ≤ 105) — the number of cards Conan has.
The next line contains n integers a1, a2, ..., an (1 ≤ ai ≤ 105), where ai is the number on the i-th card.
Output
If Conan wins, print "Conan" (without quotes), otherwise print "Agasa" (without quotes).
Examples
Input
3
4 5 7
Output
Conan
Input
2
1 1
Output
Agasa
Note
In the first example, Conan can just choose the card having number 7 on it and hence remove all the cards. After that, there are no cards left on Agasa's turn.
In the second example, no matter which card Conan chooses, there will be one one card left, which Agasa can choose. After that, there are no cards left when it becomes Conan's turn again.
Submitted Solution:
```
import sys
import string
from collections import Counter, defaultdict
from math import fsum, sqrt, gcd, ceil, factorial
from operator import add
inf = float('inf')
# input = sys.stdin.readline
flush = lambda : sys.stdout.flush
comb = lambda x , y : (factorial(x) // factorial(y)) // factorial(x - y)
#inputs
# ip = lambda : input().rstrip()
ip = lambda : input()
ii = lambda : int(input())
r = lambda : map(int, input().split())
rr = lambda : list(r())
n = ii()
arr = rr()
m = max(arr)
if arr.count(m) == n:
print(["Conan" , "Agasa"][n%2==0])
else:
print(["Conan" , "Agasa"][arr.count(m)%2==0])
``` | instruction | 0 | 2,197 | 19 | 4,394 |
No | output | 1 | 2,197 | 19 | 4,395 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Edogawa Conan got tired of solving cases, and invited his friend, Professor Agasa, over. They decided to play a game of cards. Conan has n cards, and the i-th card has a number ai written on it.
They take turns playing, starting with Conan. In each turn, the player chooses a card and removes it. Also, he removes all cards having a number strictly lesser than the number on the chosen card. Formally, if the player chooses the i-th card, he removes that card and removes the j-th card for all j such that aj < ai.
A player loses if he cannot make a move on his turn, that is, he loses if there are no cards left. Predict the outcome of the game, assuming both players play optimally.
Input
The first line contains an integer n (1 ≤ n ≤ 105) — the number of cards Conan has.
The next line contains n integers a1, a2, ..., an (1 ≤ ai ≤ 105), where ai is the number on the i-th card.
Output
If Conan wins, print "Conan" (without quotes), otherwise print "Agasa" (without quotes).
Examples
Input
3
4 5 7
Output
Conan
Input
2
1 1
Output
Agasa
Note
In the first example, Conan can just choose the card having number 7 on it and hence remove all the cards. After that, there are no cards left on Agasa's turn.
In the second example, no matter which card Conan chooses, there will be one one card left, which Agasa can choose. After that, there are no cards left when it becomes Conan's turn again.
Submitted Solution:
```
yolo=int(input())
pren=[int(z) for z in input().split()]
max=-99999999999999
k=0
for i in range(yolo):
if max<pren[i]:
max=pren[i]
k=1
elif max==pren[i]:
k+=1
if k%2==1:
print("Conan")
else:
print("Agasa")
``` | instruction | 0 | 2,198 | 19 | 4,396 |
No | output | 1 | 2,198 | 19 | 4,397 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
A telephone number is a sequence of exactly 11 digits such that its first digit is 8.
Vasya and Petya are playing a game. Initially they have a string s of length n (n is odd) consisting of digits. Vasya makes the first move, then players alternate turns. In one move the player must choose a character and erase it from the current string. For example, if the current string 1121, after the player's move it may be 112, 111 or 121. The game ends when the length of string s becomes 11. If the resulting string is a telephone number, Vasya wins, otherwise Petya wins.
You have to determine if Vasya has a winning strategy (that is, if Vasya can win the game no matter which characters Petya chooses during his moves).
Input
The first line contains one integer n (13 ≤ n < 10^5, n is odd) — the length of string s.
The second line contains the string s (|s| = n) consisting only of decimal digits.
Output
If Vasya has a strategy that guarantees him victory, print YES.
Otherwise print NO.
Examples
Input
13
8380011223344
Output
YES
Input
15
807345619350641
Output
NO
Note
In the first example Vasya needs to erase the second character. Then Petya cannot erase a character from the remaining string 880011223344 so that it does not become a telephone number.
In the second example after Vasya's turn Petya can erase one character character 8. The resulting string can't be a telephone number, because there is no digit 8 at all.
Submitted Solution:
```
'''
___ ___ ___ ___ ___ ___
/\__\ /\ \ _____ /\ \ /\ \ /\ \ /\__\
/:/ _/_ \:\ \ /::\ \ \:\ \ ___ /::\ \ |::\ \ ___ /:/ _/_
/:/ /\ \ \:\ \ /:/\:\ \ \:\ \ /\__\ /:/\:\__\ |:|:\ \ /\__\ /:/ /\ \
/:/ /::\ \ ___ \:\ \ /:/ \:\__\ ___ /::\ \ /:/__/ /:/ /:/ / __|:|\:\ \ /:/ / /:/ /::\ \
/:/_/:/\:\__\ /\ \ \:\__\ /:/__/ \:|__| /\ /:/\:\__\ /::\ \ /:/_/:/__/___ /::::|_\:\__\ /:/__/ /:/_/:/\:\__\
\:\/:/ /:/ / \:\ \ /:/ / \:\ \ /:/ / \:\/:/ \/__/ \/\:\ \__ \:\/:::::/ / \:\~~\ \/__/ /::\ \ \:\/:/ /:/ /
\::/ /:/ / \:\ /:/ / \:\ /:/ / \::/__/ ~~\:\/\__\ \::/~~/~~~~ \:\ \ /:/\:\ \ \::/ /:/ /
\/_/:/ / \:\/:/ / \:\/:/ / \:\ \ \::/ / \:\~~\ \:\ \ \/__\:\ \ \/_/:/ /
/:/ / \::/ / \::/ / \:\__\ /:/ / \:\__\ \:\__\ \:\__\ /:/ /
\/__/ \/__/ \/__/ \/__/ \/__/ \/__/ \/__/ \/__/ \/__/
'''
"""
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░░░░░░░░░░░░░░░░░░░░
"""
import sys
import math
import collections
import operator as op
from collections import deque
from math import gcd, inf, sqrt, pi, cos, sin, ceil, log2
from bisect import bisect_right, bisect_left
# sys.stdin = open('input.txt', 'r')
# sys.stdout = open('output.txt', 'w')
from functools import reduce
from sys import stdin, stdout, setrecursionlimit
setrecursionlimit(2**20)
def ncr(n, r):
r = min(r, n - r)
numer = reduce(op.mul, range(n, n - r, -1), 1)
denom = reduce(op.mul, range(1, r + 1), 1)
return numer // denom # or / in Python 2
def prime_factors(n):
i = 2
factors = []
while i * i <= n:
if n % i:
i += 1
else:
n //= i
factors.append(i)
if n > 1:
factors.append(n)
return (list(factors))
def sumDigits(no):
return 0 if no == 0 else int(no % 10) + sumDigits(int(no / 10))
MOD = 1000000007
PMOD = 998244353
N = 10**9 + 7
LOGN = 30
T = 1
# T = int(stdin.readline())
for _ in range(T):
# n = list(map(int, stdin.readline().rstrip().split()))
n = int(stdin.readline())
# a = list(map(int, stdin.readline().rstrip().split()))
# l = list(map(int, stdin.readline().rstrip().split()))
a = list(stdin.readline().strip('\n'))
# t = str(stdin.readline().strip('\n'))
# m = int(stdin.readline())
# s = list(map(int, stdin.readline().rstrip().split())
n8 = 0
ne = 0
for i in range(n):
if a[i] == '8':
n8 += 1
li = -1
for i in range(n - 1, -1, -1):
if a[i] == '8':
li = i
break
for i in range(li + 1):
if a[i] != '8':
ne += 1
break
n -= 11
if n8 > n // 2:
if ne <= n // 2 and li + 1 > n:
print('YES')
else:
print('NO')
continue
print('NO')
``` | instruction | 0 | 2,519 | 19 | 5,038 |
No | output | 1 | 2,519 | 19 | 5,039 |
Provide tags and a correct Python 3 solution for this coding contest problem.
There are n piles of stones, where the i-th pile has a_i stones. Two people play a game, where they take alternating turns removing stones.
In a move, a player may remove a positive number of stones from the first non-empty pile (the pile with the minimal index, that has at least one stone). The first player who cannot make a move (because all piles are empty) loses the game. If both players play optimally, determine the winner of the game.
Input
The first line contains a single integer t (1≤ t≤ 1000) — the number of test cases. Next 2t lines contain descriptions of test cases.
The first line of each test case contains a single integer n (1≤ n≤ 10^5) — the number of piles.
The second line of each test case contains n integers a_1,…,a_n (1≤ a_i≤ 10^9) — a_i is equal to the number of stones in the i-th pile.
It is guaranteed that the sum of n for all test cases does not exceed 10^5.
Output
For each test case, if the player who makes the first move will win, output "First". Otherwise, output "Second".
Example
Input
7
3
2 5 4
8
1 1 1 1 1 1 1 1
6
1 2 3 4 5 6
6
1 1 2 1 2 2
1
1000000000
5
1 2 2 1 1
3
1 1 1
Output
First
Second
Second
First
First
Second
First
Note
In the first test case, the first player will win the game. His winning strategy is:
1. The first player should take the stones from the first pile. He will take 1 stone. The numbers of stones in piles will be [1, 5, 4].
2. The second player should take the stones from the first pile. He will take 1 stone because he can't take any other number of stones. The numbers of stones in piles will be [0, 5, 4].
3. The first player should take the stones from the second pile because the first pile is empty. He will take 4 stones. The numbers of stones in piles will be [0, 1, 4].
4. The second player should take the stones from the second pile because the first pile is empty. He will take 1 stone because he can't take any other number of stones. The numbers of stones in piles will be [0, 0, 4].
5. The first player should take the stones from the third pile because the first and second piles are empty. He will take 4 stones. The numbers of stones in piles will be [0, 0, 0].
6. The second player will lose the game because all piles will be empty. | instruction | 0 | 2,618 | 19 | 5,236 |
Tags: dp, games
Correct Solution:
```
t = int(input())
for _ in range(t):
n = int(input())
arr = list(map(int,input().split()))
index = 0
count = 0
while index < n-1 and arr[index] == 1:
index += 1
count += 1
if count&1:
print("Second")
else:
print("First")
``` | output | 1 | 2,618 | 19 | 5,237 |
Provide tags and a correct Python 3 solution for this coding contest problem.
There are n piles of stones, where the i-th pile has a_i stones. Two people play a game, where they take alternating turns removing stones.
In a move, a player may remove a positive number of stones from the first non-empty pile (the pile with the minimal index, that has at least one stone). The first player who cannot make a move (because all piles are empty) loses the game. If both players play optimally, determine the winner of the game.
Input
The first line contains a single integer t (1≤ t≤ 1000) — the number of test cases. Next 2t lines contain descriptions of test cases.
The first line of each test case contains a single integer n (1≤ n≤ 10^5) — the number of piles.
The second line of each test case contains n integers a_1,…,a_n (1≤ a_i≤ 10^9) — a_i is equal to the number of stones in the i-th pile.
It is guaranteed that the sum of n for all test cases does not exceed 10^5.
Output
For each test case, if the player who makes the first move will win, output "First". Otherwise, output "Second".
Example
Input
7
3
2 5 4
8
1 1 1 1 1 1 1 1
6
1 2 3 4 5 6
6
1 1 2 1 2 2
1
1000000000
5
1 2 2 1 1
3
1 1 1
Output
First
Second
Second
First
First
Second
First
Note
In the first test case, the first player will win the game. His winning strategy is:
1. The first player should take the stones from the first pile. He will take 1 stone. The numbers of stones in piles will be [1, 5, 4].
2. The second player should take the stones from the first pile. He will take 1 stone because he can't take any other number of stones. The numbers of stones in piles will be [0, 5, 4].
3. The first player should take the stones from the second pile because the first pile is empty. He will take 4 stones. The numbers of stones in piles will be [0, 1, 4].
4. The second player should take the stones from the second pile because the first pile is empty. He will take 1 stone because he can't take any other number of stones. The numbers of stones in piles will be [0, 0, 4].
5. The first player should take the stones from the third pile because the first and second piles are empty. He will take 4 stones. The numbers of stones in piles will be [0, 0, 0].
6. The second player will lose the game because all piles will be empty. | instruction | 0 | 2,619 | 19 | 5,238 |
Tags: dp, games
Correct Solution:
```
for t in range(int(input())):
n=int(input())
l=list(map(int,input().split()))
if(l.count(1)==n):
if(n%2==0):
print('Second')
else:
print('First')
elif(len(l)==1):
print('First')
else:
for i in range(n):
if(l[i]>1):
if(i%2==0):
print('First')
break
else:
print('Second')
break
``` | output | 1 | 2,619 | 19 | 5,239 |
Provide tags and a correct Python 3 solution for this coding contest problem.
There are n piles of stones, where the i-th pile has a_i stones. Two people play a game, where they take alternating turns removing stones.
In a move, a player may remove a positive number of stones from the first non-empty pile (the pile with the minimal index, that has at least one stone). The first player who cannot make a move (because all piles are empty) loses the game. If both players play optimally, determine the winner of the game.
Input
The first line contains a single integer t (1≤ t≤ 1000) — the number of test cases. Next 2t lines contain descriptions of test cases.
The first line of each test case contains a single integer n (1≤ n≤ 10^5) — the number of piles.
The second line of each test case contains n integers a_1,…,a_n (1≤ a_i≤ 10^9) — a_i is equal to the number of stones in the i-th pile.
It is guaranteed that the sum of n for all test cases does not exceed 10^5.
Output
For each test case, if the player who makes the first move will win, output "First". Otherwise, output "Second".
Example
Input
7
3
2 5 4
8
1 1 1 1 1 1 1 1
6
1 2 3 4 5 6
6
1 1 2 1 2 2
1
1000000000
5
1 2 2 1 1
3
1 1 1
Output
First
Second
Second
First
First
Second
First
Note
In the first test case, the first player will win the game. His winning strategy is:
1. The first player should take the stones from the first pile. He will take 1 stone. The numbers of stones in piles will be [1, 5, 4].
2. The second player should take the stones from the first pile. He will take 1 stone because he can't take any other number of stones. The numbers of stones in piles will be [0, 5, 4].
3. The first player should take the stones from the second pile because the first pile is empty. He will take 4 stones. The numbers of stones in piles will be [0, 1, 4].
4. The second player should take the stones from the second pile because the first pile is empty. He will take 1 stone because he can't take any other number of stones. The numbers of stones in piles will be [0, 0, 4].
5. The first player should take the stones from the third pile because the first and second piles are empty. He will take 4 stones. The numbers of stones in piles will be [0, 0, 0].
6. The second player will lose the game because all piles will be empty. | instruction | 0 | 2,620 | 19 | 5,240 |
Tags: dp, games
Correct Solution:
```
'''input
7
3
2 5 4
8
1 1 1 1 1 1 1 1
6
1 2 3 4 5 6
6
1 1 2 1 2 2
1
1000000000
5
1 2 2 1 1
3
1 1 1
'''
import math
def solve():
n = int(input())
l = list(map(int,input().split()))
dp = [0]*n
dp[n-1] = 1
for i in range(n-2,-1,-1):
if dp[i+1] == 1:
# next state is winning
if l[i] == 1:
dp[i] = 0
else:
dp[i] = 1
else:
# next state is losing
dp[i] = 1
if dp[0] == 1:
print("First")
else:
print("Second")
t = 1
t = int(input())
while t > 0:
t-=1
solve()
``` | output | 1 | 2,620 | 19 | 5,241 |
Provide tags and a correct Python 3 solution for this coding contest problem.
There are n piles of stones, where the i-th pile has a_i stones. Two people play a game, where they take alternating turns removing stones.
In a move, a player may remove a positive number of stones from the first non-empty pile (the pile with the minimal index, that has at least one stone). The first player who cannot make a move (because all piles are empty) loses the game. If both players play optimally, determine the winner of the game.
Input
The first line contains a single integer t (1≤ t≤ 1000) — the number of test cases. Next 2t lines contain descriptions of test cases.
The first line of each test case contains a single integer n (1≤ n≤ 10^5) — the number of piles.
The second line of each test case contains n integers a_1,…,a_n (1≤ a_i≤ 10^9) — a_i is equal to the number of stones in the i-th pile.
It is guaranteed that the sum of n for all test cases does not exceed 10^5.
Output
For each test case, if the player who makes the first move will win, output "First". Otherwise, output "Second".
Example
Input
7
3
2 5 4
8
1 1 1 1 1 1 1 1
6
1 2 3 4 5 6
6
1 1 2 1 2 2
1
1000000000
5
1 2 2 1 1
3
1 1 1
Output
First
Second
Second
First
First
Second
First
Note
In the first test case, the first player will win the game. His winning strategy is:
1. The first player should take the stones from the first pile. He will take 1 stone. The numbers of stones in piles will be [1, 5, 4].
2. The second player should take the stones from the first pile. He will take 1 stone because he can't take any other number of stones. The numbers of stones in piles will be [0, 5, 4].
3. The first player should take the stones from the second pile because the first pile is empty. He will take 4 stones. The numbers of stones in piles will be [0, 1, 4].
4. The second player should take the stones from the second pile because the first pile is empty. He will take 1 stone because he can't take any other number of stones. The numbers of stones in piles will be [0, 0, 4].
5. The first player should take the stones from the third pile because the first and second piles are empty. He will take 4 stones. The numbers of stones in piles will be [0, 0, 0].
6. The second player will lose the game because all piles will be empty. | instruction | 0 | 2,621 | 19 | 5,242 |
Tags: dp, games
Correct Solution:
```
import sys
INP = lambda: sys.stdin.readline().strip()
INT = lambda: int(INP())
MAP = lambda: map(int, INP().split())
ARR = lambda: [int(i) for i in INP().split()]
def JOIN(arr, x=' '): return x.join([str(i) for i in arr])
def EXIT(x='NO'): print(x); exit()
for _ in range(INT()):
n = INT()
arr = ARR()
c = 0
for x in arr[:-1]:
if x>1: break
c += 1
if c%2: print('Second')
else: print('First')
``` | output | 1 | 2,621 | 19 | 5,243 |
Provide tags and a correct Python 3 solution for this coding contest problem.
There are n piles of stones, where the i-th pile has a_i stones. Two people play a game, where they take alternating turns removing stones.
In a move, a player may remove a positive number of stones from the first non-empty pile (the pile with the minimal index, that has at least one stone). The first player who cannot make a move (because all piles are empty) loses the game. If both players play optimally, determine the winner of the game.
Input
The first line contains a single integer t (1≤ t≤ 1000) — the number of test cases. Next 2t lines contain descriptions of test cases.
The first line of each test case contains a single integer n (1≤ n≤ 10^5) — the number of piles.
The second line of each test case contains n integers a_1,…,a_n (1≤ a_i≤ 10^9) — a_i is equal to the number of stones in the i-th pile.
It is guaranteed that the sum of n for all test cases does not exceed 10^5.
Output
For each test case, if the player who makes the first move will win, output "First". Otherwise, output "Second".
Example
Input
7
3
2 5 4
8
1 1 1 1 1 1 1 1
6
1 2 3 4 5 6
6
1 1 2 1 2 2
1
1000000000
5
1 2 2 1 1
3
1 1 1
Output
First
Second
Second
First
First
Second
First
Note
In the first test case, the first player will win the game. His winning strategy is:
1. The first player should take the stones from the first pile. He will take 1 stone. The numbers of stones in piles will be [1, 5, 4].
2. The second player should take the stones from the first pile. He will take 1 stone because he can't take any other number of stones. The numbers of stones in piles will be [0, 5, 4].
3. The first player should take the stones from the second pile because the first pile is empty. He will take 4 stones. The numbers of stones in piles will be [0, 1, 4].
4. The second player should take the stones from the second pile because the first pile is empty. He will take 1 stone because he can't take any other number of stones. The numbers of stones in piles will be [0, 0, 4].
5. The first player should take the stones from the third pile because the first and second piles are empty. He will take 4 stones. The numbers of stones in piles will be [0, 0, 0].
6. The second player will lose the game because all piles will be empty. | instruction | 0 | 2,622 | 19 | 5,244 |
Tags: dp, games
Correct Solution:
```
t = int(input())
for k in range(t):
n = int(input())
*a, = map(int, input().split())
if n == 1:
print('First')
continue
for i in range(n):
if a[i] > 1:
a[i] = 2
prev = 0
for i in range(n - 2, 0, -1):
if prev == 0:
if a[i] == 2:
continue
else:
prev = 1
else:
prev = 0
if prev == 0:
if a[0] == 2:
print('First')
else:
print('Second')
else:
print('First')
``` | output | 1 | 2,622 | 19 | 5,245 |
Provide tags and a correct Python 3 solution for this coding contest problem.
There are n piles of stones, where the i-th pile has a_i stones. Two people play a game, where they take alternating turns removing stones.
In a move, a player may remove a positive number of stones from the first non-empty pile (the pile with the minimal index, that has at least one stone). The first player who cannot make a move (because all piles are empty) loses the game. If both players play optimally, determine the winner of the game.
Input
The first line contains a single integer t (1≤ t≤ 1000) — the number of test cases. Next 2t lines contain descriptions of test cases.
The first line of each test case contains a single integer n (1≤ n≤ 10^5) — the number of piles.
The second line of each test case contains n integers a_1,…,a_n (1≤ a_i≤ 10^9) — a_i is equal to the number of stones in the i-th pile.
It is guaranteed that the sum of n for all test cases does not exceed 10^5.
Output
For each test case, if the player who makes the first move will win, output "First". Otherwise, output "Second".
Example
Input
7
3
2 5 4
8
1 1 1 1 1 1 1 1
6
1 2 3 4 5 6
6
1 1 2 1 2 2
1
1000000000
5
1 2 2 1 1
3
1 1 1
Output
First
Second
Second
First
First
Second
First
Note
In the first test case, the first player will win the game. His winning strategy is:
1. The first player should take the stones from the first pile. He will take 1 stone. The numbers of stones in piles will be [1, 5, 4].
2. The second player should take the stones from the first pile. He will take 1 stone because he can't take any other number of stones. The numbers of stones in piles will be [0, 5, 4].
3. The first player should take the stones from the second pile because the first pile is empty. He will take 4 stones. The numbers of stones in piles will be [0, 1, 4].
4. The second player should take the stones from the second pile because the first pile is empty. He will take 1 stone because he can't take any other number of stones. The numbers of stones in piles will be [0, 0, 4].
5. The first player should take the stones from the third pile because the first and second piles are empty. He will take 4 stones. The numbers of stones in piles will be [0, 0, 0].
6. The second player will lose the game because all piles will be empty. | instruction | 0 | 2,623 | 19 | 5,246 |
Tags: dp, games
Correct Solution:
```
# def return_winner(a,int_winner):
# if a[0]!=1:
# print('First')
# else:
# b = a[:-1]
# b = b[1:]
# print(b)
# if 1 in b:
# c = b.index(1)
# print(c)
# if list(set(b[:c+1]))!=[1]:
# print('Second')
# else:
# print('First')
# else:
# print('Second')
# pass
t = int(input())
for t1 in range(t):
n = int(input())
a = [int(n1) for n1 in input().split()]
count = 0
for i in range(len(a)):
if a[i]!=1:
count = 1
if i%2==0:
print('First')
break
else:
print('Second')
break
else:
pass
if count==0:
if n%2==0:
print('Second')
else:
print('First')
# if list(set(a))==[1]:
# if len(a)%2==0:
# print('Second')
# else:
# print('First')
# elif a[0]!=1:
# print('First')
# else:
# b = a[:-1]
# b = b[1:]
# print(b)
# if 1 in b:
# c = b.index(1)
# print(c)
# if list(set(b[:c+1]))!=[1]:
# print('Second')
# else:
# print('First')
# else:
# print('Second')
``` | output | 1 | 2,623 | 19 | 5,247 |
Provide tags and a correct Python 3 solution for this coding contest problem.
There are n piles of stones, where the i-th pile has a_i stones. Two people play a game, where they take alternating turns removing stones.
In a move, a player may remove a positive number of stones from the first non-empty pile (the pile with the minimal index, that has at least one stone). The first player who cannot make a move (because all piles are empty) loses the game. If both players play optimally, determine the winner of the game.
Input
The first line contains a single integer t (1≤ t≤ 1000) — the number of test cases. Next 2t lines contain descriptions of test cases.
The first line of each test case contains a single integer n (1≤ n≤ 10^5) — the number of piles.
The second line of each test case contains n integers a_1,…,a_n (1≤ a_i≤ 10^9) — a_i is equal to the number of stones in the i-th pile.
It is guaranteed that the sum of n for all test cases does not exceed 10^5.
Output
For each test case, if the player who makes the first move will win, output "First". Otherwise, output "Second".
Example
Input
7
3
2 5 4
8
1 1 1 1 1 1 1 1
6
1 2 3 4 5 6
6
1 1 2 1 2 2
1
1000000000
5
1 2 2 1 1
3
1 1 1
Output
First
Second
Second
First
First
Second
First
Note
In the first test case, the first player will win the game. His winning strategy is:
1. The first player should take the stones from the first pile. He will take 1 stone. The numbers of stones in piles will be [1, 5, 4].
2. The second player should take the stones from the first pile. He will take 1 stone because he can't take any other number of stones. The numbers of stones in piles will be [0, 5, 4].
3. The first player should take the stones from the second pile because the first pile is empty. He will take 4 stones. The numbers of stones in piles will be [0, 1, 4].
4. The second player should take the stones from the second pile because the first pile is empty. He will take 1 stone because he can't take any other number of stones. The numbers of stones in piles will be [0, 0, 4].
5. The first player should take the stones from the third pile because the first and second piles are empty. He will take 4 stones. The numbers of stones in piles will be [0, 0, 0].
6. The second player will lose the game because all piles will be empty. | instruction | 0 | 2,624 | 19 | 5,248 |
Tags: dp, games
Correct Solution:
```
t=int(input())
for _ in range(t):
n=int(input())
arr=list(map(int,input().split()))
cnt=arr.count(1)
if cnt==0:
print('First')
elif cnt==n:
if cnt%2==0:
print('Second')
else:
print('First')
else:
for i in range(n):
if arr[i]!=1:
if i%2==0:
print('First')
break
else:
print('Second')
break
``` | output | 1 | 2,624 | 19 | 5,249 |
Provide tags and a correct Python 3 solution for this coding contest problem.
There are n piles of stones, where the i-th pile has a_i stones. Two people play a game, where they take alternating turns removing stones.
In a move, a player may remove a positive number of stones from the first non-empty pile (the pile with the minimal index, that has at least one stone). The first player who cannot make a move (because all piles are empty) loses the game. If both players play optimally, determine the winner of the game.
Input
The first line contains a single integer t (1≤ t≤ 1000) — the number of test cases. Next 2t lines contain descriptions of test cases.
The first line of each test case contains a single integer n (1≤ n≤ 10^5) — the number of piles.
The second line of each test case contains n integers a_1,…,a_n (1≤ a_i≤ 10^9) — a_i is equal to the number of stones in the i-th pile.
It is guaranteed that the sum of n for all test cases does not exceed 10^5.
Output
For each test case, if the player who makes the first move will win, output "First". Otherwise, output "Second".
Example
Input
7
3
2 5 4
8
1 1 1 1 1 1 1 1
6
1 2 3 4 5 6
6
1 1 2 1 2 2
1
1000000000
5
1 2 2 1 1
3
1 1 1
Output
First
Second
Second
First
First
Second
First
Note
In the first test case, the first player will win the game. His winning strategy is:
1. The first player should take the stones from the first pile. He will take 1 stone. The numbers of stones in piles will be [1, 5, 4].
2. The second player should take the stones from the first pile. He will take 1 stone because he can't take any other number of stones. The numbers of stones in piles will be [0, 5, 4].
3. The first player should take the stones from the second pile because the first pile is empty. He will take 4 stones. The numbers of stones in piles will be [0, 1, 4].
4. The second player should take the stones from the second pile because the first pile is empty. He will take 1 stone because he can't take any other number of stones. The numbers of stones in piles will be [0, 0, 4].
5. The first player should take the stones from the third pile because the first and second piles are empty. He will take 4 stones. The numbers of stones in piles will be [0, 0, 0].
6. The second player will lose the game because all piles will be empty. | instruction | 0 | 2,625 | 19 | 5,250 |
Tags: dp, games
Correct Solution:
```
for i in range(int(input())):
n=int(input())
l=[int(num) for num in input().split()]
k=-1
for i in range(n):
if(l[i]>1):
k=i
break
if(k!=-1):
if(k%2!=0):
print("Second")
else:
print("First")
else:
if(n%2==0):
print("Second")
else:
print("First")
``` | output | 1 | 2,625 | 19 | 5,251 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There are n piles of stones, where the i-th pile has a_i stones. Two people play a game, where they take alternating turns removing stones.
In a move, a player may remove a positive number of stones from the first non-empty pile (the pile with the minimal index, that has at least one stone). The first player who cannot make a move (because all piles are empty) loses the game. If both players play optimally, determine the winner of the game.
Input
The first line contains a single integer t (1≤ t≤ 1000) — the number of test cases. Next 2t lines contain descriptions of test cases.
The first line of each test case contains a single integer n (1≤ n≤ 10^5) — the number of piles.
The second line of each test case contains n integers a_1,…,a_n (1≤ a_i≤ 10^9) — a_i is equal to the number of stones in the i-th pile.
It is guaranteed that the sum of n for all test cases does not exceed 10^5.
Output
For each test case, if the player who makes the first move will win, output "First". Otherwise, output "Second".
Example
Input
7
3
2 5 4
8
1 1 1 1 1 1 1 1
6
1 2 3 4 5 6
6
1 1 2 1 2 2
1
1000000000
5
1 2 2 1 1
3
1 1 1
Output
First
Second
Second
First
First
Second
First
Note
In the first test case, the first player will win the game. His winning strategy is:
1. The first player should take the stones from the first pile. He will take 1 stone. The numbers of stones in piles will be [1, 5, 4].
2. The second player should take the stones from the first pile. He will take 1 stone because he can't take any other number of stones. The numbers of stones in piles will be [0, 5, 4].
3. The first player should take the stones from the second pile because the first pile is empty. He will take 4 stones. The numbers of stones in piles will be [0, 1, 4].
4. The second player should take the stones from the second pile because the first pile is empty. He will take 1 stone because he can't take any other number of stones. The numbers of stones in piles will be [0, 0, 4].
5. The first player should take the stones from the third pile because the first and second piles are empty. He will take 4 stones. The numbers of stones in piles will be [0, 0, 0].
6. The second player will lose the game because all piles will be empty.
Submitted Solution:
```
t = int(input())
for _ in range(t):
n = int(input())
inp = [int(j) for j in input().split()]
cntOnes = 0
for i in range(n):
if inp[i] != 1:
break
if inp[i] == 1:
cntOnes = cntOnes+1
if cntOnes == n and n%2 == 0:
print("Second")
continue
if cntOnes == n and n%2 == 1:
print("First")
continue
if (cntOnes)%2 == 1:
print("Second")
else:
print("First")
``` | instruction | 0 | 2,626 | 19 | 5,252 |
Yes | output | 1 | 2,626 | 19 | 5,253 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There are n piles of stones, where the i-th pile has a_i stones. Two people play a game, where they take alternating turns removing stones.
In a move, a player may remove a positive number of stones from the first non-empty pile (the pile with the minimal index, that has at least one stone). The first player who cannot make a move (because all piles are empty) loses the game. If both players play optimally, determine the winner of the game.
Input
The first line contains a single integer t (1≤ t≤ 1000) — the number of test cases. Next 2t lines contain descriptions of test cases.
The first line of each test case contains a single integer n (1≤ n≤ 10^5) — the number of piles.
The second line of each test case contains n integers a_1,…,a_n (1≤ a_i≤ 10^9) — a_i is equal to the number of stones in the i-th pile.
It is guaranteed that the sum of n for all test cases does not exceed 10^5.
Output
For each test case, if the player who makes the first move will win, output "First". Otherwise, output "Second".
Example
Input
7
3
2 5 4
8
1 1 1 1 1 1 1 1
6
1 2 3 4 5 6
6
1 1 2 1 2 2
1
1000000000
5
1 2 2 1 1
3
1 1 1
Output
First
Second
Second
First
First
Second
First
Note
In the first test case, the first player will win the game. His winning strategy is:
1. The first player should take the stones from the first pile. He will take 1 stone. The numbers of stones in piles will be [1, 5, 4].
2. The second player should take the stones from the first pile. He will take 1 stone because he can't take any other number of stones. The numbers of stones in piles will be [0, 5, 4].
3. The first player should take the stones from the second pile because the first pile is empty. He will take 4 stones. The numbers of stones in piles will be [0, 1, 4].
4. The second player should take the stones from the second pile because the first pile is empty. He will take 1 stone because he can't take any other number of stones. The numbers of stones in piles will be [0, 0, 4].
5. The first player should take the stones from the third pile because the first and second piles are empty. He will take 4 stones. The numbers of stones in piles will be [0, 0, 0].
6. The second player will lose the game because all piles will be empty.
Submitted Solution:
```
#list(map(int,input().split()))
for _ in range(int(input())):
n=int(input())
l=list(map(int,input().split()))
fl=0
flag=0
for i in range(len(l)):
if(l[i]==1):
flag=(flag+1)%2
else:
fl=1
if(flag==0):
print("First")
else:
print("Second")
break
if(fl==0):
if(flag==0):
print("Second")
else:
print("First")
``` | instruction | 0 | 2,627 | 19 | 5,254 |
Yes | output | 1 | 2,627 | 19 | 5,255 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There are n piles of stones, where the i-th pile has a_i stones. Two people play a game, where they take alternating turns removing stones.
In a move, a player may remove a positive number of stones from the first non-empty pile (the pile with the minimal index, that has at least one stone). The first player who cannot make a move (because all piles are empty) loses the game. If both players play optimally, determine the winner of the game.
Input
The first line contains a single integer t (1≤ t≤ 1000) — the number of test cases. Next 2t lines contain descriptions of test cases.
The first line of each test case contains a single integer n (1≤ n≤ 10^5) — the number of piles.
The second line of each test case contains n integers a_1,…,a_n (1≤ a_i≤ 10^9) — a_i is equal to the number of stones in the i-th pile.
It is guaranteed that the sum of n for all test cases does not exceed 10^5.
Output
For each test case, if the player who makes the first move will win, output "First". Otherwise, output "Second".
Example
Input
7
3
2 5 4
8
1 1 1 1 1 1 1 1
6
1 2 3 4 5 6
6
1 1 2 1 2 2
1
1000000000
5
1 2 2 1 1
3
1 1 1
Output
First
Second
Second
First
First
Second
First
Note
In the first test case, the first player will win the game. His winning strategy is:
1. The first player should take the stones from the first pile. He will take 1 stone. The numbers of stones in piles will be [1, 5, 4].
2. The second player should take the stones from the first pile. He will take 1 stone because he can't take any other number of stones. The numbers of stones in piles will be [0, 5, 4].
3. The first player should take the stones from the second pile because the first pile is empty. He will take 4 stones. The numbers of stones in piles will be [0, 1, 4].
4. The second player should take the stones from the second pile because the first pile is empty. He will take 1 stone because he can't take any other number of stones. The numbers of stones in piles will be [0, 0, 4].
5. The first player should take the stones from the third pile because the first and second piles are empty. He will take 4 stones. The numbers of stones in piles will be [0, 0, 0].
6. The second player will lose the game because all piles will be empty.
Submitted Solution:
```
t=int(input())
ans=[]
for i in range(t):
n = int(input())
p = input()
a = list(map(int, p.split()))
a=list(filter(lambda i: i!=0, a))
c=0
j=0
while j<len(a)-1 and a[j]==1:
c+=1
j+=1
if c%2==0:
ans.append('First')
else:
ans.append('Second')
for i in ans:
print(i)
``` | instruction | 0 | 2,628 | 19 | 5,256 |
Yes | output | 1 | 2,628 | 19 | 5,257 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There are n piles of stones, where the i-th pile has a_i stones. Two people play a game, where they take alternating turns removing stones.
In a move, a player may remove a positive number of stones from the first non-empty pile (the pile with the minimal index, that has at least one stone). The first player who cannot make a move (because all piles are empty) loses the game. If both players play optimally, determine the winner of the game.
Input
The first line contains a single integer t (1≤ t≤ 1000) — the number of test cases. Next 2t lines contain descriptions of test cases.
The first line of each test case contains a single integer n (1≤ n≤ 10^5) — the number of piles.
The second line of each test case contains n integers a_1,…,a_n (1≤ a_i≤ 10^9) — a_i is equal to the number of stones in the i-th pile.
It is guaranteed that the sum of n for all test cases does not exceed 10^5.
Output
For each test case, if the player who makes the first move will win, output "First". Otherwise, output "Second".
Example
Input
7
3
2 5 4
8
1 1 1 1 1 1 1 1
6
1 2 3 4 5 6
6
1 1 2 1 2 2
1
1000000000
5
1 2 2 1 1
3
1 1 1
Output
First
Second
Second
First
First
Second
First
Note
In the first test case, the first player will win the game. His winning strategy is:
1. The first player should take the stones from the first pile. He will take 1 stone. The numbers of stones in piles will be [1, 5, 4].
2. The second player should take the stones from the first pile. He will take 1 stone because he can't take any other number of stones. The numbers of stones in piles will be [0, 5, 4].
3. The first player should take the stones from the second pile because the first pile is empty. He will take 4 stones. The numbers of stones in piles will be [0, 1, 4].
4. The second player should take the stones from the second pile because the first pile is empty. He will take 1 stone because he can't take any other number of stones. The numbers of stones in piles will be [0, 0, 4].
5. The first player should take the stones from the third pile because the first and second piles are empty. He will take 4 stones. The numbers of stones in piles will be [0, 0, 0].
6. The second player will lose the game because all piles will be empty.
Submitted Solution:
```
def func():
n = int(input())
arr = [int(i) for i in input().split()]
c1 = 0
for i in arr:
if (i == 1):
c1 += 1
if (c1 == n):
if (n%2 == 1):
print ("First")
else:
print ("Second")
else:
win = "First"
curr = "First"
for i in range(n):
if (arr[i] == 1):
if (curr == "First"):
curr = "Second"
else:
curr = "First"
elif (arr[i] > 1):
if (curr == "First"):
win = "First"
else:
win = "Second"
break
else:
if (curr == "First"):
curr = "Second"
else:
curr = "First"
print (win)
t = int(input())
for i in range(t):
func()
``` | instruction | 0 | 2,629 | 19 | 5,258 |
Yes | output | 1 | 2,629 | 19 | 5,259 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There are n piles of stones, where the i-th pile has a_i stones. Two people play a game, where they take alternating turns removing stones.
In a move, a player may remove a positive number of stones from the first non-empty pile (the pile with the minimal index, that has at least one stone). The first player who cannot make a move (because all piles are empty) loses the game. If both players play optimally, determine the winner of the game.
Input
The first line contains a single integer t (1≤ t≤ 1000) — the number of test cases. Next 2t lines contain descriptions of test cases.
The first line of each test case contains a single integer n (1≤ n≤ 10^5) — the number of piles.
The second line of each test case contains n integers a_1,…,a_n (1≤ a_i≤ 10^9) — a_i is equal to the number of stones in the i-th pile.
It is guaranteed that the sum of n for all test cases does not exceed 10^5.
Output
For each test case, if the player who makes the first move will win, output "First". Otherwise, output "Second".
Example
Input
7
3
2 5 4
8
1 1 1 1 1 1 1 1
6
1 2 3 4 5 6
6
1 1 2 1 2 2
1
1000000000
5
1 2 2 1 1
3
1 1 1
Output
First
Second
Second
First
First
Second
First
Note
In the first test case, the first player will win the game. His winning strategy is:
1. The first player should take the stones from the first pile. He will take 1 stone. The numbers of stones in piles will be [1, 5, 4].
2. The second player should take the stones from the first pile. He will take 1 stone because he can't take any other number of stones. The numbers of stones in piles will be [0, 5, 4].
3. The first player should take the stones from the second pile because the first pile is empty. He will take 4 stones. The numbers of stones in piles will be [0, 1, 4].
4. The second player should take the stones from the second pile because the first pile is empty. He will take 1 stone because he can't take any other number of stones. The numbers of stones in piles will be [0, 0, 4].
5. The first player should take the stones from the third pile because the first and second piles are empty. He will take 4 stones. The numbers of stones in piles will be [0, 0, 0].
6. The second player will lose the game because all piles will be empty.
Submitted Solution:
```
"""
Code of Ayush Tiwari
Codeforces: servermonk
Codechef: ayush572000
"""
# import sys
# input = sys.stdin.buffer.readline
def solution():
for _ in range(int(input())):
# This is the main code
n=int(input())
l=list(map(int,input().split()))
ind=-1
cnt=0
for i in range(n):
if l[i]==1:
cnt+=1
else:
if ind==-1:
ind=i
ind+=1
if cnt!=n:
if((ind)%2)!=0:
print('FIRST')
else:
print('SECOND')
else:
if n%2!=0:
print('FIRST')
else:
print('SECOND')
solution()
``` | instruction | 0 | 2,630 | 19 | 5,260 |
No | output | 1 | 2,630 | 19 | 5,261 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There are n piles of stones, where the i-th pile has a_i stones. Two people play a game, where they take alternating turns removing stones.
In a move, a player may remove a positive number of stones from the first non-empty pile (the pile with the minimal index, that has at least one stone). The first player who cannot make a move (because all piles are empty) loses the game. If both players play optimally, determine the winner of the game.
Input
The first line contains a single integer t (1≤ t≤ 1000) — the number of test cases. Next 2t lines contain descriptions of test cases.
The first line of each test case contains a single integer n (1≤ n≤ 10^5) — the number of piles.
The second line of each test case contains n integers a_1,…,a_n (1≤ a_i≤ 10^9) — a_i is equal to the number of stones in the i-th pile.
It is guaranteed that the sum of n for all test cases does not exceed 10^5.
Output
For each test case, if the player who makes the first move will win, output "First". Otherwise, output "Second".
Example
Input
7
3
2 5 4
8
1 1 1 1 1 1 1 1
6
1 2 3 4 5 6
6
1 1 2 1 2 2
1
1000000000
5
1 2 2 1 1
3
1 1 1
Output
First
Second
Second
First
First
Second
First
Note
In the first test case, the first player will win the game. His winning strategy is:
1. The first player should take the stones from the first pile. He will take 1 stone. The numbers of stones in piles will be [1, 5, 4].
2. The second player should take the stones from the first pile. He will take 1 stone because he can't take any other number of stones. The numbers of stones in piles will be [0, 5, 4].
3. The first player should take the stones from the second pile because the first pile is empty. He will take 4 stones. The numbers of stones in piles will be [0, 1, 4].
4. The second player should take the stones from the second pile because the first pile is empty. He will take 1 stone because he can't take any other number of stones. The numbers of stones in piles will be [0, 0, 4].
5. The first player should take the stones from the third pile because the first and second piles are empty. He will take 4 stones. The numbers of stones in piles will be [0, 0, 0].
6. The second player will lose the game because all piles will be empty.
Submitted Solution:
```
import math
t=int(input())
for _ in range(t):
n=int(input())
seq=list(map(int,input().split()))
p=1
i=0
while i<n-1:
if seq[i]==1:
if p==1:p=2
else: p=1
i+=1
else:
if seq[i+1]==1 and i!=n-2:
if p==1:p=2
else:p=1
i+=1
else:
p=p
i+=1
if p==1:
print("First")
else:
print("Second")
``` | instruction | 0 | 2,631 | 19 | 5,262 |
No | output | 1 | 2,631 | 19 | 5,263 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There are n piles of stones, where the i-th pile has a_i stones. Two people play a game, where they take alternating turns removing stones.
In a move, a player may remove a positive number of stones from the first non-empty pile (the pile with the minimal index, that has at least one stone). The first player who cannot make a move (because all piles are empty) loses the game. If both players play optimally, determine the winner of the game.
Input
The first line contains a single integer t (1≤ t≤ 1000) — the number of test cases. Next 2t lines contain descriptions of test cases.
The first line of each test case contains a single integer n (1≤ n≤ 10^5) — the number of piles.
The second line of each test case contains n integers a_1,…,a_n (1≤ a_i≤ 10^9) — a_i is equal to the number of stones in the i-th pile.
It is guaranteed that the sum of n for all test cases does not exceed 10^5.
Output
For each test case, if the player who makes the first move will win, output "First". Otherwise, output "Second".
Example
Input
7
3
2 5 4
8
1 1 1 1 1 1 1 1
6
1 2 3 4 5 6
6
1 1 2 1 2 2
1
1000000000
5
1 2 2 1 1
3
1 1 1
Output
First
Second
Second
First
First
Second
First
Note
In the first test case, the first player will win the game. His winning strategy is:
1. The first player should take the stones from the first pile. He will take 1 stone. The numbers of stones in piles will be [1, 5, 4].
2. The second player should take the stones from the first pile. He will take 1 stone because he can't take any other number of stones. The numbers of stones in piles will be [0, 5, 4].
3. The first player should take the stones from the second pile because the first pile is empty. He will take 4 stones. The numbers of stones in piles will be [0, 1, 4].
4. The second player should take the stones from the second pile because the first pile is empty. He will take 1 stone because he can't take any other number of stones. The numbers of stones in piles will be [0, 0, 4].
5. The first player should take the stones from the third pile because the first and second piles are empty. He will take 4 stones. The numbers of stones in piles will be [0, 0, 0].
6. The second player will lose the game because all piles will be empty.
Submitted Solution:
```
def func(n):
n = list(map(int, n.split()))
current = 'First'
next = 'Second'
n = n[::-1]
while len(n)>0:
if len(n) == 1:
n.pop()
elif n[-1] == 1:
n.pop()
else:
if n[-2] == 1:
n.pop()
else:
n[-1] = 1
current,next = next,current
return next
def main():
t = int(input())
t_input = []
for i in range(t):
input()
t_input.append(input())
for i in list(map(func,t_input)):
print(i)
main()
``` | instruction | 0 | 2,632 | 19 | 5,264 |
No | output | 1 | 2,632 | 19 | 5,265 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There are n piles of stones, where the i-th pile has a_i stones. Two people play a game, where they take alternating turns removing stones.
In a move, a player may remove a positive number of stones from the first non-empty pile (the pile with the minimal index, that has at least one stone). The first player who cannot make a move (because all piles are empty) loses the game. If both players play optimally, determine the winner of the game.
Input
The first line contains a single integer t (1≤ t≤ 1000) — the number of test cases. Next 2t lines contain descriptions of test cases.
The first line of each test case contains a single integer n (1≤ n≤ 10^5) — the number of piles.
The second line of each test case contains n integers a_1,…,a_n (1≤ a_i≤ 10^9) — a_i is equal to the number of stones in the i-th pile.
It is guaranteed that the sum of n for all test cases does not exceed 10^5.
Output
For each test case, if the player who makes the first move will win, output "First". Otherwise, output "Second".
Example
Input
7
3
2 5 4
8
1 1 1 1 1 1 1 1
6
1 2 3 4 5 6
6
1 1 2 1 2 2
1
1000000000
5
1 2 2 1 1
3
1 1 1
Output
First
Second
Second
First
First
Second
First
Note
In the first test case, the first player will win the game. His winning strategy is:
1. The first player should take the stones from the first pile. He will take 1 stone. The numbers of stones in piles will be [1, 5, 4].
2. The second player should take the stones from the first pile. He will take 1 stone because he can't take any other number of stones. The numbers of stones in piles will be [0, 5, 4].
3. The first player should take the stones from the second pile because the first pile is empty. He will take 4 stones. The numbers of stones in piles will be [0, 1, 4].
4. The second player should take the stones from the second pile because the first pile is empty. He will take 1 stone because he can't take any other number of stones. The numbers of stones in piles will be [0, 0, 4].
5. The first player should take the stones from the third pile because the first and second piles are empty. He will take 4 stones. The numbers of stones in piles will be [0, 0, 0].
6. The second player will lose the game because all piles will be empty.
Submitted Solution:
```
from sys import stdin,stdout
import array
import sys
input_ = stdin.readline
n = int(input_())
def change_player(s):
if s == 'First':
return "Second"
return "First"
for _ in range(n):
k = input_()
arr = list(map(int,input_().split()))
player = "First"
for i in range(len(arr)):
if i == len(arr)-1:
break
elif arr[i] == 1:
player = change_player(player)
continue
# elif arr[i+1]==1 and arr[i+1] == len(arr)-1:
# continue
elif arr[i+1] == 1 and arr[i+1] != len(arr)-1:
player = change_player(player)
else:
continue
print(player)
``` | instruction | 0 | 2,633 | 19 | 5,266 |
No | output | 1 | 2,633 | 19 | 5,267 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Lately, Mr. Chanek frequently plays the game Arena of Greed. As the name implies, the game's goal is to find the greediest of them all, who will then be crowned king of Compfestnesia.
The game is played by two people taking turns, where Mr. Chanek takes the first turn. Initially, there is a treasure chest containing N gold coins. The game ends if there are no more gold coins in the chest. In each turn, the players can make one of the following moves:
* Take one gold coin from the chest.
* Take half of the gold coins on the chest. This move is only available if the number of coins in the chest is even.
Both players will try to maximize the number of coins they have. Mr. Chanek asks your help to find the maximum number of coins he can get at the end of the game if both he and the opponent plays optimally.
Input
The first line contains a single integer T (1 ≤ T ≤ 10^5) denotes the number of test cases.
The next T lines each contain a single integer N (1 ≤ N ≤ 10^{18}).
Output
T lines, each line is the answer requested by Mr. Chanek.
Example
Input
2
5
6
Output
2
4
Note
For the first case, the game is as follows:
1. Mr. Chanek takes one coin.
2. The opponent takes two coins.
3. Mr. Chanek takes one coin.
4. The opponent takes one coin.
For the second case, the game is as follows:
1. Mr. Chanek takes three coins.
2. The opponent takes one coin.
3. Mr. Chanek takes one coin.
4. The opponent takes one coin. | instruction | 0 | 2,634 | 19 | 5,268 |
Tags: games, greedy
Correct Solution:
```
from sys import stdin
input = stdin.readline
def funciona(n):
ans = 0
while n != 0:
if n == 4:
ans += 3
n = 0
continue
elif n % 4 == 0:
ans += 1
n -= 2
else:
ans += n//2
n -= n//2+1
return ans
for _ in range(0, int(input())):
n = int(input())
if n % 2 == 1:
print(n-funciona(n-1))
else:
print(funciona(n))
``` | output | 1 | 2,634 | 19 | 5,269 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Lately, Mr. Chanek frequently plays the game Arena of Greed. As the name implies, the game's goal is to find the greediest of them all, who will then be crowned king of Compfestnesia.
The game is played by two people taking turns, where Mr. Chanek takes the first turn. Initially, there is a treasure chest containing N gold coins. The game ends if there are no more gold coins in the chest. In each turn, the players can make one of the following moves:
* Take one gold coin from the chest.
* Take half of the gold coins on the chest. This move is only available if the number of coins in the chest is even.
Both players will try to maximize the number of coins they have. Mr. Chanek asks your help to find the maximum number of coins he can get at the end of the game if both he and the opponent plays optimally.
Input
The first line contains a single integer T (1 ≤ T ≤ 10^5) denotes the number of test cases.
The next T lines each contain a single integer N (1 ≤ N ≤ 10^{18}).
Output
T lines, each line is the answer requested by Mr. Chanek.
Example
Input
2
5
6
Output
2
4
Note
For the first case, the game is as follows:
1. Mr. Chanek takes one coin.
2. The opponent takes two coins.
3. Mr. Chanek takes one coin.
4. The opponent takes one coin.
For the second case, the game is as follows:
1. Mr. Chanek takes three coins.
2. The opponent takes one coin.
3. Mr. Chanek takes one coin.
4. The opponent takes one coin. | instruction | 0 | 2,635 | 19 | 5,270 |
Tags: games, greedy
Correct Solution:
```
input=__import__('sys').stdin.readline
for _ in range(int(input())):
n=int(input())
ans=0
c=1
while n:
r=0
if n%2==0 and n//2%2 or n==4:n//=2;r=n
else:r=1;n-=1
if c:ans+=r
c^=1
print(ans)
``` | output | 1 | 2,635 | 19 | 5,271 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Lately, Mr. Chanek frequently plays the game Arena of Greed. As the name implies, the game's goal is to find the greediest of them all, who will then be crowned king of Compfestnesia.
The game is played by two people taking turns, where Mr. Chanek takes the first turn. Initially, there is a treasure chest containing N gold coins. The game ends if there are no more gold coins in the chest. In each turn, the players can make one of the following moves:
* Take one gold coin from the chest.
* Take half of the gold coins on the chest. This move is only available if the number of coins in the chest is even.
Both players will try to maximize the number of coins they have. Mr. Chanek asks your help to find the maximum number of coins he can get at the end of the game if both he and the opponent plays optimally.
Input
The first line contains a single integer T (1 ≤ T ≤ 10^5) denotes the number of test cases.
The next T lines each contain a single integer N (1 ≤ N ≤ 10^{18}).
Output
T lines, each line is the answer requested by Mr. Chanek.
Example
Input
2
5
6
Output
2
4
Note
For the first case, the game is as follows:
1. Mr. Chanek takes one coin.
2. The opponent takes two coins.
3. Mr. Chanek takes one coin.
4. The opponent takes one coin.
For the second case, the game is as follows:
1. Mr. Chanek takes three coins.
2. The opponent takes one coin.
3. Mr. Chanek takes one coin.
4. The opponent takes one coin. | instruction | 0 | 2,636 | 19 | 5,272 |
Tags: games, greedy
Correct Solution:
```
# This code is contributed by Siddharth
from sys import *
input = stdin.readline
# setrecursionlimit(10**6)
# from sys import *
import random
from bisect import *
import math
from collections import *
import operator
from heapq import *
from itertools import *
inf=10**18
mod=10**9+7
# inverse modulo power pow(a,-1,mod) - it only works on py 3.8 ( *not in pypy )
# ==========================================> Code Starts Here <=====================================================================
for test in range(int(input())):
n=int(input())
ans=0
t=0
while n:
if n%2==0 and n//2%2!=0 or n==4:
n//=2
c=n
else:
n-=1
c=1
if t==0:
ans+=c
t^=1
print(ans)
``` | output | 1 | 2,636 | 19 | 5,273 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Lately, Mr. Chanek frequently plays the game Arena of Greed. As the name implies, the game's goal is to find the greediest of them all, who will then be crowned king of Compfestnesia.
The game is played by two people taking turns, where Mr. Chanek takes the first turn. Initially, there is a treasure chest containing N gold coins. The game ends if there are no more gold coins in the chest. In each turn, the players can make one of the following moves:
* Take one gold coin from the chest.
* Take half of the gold coins on the chest. This move is only available if the number of coins in the chest is even.
Both players will try to maximize the number of coins they have. Mr. Chanek asks your help to find the maximum number of coins he can get at the end of the game if both he and the opponent plays optimally.
Input
The first line contains a single integer T (1 ≤ T ≤ 10^5) denotes the number of test cases.
The next T lines each contain a single integer N (1 ≤ N ≤ 10^{18}).
Output
T lines, each line is the answer requested by Mr. Chanek.
Example
Input
2
5
6
Output
2
4
Note
For the first case, the game is as follows:
1. Mr. Chanek takes one coin.
2. The opponent takes two coins.
3. Mr. Chanek takes one coin.
4. The opponent takes one coin.
For the second case, the game is as follows:
1. Mr. Chanek takes three coins.
2. The opponent takes one coin.
3. Mr. Chanek takes one coin.
4. The opponent takes one coin. | instruction | 0 | 2,637 | 19 | 5,274 |
Tags: games, greedy
Correct Solution:
```
from math import log2
from sys import stdin,stdout
# print('9'*17)
for _ in range(int(stdin.readline())):
n = int(stdin.readline())
c = 0
k = 0
while n>4:
if n%2==0:
if (n//2)%2==0:
n -= 1
if k==0:
c += 1
k = 1
else:
k = 0
else:
if k==0:
c += n//2
k = 1
else:
k = 0
n//=2
if n%2==1:
if k==0:
c += 1
k = 1
else:
k = 0
n -= 1
if n==4:
if k==0:
c += 3
else:
c += 1
elif n==3:
if k==0:
c += 2
else:
c += 1
elif n==2:
c += 1
elif n==1:
if k==0:
c += 1
stdout.write(str(c)+'\n')
# print(v)
``` | output | 1 | 2,637 | 19 | 5,275 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Lately, Mr. Chanek frequently plays the game Arena of Greed. As the name implies, the game's goal is to find the greediest of them all, who will then be crowned king of Compfestnesia.
The game is played by two people taking turns, where Mr. Chanek takes the first turn. Initially, there is a treasure chest containing N gold coins. The game ends if there are no more gold coins in the chest. In each turn, the players can make one of the following moves:
* Take one gold coin from the chest.
* Take half of the gold coins on the chest. This move is only available if the number of coins in the chest is even.
Both players will try to maximize the number of coins they have. Mr. Chanek asks your help to find the maximum number of coins he can get at the end of the game if both he and the opponent plays optimally.
Input
The first line contains a single integer T (1 ≤ T ≤ 10^5) denotes the number of test cases.
The next T lines each contain a single integer N (1 ≤ N ≤ 10^{18}).
Output
T lines, each line is the answer requested by Mr. Chanek.
Example
Input
2
5
6
Output
2
4
Note
For the first case, the game is as follows:
1. Mr. Chanek takes one coin.
2. The opponent takes two coins.
3. Mr. Chanek takes one coin.
4. The opponent takes one coin.
For the second case, the game is as follows:
1. Mr. Chanek takes three coins.
2. The opponent takes one coin.
3. Mr. Chanek takes one coin.
4. The opponent takes one coin. | instruction | 0 | 2,638 | 19 | 5,276 |
Tags: games, greedy
Correct Solution:
```
input=__import__('sys').stdin.readline
for _ in range(int(input())):
n = int(input())
ans = 0
c = 1
while n:
r = 0
if (n %2 == 0 and n//2%2) or n == 4:
n //= 2
r = n
else:
r = 1
n -= 1
if c:
ans += r
c^= 1
print(ans)
``` | output | 1 | 2,638 | 19 | 5,277 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Lately, Mr. Chanek frequently plays the game Arena of Greed. As the name implies, the game's goal is to find the greediest of them all, who will then be crowned king of Compfestnesia.
The game is played by two people taking turns, where Mr. Chanek takes the first turn. Initially, there is a treasure chest containing N gold coins. The game ends if there are no more gold coins in the chest. In each turn, the players can make one of the following moves:
* Take one gold coin from the chest.
* Take half of the gold coins on the chest. This move is only available if the number of coins in the chest is even.
Both players will try to maximize the number of coins they have. Mr. Chanek asks your help to find the maximum number of coins he can get at the end of the game if both he and the opponent plays optimally.
Input
The first line contains a single integer T (1 ≤ T ≤ 10^5) denotes the number of test cases.
The next T lines each contain a single integer N (1 ≤ N ≤ 10^{18}).
Output
T lines, each line is the answer requested by Mr. Chanek.
Example
Input
2
5
6
Output
2
4
Note
For the first case, the game is as follows:
1. Mr. Chanek takes one coin.
2. The opponent takes two coins.
3. Mr. Chanek takes one coin.
4. The opponent takes one coin.
For the second case, the game is as follows:
1. Mr. Chanek takes three coins.
2. The opponent takes one coin.
3. Mr. Chanek takes one coin.
4. The opponent takes one coin. | instruction | 0 | 2,639 | 19 | 5,278 |
Tags: games, greedy
Correct Solution:
```
import sys
input = sys.stdin.readline
I = lambda : list(map(int,input().split()))
t,=I()
ans=[]
for _ in range(t):
n,=I()
an=0
while n:
#for chanek
if n==4:
an+=3;break
if n%2:
an+=1;n-=1
else:
if (n//2)%2:
an+=n//2;n//=2 #main part of question ,if odd then take half asap
else:
an+=1;n-=1 #if n//2 is even then intentionaly minus 1
#now opponent turn
if n:
if n==4:
an+=1;break
if n%2:
n-=1
else:
if (n//2)%2:
n//=2
else:
n-=1
ans.append(str(an))
#just opposite of above bcz opponent want his benefit
sys.stdout.write("\n".join(ans))
``` | output | 1 | 2,639 | 19 | 5,279 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Lately, Mr. Chanek frequently plays the game Arena of Greed. As the name implies, the game's goal is to find the greediest of them all, who will then be crowned king of Compfestnesia.
The game is played by two people taking turns, where Mr. Chanek takes the first turn. Initially, there is a treasure chest containing N gold coins. The game ends if there are no more gold coins in the chest. In each turn, the players can make one of the following moves:
* Take one gold coin from the chest.
* Take half of the gold coins on the chest. This move is only available if the number of coins in the chest is even.
Both players will try to maximize the number of coins they have. Mr. Chanek asks your help to find the maximum number of coins he can get at the end of the game if both he and the opponent plays optimally.
Input
The first line contains a single integer T (1 ≤ T ≤ 10^5) denotes the number of test cases.
The next T lines each contain a single integer N (1 ≤ N ≤ 10^{18}).
Output
T lines, each line is the answer requested by Mr. Chanek.
Example
Input
2
5
6
Output
2
4
Note
For the first case, the game is as follows:
1. Mr. Chanek takes one coin.
2. The opponent takes two coins.
3. Mr. Chanek takes one coin.
4. The opponent takes one coin.
For the second case, the game is as follows:
1. Mr. Chanek takes three coins.
2. The opponent takes one coin.
3. Mr. Chanek takes one coin.
4. The opponent takes one coin. | instruction | 0 | 2,640 | 19 | 5,280 |
Tags: games, greedy
Correct Solution:
```
import sys
# problem a
# template by:
# https://github.com/rajatg98
'''input
'''
import math
import bisect
from sys import stdin,stdout
from math import gcd,floor,sqrt,log
from collections import defaultdict as dd
from bisect import bisect_left as bl,bisect_right as br
# sys.setrecursionlimit(100000000)
input=__import__('sys').stdin.readline
inp =lambda: int(input())
strng =lambda: input().strip()
jn =lambda x,l: x.join(map(str,l))
strl =lambda: list(input().strip())
mul =lambda: map(int,input().strip().split())
mulf =lambda: map(float,input().strip().split())
seq =lambda: list(map(int,input().strip().split()))
ceil =lambda x: int(x) if(x==int(x)) else int(x)+1
ceildiv=lambda x,d: x//d if(x%d==0) else x//d+1
flush =lambda: stdout.flush()
stdstr =lambda: stdin.readline()
stdint =lambda: int(stdin.readline())
stdpr =lambda x: stdout.write(str(x))
mod=1000000007
#main code
# extended euclidean algorithm
# obtained from:
# https://brilliant.org/wiki/extended-euclidean-algorithm/
def egcd(a, b):
x,y, u,v = 0,1, 1,0
while a != 0:
q, r = b//a, b%a
m, n = x-u*q, y-v*q
b,a, x,y, u,v = a,r, u,v, m,n
gcd = b
return gcd, x, y
# Primes:
# Obtianed from: https://primes.utm.edu/lists/small/10000.txt
primes = list(map(int, """
2 3 5 7 11 13 17 19 23 29
31 37 41 43 47 53 59 61 67 71
73 79 83 89 97 101 103 107 109 113
127 131 137 139 149 151 157 163 167 173
179 181 191 193 197 199 211 223 227 229
233 239 241 251 257 263 269 271 277 281
283 293 307 311 313 317 331 337 347 349
353 359 367 373 379 383 389 397 401 409
419 421 431 433 439 443 449 457 461 463
467 479 487 491 499 503 509 521 523 541
547 557 563 569 571 577 587 593 599 601
607 613 617 619 631 641 643 647 653 659
661 673 677 683 691 701 709 719 727 733
739 743 751 757 761 769 773 787 797 809
811 821 823 827 829 839 853 857 859 863
877 881 883 887 907 911 919 929 937 941
947 953 967 971 977 983 991 997 1009
""".split()))
primes_set = set(primes)
# print(primes)
def solve():
n = inp()
ch = 0
ch_turn = True
while n > 0:
if n%4 == 0 and n > 8:
n -= 1
if ch_turn:
ch += 1
elif n%2 == 0:
n //= 2
if ch_turn:
ch += n
else:
n -= 1
if ch_turn:
ch += 1
# print("coins:", n)
# print("turn: %s" % ("chanek" if ch_turn else "other dude"))
ch_turn = not ch_turn
print(ch)
def main():
tests = inp()
for _ in range(tests):
solve()
if __name__ == "__main__":
main()
``` | output | 1 | 2,640 | 19 | 5,281 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Lately, Mr. Chanek frequently plays the game Arena of Greed. As the name implies, the game's goal is to find the greediest of them all, who will then be crowned king of Compfestnesia.
The game is played by two people taking turns, where Mr. Chanek takes the first turn. Initially, there is a treasure chest containing N gold coins. The game ends if there are no more gold coins in the chest. In each turn, the players can make one of the following moves:
* Take one gold coin from the chest.
* Take half of the gold coins on the chest. This move is only available if the number of coins in the chest is even.
Both players will try to maximize the number of coins they have. Mr. Chanek asks your help to find the maximum number of coins he can get at the end of the game if both he and the opponent plays optimally.
Input
The first line contains a single integer T (1 ≤ T ≤ 10^5) denotes the number of test cases.
The next T lines each contain a single integer N (1 ≤ N ≤ 10^{18}).
Output
T lines, each line is the answer requested by Mr. Chanek.
Example
Input
2
5
6
Output
2
4
Note
For the first case, the game is as follows:
1. Mr. Chanek takes one coin.
2. The opponent takes two coins.
3. Mr. Chanek takes one coin.
4. The opponent takes one coin.
For the second case, the game is as follows:
1. Mr. Chanek takes three coins.
2. The opponent takes one coin.
3. Mr. Chanek takes one coin.
4. The opponent takes one coin. | instruction | 0 | 2,641 | 19 | 5,282 |
Tags: games, greedy
Correct Solution:
```
import sys,functools,collections,bisect,math,heapq
input = sys.stdin.readline
#print = sys.stdout.write
sys.setrecursionlimit(300000)
def fun(n):
if n == 0:
return 0,0
if n%2 or (n%4==0 and n > 8):
a,b = fun(n-1)
return 1+b,a
else:
a,b = fun(n//2)
return n//2+b,a
t = int(input())
for _ in range(t):
n = int(input())
chanek = True
count = 0
while n > 0:
if chanek == True:
if n % 2 == 0:
div = n // 2
if div % 2 == 0 and n > 4:
count += 1
n -= 1
else:
count += n // 2
n = n // 2
else:
count += 1
n -= 1
chanek = False
elif chanek == False:
if n % 2 == 0:
div = n // 2
if div % 2 == 0 and n > 4:
n -= 1
else:
n = n // 2
else:
n -= 1
chanek = True
print(count)
``` | output | 1 | 2,641 | 19 | 5,283 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Lately, Mr. Chanek frequently plays the game Arena of Greed. As the name implies, the game's goal is to find the greediest of them all, who will then be crowned king of Compfestnesia.
The game is played by two people taking turns, where Mr. Chanek takes the first turn. Initially, there is a treasure chest containing N gold coins. The game ends if there are no more gold coins in the chest. In each turn, the players can make one of the following moves:
* Take one gold coin from the chest.
* Take half of the gold coins on the chest. This move is only available if the number of coins in the chest is even.
Both players will try to maximize the number of coins they have. Mr. Chanek asks your help to find the maximum number of coins he can get at the end of the game if both he and the opponent plays optimally.
Input
The first line contains a single integer T (1 ≤ T ≤ 10^5) denotes the number of test cases.
The next T lines each contain a single integer N (1 ≤ N ≤ 10^{18}).
Output
T lines, each line is the answer requested by Mr. Chanek.
Example
Input
2
5
6
Output
2
4
Note
For the first case, the game is as follows:
1. Mr. Chanek takes one coin.
2. The opponent takes two coins.
3. Mr. Chanek takes one coin.
4. The opponent takes one coin.
For the second case, the game is as follows:
1. Mr. Chanek takes three coins.
2. The opponent takes one coin.
3. Mr. Chanek takes one coin.
4. The opponent takes one coin.
Submitted Solution:
```
input=__import__('sys').stdin.readline
t=int(input())
for i in range(t):
n=int(input())
c=0
while n>0:
if n%2==0 and (n==4 or n%4!=0):
n=n//2
c=c+n
if n%2==0:
n=n//2
else:
n=n-1
else:
c=c+1
n=n-1
if n%2==0 and (n==4 or n%4!=0):
n=n//2
else:
n=n-1
#print(n,c)
print(c)
``` | instruction | 0 | 2,642 | 19 | 5,284 |
Yes | output | 1 | 2,642 | 19 | 5,285 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Lately, Mr. Chanek frequently plays the game Arena of Greed. As the name implies, the game's goal is to find the greediest of them all, who will then be crowned king of Compfestnesia.
The game is played by two people taking turns, where Mr. Chanek takes the first turn. Initially, there is a treasure chest containing N gold coins. The game ends if there are no more gold coins in the chest. In each turn, the players can make one of the following moves:
* Take one gold coin from the chest.
* Take half of the gold coins on the chest. This move is only available if the number of coins in the chest is even.
Both players will try to maximize the number of coins they have. Mr. Chanek asks your help to find the maximum number of coins he can get at the end of the game if both he and the opponent plays optimally.
Input
The first line contains a single integer T (1 ≤ T ≤ 10^5) denotes the number of test cases.
The next T lines each contain a single integer N (1 ≤ N ≤ 10^{18}).
Output
T lines, each line is the answer requested by Mr. Chanek.
Example
Input
2
5
6
Output
2
4
Note
For the first case, the game is as follows:
1. Mr. Chanek takes one coin.
2. The opponent takes two coins.
3. Mr. Chanek takes one coin.
4. The opponent takes one coin.
For the second case, the game is as follows:
1. Mr. Chanek takes three coins.
2. The opponent takes one coin.
3. Mr. Chanek takes one coin.
4. The opponent takes one coin.
Submitted Solution:
```
input=__import__('sys').stdin.readline
t=int(input())
for i in range(t):
n=int(input())
ans=0
turn=0
while n>0:
coin=0
turn+=1
if n%2==1 or n>4 and n%4==0:
coin=1
n-=1
else:
coin=n//2
n=n//2
ans+=coin*(turn%2)
print(ans)
``` | instruction | 0 | 2,643 | 19 | 5,286 |
Yes | output | 1 | 2,643 | 19 | 5,287 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Lately, Mr. Chanek frequently plays the game Arena of Greed. As the name implies, the game's goal is to find the greediest of them all, who will then be crowned king of Compfestnesia.
The game is played by two people taking turns, where Mr. Chanek takes the first turn. Initially, there is a treasure chest containing N gold coins. The game ends if there are no more gold coins in the chest. In each turn, the players can make one of the following moves:
* Take one gold coin from the chest.
* Take half of the gold coins on the chest. This move is only available if the number of coins in the chest is even.
Both players will try to maximize the number of coins they have. Mr. Chanek asks your help to find the maximum number of coins he can get at the end of the game if both he and the opponent plays optimally.
Input
The first line contains a single integer T (1 ≤ T ≤ 10^5) denotes the number of test cases.
The next T lines each contain a single integer N (1 ≤ N ≤ 10^{18}).
Output
T lines, each line is the answer requested by Mr. Chanek.
Example
Input
2
5
6
Output
2
4
Note
For the first case, the game is as follows:
1. Mr. Chanek takes one coin.
2. The opponent takes two coins.
3. Mr. Chanek takes one coin.
4. The opponent takes one coin.
For the second case, the game is as follows:
1. Mr. Chanek takes three coins.
2. The opponent takes one coin.
3. Mr. Chanek takes one coin.
4. The opponent takes one coin.
Submitted Solution:
```
from sys import stdin
n = int(stdin.readline())
for _ in range(n):
ans = 0
turn = 1
start = int(stdin.readline())
while(start > 0):
if turn:
turn = 0
if start % 4 == 2 or start == 4:
ans += start // 2
start = start // 2
else:
start -= 1
ans += 1
else:
turn = 1
if start % 4 == 2 or start == 4:
start = start // 2
else:
start -= 1
print(ans)
``` | instruction | 0 | 2,644 | 19 | 5,288 |
Yes | output | 1 | 2,644 | 19 | 5,289 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Lately, Mr. Chanek frequently plays the game Arena of Greed. As the name implies, the game's goal is to find the greediest of them all, who will then be crowned king of Compfestnesia.
The game is played by two people taking turns, where Mr. Chanek takes the first turn. Initially, there is a treasure chest containing N gold coins. The game ends if there are no more gold coins in the chest. In each turn, the players can make one of the following moves:
* Take one gold coin from the chest.
* Take half of the gold coins on the chest. This move is only available if the number of coins in the chest is even.
Both players will try to maximize the number of coins they have. Mr. Chanek asks your help to find the maximum number of coins he can get at the end of the game if both he and the opponent plays optimally.
Input
The first line contains a single integer T (1 ≤ T ≤ 10^5) denotes the number of test cases.
The next T lines each contain a single integer N (1 ≤ N ≤ 10^{18}).
Output
T lines, each line is the answer requested by Mr. Chanek.
Example
Input
2
5
6
Output
2
4
Note
For the first case, the game is as follows:
1. Mr. Chanek takes one coin.
2. The opponent takes two coins.
3. Mr. Chanek takes one coin.
4. The opponent takes one coin.
For the second case, the game is as follows:
1. Mr. Chanek takes three coins.
2. The opponent takes one coin.
3. Mr. Chanek takes one coin.
4. The opponent takes one coin.
Submitted Solution:
```
BUFSIZE = 8192
import os
import sys
import math
from io import BytesIO, IOBase
from bisect import bisect_left #c++ lowerbound bl(array,element)
from bisect import bisect_right #c++ upperbound br(array,element)
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")
for _ in range(int(input())):
n=int(input())
c=0
f=0
while (n>0):
f+=1
if n%2==1 or n%4==0 and n>5:
if f%2==1:
c+=1
n-=1
else:
if f%2==1:
c+=n//2
n=n//2
print(c)
``` | instruction | 0 | 2,645 | 19 | 5,290 |
Yes | output | 1 | 2,645 | 19 | 5,291 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Lately, Mr. Chanek frequently plays the game Arena of Greed. As the name implies, the game's goal is to find the greediest of them all, who will then be crowned king of Compfestnesia.
The game is played by two people taking turns, where Mr. Chanek takes the first turn. Initially, there is a treasure chest containing N gold coins. The game ends if there are no more gold coins in the chest. In each turn, the players can make one of the following moves:
* Take one gold coin from the chest.
* Take half of the gold coins on the chest. This move is only available if the number of coins in the chest is even.
Both players will try to maximize the number of coins they have. Mr. Chanek asks your help to find the maximum number of coins he can get at the end of the game if both he and the opponent plays optimally.
Input
The first line contains a single integer T (1 ≤ T ≤ 10^5) denotes the number of test cases.
The next T lines each contain a single integer N (1 ≤ N ≤ 10^{18}).
Output
T lines, each line is the answer requested by Mr. Chanek.
Example
Input
2
5
6
Output
2
4
Note
For the first case, the game is as follows:
1. Mr. Chanek takes one coin.
2. The opponent takes two coins.
3. Mr. Chanek takes one coin.
4. The opponent takes one coin.
For the second case, the game is as follows:
1. Mr. Chanek takes three coins.
2. The opponent takes one coin.
3. Mr. Chanek takes one coin.
4. The opponent takes one coin.
Submitted Solution:
```
import sys
import itertools as it
import math as mt
import collections as cc
input=sys.stdin.readline
I=lambda:list(map(int,input().split()))
for tc in range(int(input())):
n,=I()
ans=0
cur=0
while n:
if n%2==0:
if (n//2)%2==0:
if cur%2==0:
ans+=(n//2)
n//=2
else:
n-=1
if cur%2==0:
ans+=1
else:
n-=1
if cur%2==0:
ans+=1
cur+=1
print(ans)
``` | instruction | 0 | 2,646 | 19 | 5,292 |
No | output | 1 | 2,646 | 19 | 5,293 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Lately, Mr. Chanek frequently plays the game Arena of Greed. As the name implies, the game's goal is to find the greediest of them all, who will then be crowned king of Compfestnesia.
The game is played by two people taking turns, where Mr. Chanek takes the first turn. Initially, there is a treasure chest containing N gold coins. The game ends if there are no more gold coins in the chest. In each turn, the players can make one of the following moves:
* Take one gold coin from the chest.
* Take half of the gold coins on the chest. This move is only available if the number of coins in the chest is even.
Both players will try to maximize the number of coins they have. Mr. Chanek asks your help to find the maximum number of coins he can get at the end of the game if both he and the opponent plays optimally.
Input
The first line contains a single integer T (1 ≤ T ≤ 10^5) denotes the number of test cases.
The next T lines each contain a single integer N (1 ≤ N ≤ 10^{18}).
Output
T lines, each line is the answer requested by Mr. Chanek.
Example
Input
2
5
6
Output
2
4
Note
For the first case, the game is as follows:
1. Mr. Chanek takes one coin.
2. The opponent takes two coins.
3. Mr. Chanek takes one coin.
4. The opponent takes one coin.
For the second case, the game is as follows:
1. Mr. Chanek takes three coins.
2. The opponent takes one coin.
3. Mr. Chanek takes one coin.
4. The opponent takes one coin.
Submitted Solution:
```
t=int(input())
po=set()
for i in range(55):
po.add(2**i)
for _ in range(t):
n=int(input())
player1=0
player2=0
i=0
while(n):
if(n not in po):
if(i==0 and n%2==1):
player1+=1
i=1
n-=1
elif(i==1 and n%2==1):
player2+=1
i=0
n-=1
elif(i==0 and n%2==0):
player1+=(n//2)
i=1
n-=(n//2)
else:
player2+=(n//2)
i=0
n-=(n//2)
else:
if(i==0):
player1+=1
i=1
n-=1
else:
player2+=1
i=0
n-=1
print(player1)
``` | instruction | 0 | 2,647 | 19 | 5,294 |
No | output | 1 | 2,647 | 19 | 5,295 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Lately, Mr. Chanek frequently plays the game Arena of Greed. As the name implies, the game's goal is to find the greediest of them all, who will then be crowned king of Compfestnesia.
The game is played by two people taking turns, where Mr. Chanek takes the first turn. Initially, there is a treasure chest containing N gold coins. The game ends if there are no more gold coins in the chest. In each turn, the players can make one of the following moves:
* Take one gold coin from the chest.
* Take half of the gold coins on the chest. This move is only available if the number of coins in the chest is even.
Both players will try to maximize the number of coins they have. Mr. Chanek asks your help to find the maximum number of coins he can get at the end of the game if both he and the opponent plays optimally.
Input
The first line contains a single integer T (1 ≤ T ≤ 10^5) denotes the number of test cases.
The next T lines each contain a single integer N (1 ≤ N ≤ 10^{18}).
Output
T lines, each line is the answer requested by Mr. Chanek.
Example
Input
2
5
6
Output
2
4
Note
For the first case, the game is as follows:
1. Mr. Chanek takes one coin.
2. The opponent takes two coins.
3. Mr. Chanek takes one coin.
4. The opponent takes one coin.
For the second case, the game is as follows:
1. Mr. Chanek takes three coins.
2. The opponent takes one coin.
3. Mr. Chanek takes one coin.
4. The opponent takes one coin.
Submitted Solution:
```
t = int(input())
turn = 0
n = 0
chanekCoins = 0
def Main():
global n
global turn
global chanekCoins
for i in range(t):
turn = 1
chanekCoins = 0
n = int(input())
while(n > 0):
if(turn == 1):
Chanek()
elif(turn == 2):
Opponent()
print(int(chanekCoins))
def Chanek():
global turn
global n
global chanekCoins
if(n % 2 == 0 and n % 4 != 0):
n = n/2
chanekCoins += n/2
elif(n % 4 == 0 and n > 8):
n = n/2
chanekCoins += n/2
else:
n = n-1
chanekCoins += 1
turn = 2
def Opponent():
global turn
global n
if(n % 2 == 0 and n % 4 != 0):
n = n/2
elif(n % 4 == 0 and n > 8):
n = n/2
else:
n = n-1
turn = 1
Main()
``` | instruction | 0 | 2,648 | 19 | 5,296 |
No | output | 1 | 2,648 | 19 | 5,297 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Lately, Mr. Chanek frequently plays the game Arena of Greed. As the name implies, the game's goal is to find the greediest of them all, who will then be crowned king of Compfestnesia.
The game is played by two people taking turns, where Mr. Chanek takes the first turn. Initially, there is a treasure chest containing N gold coins. The game ends if there are no more gold coins in the chest. In each turn, the players can make one of the following moves:
* Take one gold coin from the chest.
* Take half of the gold coins on the chest. This move is only available if the number of coins in the chest is even.
Both players will try to maximize the number of coins they have. Mr. Chanek asks your help to find the maximum number of coins he can get at the end of the game if both he and the opponent plays optimally.
Input
The first line contains a single integer T (1 ≤ T ≤ 10^5) denotes the number of test cases.
The next T lines each contain a single integer N (1 ≤ N ≤ 10^{18}).
Output
T lines, each line is the answer requested by Mr. Chanek.
Example
Input
2
5
6
Output
2
4
Note
For the first case, the game is as follows:
1. Mr. Chanek takes one coin.
2. The opponent takes two coins.
3. Mr. Chanek takes one coin.
4. The opponent takes one coin.
For the second case, the game is as follows:
1. Mr. Chanek takes three coins.
2. The opponent takes one coin.
3. Mr. Chanek takes one coin.
4. The opponent takes one coin.
Submitted Solution:
```
for test in range(int(input())):
n=int(input())
ans=0
t=0
while n:
if n%2==0:
n=n//2
c=n
else:
n-=1
c=1
if t==0:
ans+=c
t=1
else:
t=0
print(ans)
``` | instruction | 0 | 2,649 | 19 | 5,298 |
No | output | 1 | 2,649 | 19 | 5,299 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Vasya plays Robot Bicorn Attack.
The game consists of three rounds. For each one a non-negative integer amount of points is given. The result of the game is the sum of obtained points. Vasya has already played three rounds and wrote obtained points one by one (without leading zeros) into the string s. Vasya decided to brag about his achievement to the friends. However, he has forgotten how many points he got for each round. The only thing he remembers is the string s.
Help Vasya to find out what is the maximum amount of points he could get. Take into account that Vasya played Robot Bicorn Attack for the first time, so he could not get more than 1000000 (106) points for one round.
Input
The only line of input contains non-empty string s obtained by Vasya. The string consists of digits only. The string length does not exceed 30 characters.
Output
Print the only number — the maximum amount of points Vasya could get. If Vasya is wrong and the string could not be obtained according to the rules then output number -1.
Examples
Input
1234
Output
37
Input
9000
Output
90
Input
0009
Output
-1
Note
In the first example the string must be split into numbers 1, 2 and 34.
In the second example the string must be split into numbers 90, 0 and 0.
In the third example the string is incorrect, because after splitting the string into 3 numbers number 00 or 09 will be obtained, but numbers cannot have leading zeroes. | instruction | 0 | 2,703 | 19 | 5,406 |
Tags: brute force, implementation
Correct Solution:
```
s = input()
n = len(s)
max_points = -1
for i in range(1, n - 1):
for j in range(i + 1, n):
a = s[:i]
b = s[i:j]
c = s[j:]
if(int(a) <= 10 ** 6 and int(b) <= 10 ** 6 and int(c) <= 10 ** 6):
if((a[0] == "0" and len(a) > 1) or (b[0] == "0" and len(b) > 1) or (c[0] == "0" and len(c) > 1)):
continue
else:
points = int(a) + int(b) + int(c)
if(max_points < points):
max_points = points
print(max_points)
``` | output | 1 | 2,703 | 19 | 5,407 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Vasya plays Robot Bicorn Attack.
The game consists of three rounds. For each one a non-negative integer amount of points is given. The result of the game is the sum of obtained points. Vasya has already played three rounds and wrote obtained points one by one (without leading zeros) into the string s. Vasya decided to brag about his achievement to the friends. However, he has forgotten how many points he got for each round. The only thing he remembers is the string s.
Help Vasya to find out what is the maximum amount of points he could get. Take into account that Vasya played Robot Bicorn Attack for the first time, so he could not get more than 1000000 (106) points for one round.
Input
The only line of input contains non-empty string s obtained by Vasya. The string consists of digits only. The string length does not exceed 30 characters.
Output
Print the only number — the maximum amount of points Vasya could get. If Vasya is wrong and the string could not be obtained according to the rules then output number -1.
Examples
Input
1234
Output
37
Input
9000
Output
90
Input
0009
Output
-1
Note
In the first example the string must be split into numbers 1, 2 and 34.
In the second example the string must be split into numbers 90, 0 and 0.
In the third example the string is incorrect, because after splitting the string into 3 numbers number 00 or 09 will be obtained, but numbers cannot have leading zeroes. | instruction | 0 | 2,704 | 19 | 5,408 |
Tags: brute force, implementation
Correct Solution:
```
s=input()
a=-1
for i in range(1,len(s)-1):
for j in range(i+1,len(s)):
x=int(s[:i])
y=int(s[i:j])
z=int(s[j:])
if s[0]=='0' and len(s[:i])>1:
continue
if s[i]=='0' and len(s[i:j])>1:
continue
if s[j]=='0' and len(s[j:])>1:
continue
if x>1e6 or y>1e6 or z>1e6:
continue
a=max(a,x+y+z)
print(a)
``` | output | 1 | 2,704 | 19 | 5,409 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Vasya plays Robot Bicorn Attack.
The game consists of three rounds. For each one a non-negative integer amount of points is given. The result of the game is the sum of obtained points. Vasya has already played three rounds and wrote obtained points one by one (without leading zeros) into the string s. Vasya decided to brag about his achievement to the friends. However, he has forgotten how many points he got for each round. The only thing he remembers is the string s.
Help Vasya to find out what is the maximum amount of points he could get. Take into account that Vasya played Robot Bicorn Attack for the first time, so he could not get more than 1000000 (106) points for one round.
Input
The only line of input contains non-empty string s obtained by Vasya. The string consists of digits only. The string length does not exceed 30 characters.
Output
Print the only number — the maximum amount of points Vasya could get. If Vasya is wrong and the string could not be obtained according to the rules then output number -1.
Examples
Input
1234
Output
37
Input
9000
Output
90
Input
0009
Output
-1
Note
In the first example the string must be split into numbers 1, 2 and 34.
In the second example the string must be split into numbers 90, 0 and 0.
In the third example the string is incorrect, because after splitting the string into 3 numbers number 00 or 09 will be obtained, but numbers cannot have leading zeroes. | instruction | 0 | 2,705 | 19 | 5,410 |
Tags: brute force, implementation
Correct Solution:
```
def max_score(n):
max_score = 0
any_choice = False
for i in range(0, len(n)-2):
for j in range(i+1, len(n)-1):
if ((n[:i+1][0] == '0' and len(n[:i+1]) > 1)
or (n[i+1:j+1][0] == '0' and len(n[i+1:j+1]) > 1)
or (n[j+1:][0] == '0' and len(n[j+1:]) > 1)
or int(n[:i+1]) > 1000000
or int(n[i+1:j+1]) > 1000000
or int(n[j+1:]) > 1000000):
continue
else:
any_choice = True
new_score = int(n[:i+1]) + int(n[i+1:j+1]) + int(n[j+1:])
if new_score > max_score:
max_score = new_score
if any_choice:
return max_score
else:
return -1
def main():
allscores = input()
print(max_score(allscores))
main()
``` | output | 1 | 2,705 | 19 | 5,411 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Vasya plays Robot Bicorn Attack.
The game consists of three rounds. For each one a non-negative integer amount of points is given. The result of the game is the sum of obtained points. Vasya has already played three rounds and wrote obtained points one by one (without leading zeros) into the string s. Vasya decided to brag about his achievement to the friends. However, he has forgotten how many points he got for each round. The only thing he remembers is the string s.
Help Vasya to find out what is the maximum amount of points he could get. Take into account that Vasya played Robot Bicorn Attack for the first time, so he could not get more than 1000000 (106) points for one round.
Input
The only line of input contains non-empty string s obtained by Vasya. The string consists of digits only. The string length does not exceed 30 characters.
Output
Print the only number — the maximum amount of points Vasya could get. If Vasya is wrong and the string could not be obtained according to the rules then output number -1.
Examples
Input
1234
Output
37
Input
9000
Output
90
Input
0009
Output
-1
Note
In the first example the string must be split into numbers 1, 2 and 34.
In the second example the string must be split into numbers 90, 0 and 0.
In the third example the string is incorrect, because after splitting the string into 3 numbers number 00 or 09 will be obtained, but numbers cannot have leading zeroes.
Submitted Solution:
```
x=input()
if ( x.startswith('0') ):
print(-1)
else:
try1=int(x[0:len(x)-2])+int(x[len(x)-2])+int(x[len(x)-1])
try2=int(x[1:len(x)-1])+int(x[0])+int(x[len(x)-1])
try3=int(x[2:len(x)])+int(x[0])+int(x[1])
print(max(try1,try2,try3))
``` | instruction | 0 | 2,714 | 19 | 5,428 |
No | output | 1 | 2,714 | 19 | 5,429 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Vasya plays Robot Bicorn Attack.
The game consists of three rounds. For each one a non-negative integer amount of points is given. The result of the game is the sum of obtained points. Vasya has already played three rounds and wrote obtained points one by one (without leading zeros) into the string s. Vasya decided to brag about his achievement to the friends. However, he has forgotten how many points he got for each round. The only thing he remembers is the string s.
Help Vasya to find out what is the maximum amount of points he could get. Take into account that Vasya played Robot Bicorn Attack for the first time, so he could not get more than 1000000 (106) points for one round.
Input
The only line of input contains non-empty string s obtained by Vasya. The string consists of digits only. The string length does not exceed 30 characters.
Output
Print the only number — the maximum amount of points Vasya could get. If Vasya is wrong and the string could not be obtained according to the rules then output number -1.
Examples
Input
1234
Output
37
Input
9000
Output
90
Input
0009
Output
-1
Note
In the first example the string must be split into numbers 1, 2 and 34.
In the second example the string must be split into numbers 90, 0 and 0.
In the third example the string is incorrect, because after splitting the string into 3 numbers number 00 or 09 will be obtained, but numbers cannot have leading zeroes.
Submitted Solution:
```
s=str(input())
n=len(s)
ans = []
if (n==3):
print(int(s[0])+int(s[1])+int(s[2]));
exit();
if (s[2]!="0"):
ans.append(int(s[0])+int(s[1])+int(s[2:]))
if (s[1]!="0"):
ans.append(int(s[0])+int(s[1:n-1])+int(s[-1]))
if (s[0]!="0"):
ans.append(int(s[0:n-2])+int(s[-2])+int(s[-1]))
if (len(ans)==0):
print(-1)
else:
print(max(ans))
``` | instruction | 0 | 2,715 | 19 | 5,430 |
No | output | 1 | 2,715 | 19 | 5,431 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Manao is trying to open a rather challenging lock. The lock has n buttons on it and to open it, you should press the buttons in a certain order to open the lock. When you push some button, it either stays pressed into the lock (that means that you've guessed correctly and pushed the button that goes next in the sequence), or all pressed buttons return to the initial position. When all buttons are pressed into the lock at once, the lock opens.
Consider an example with three buttons. Let's say that the opening sequence is: {2, 3, 1}. If you first press buttons 1 or 3, the buttons unpress immediately. If you first press button 2, it stays pressed. If you press 1 after 2, all buttons unpress. If you press 3 after 2, buttons 3 and 2 stay pressed. As soon as you've got two pressed buttons, you only need to press button 1 to open the lock.
Manao doesn't know the opening sequence. But he is really smart and he is going to act in the optimal way. Calculate the number of times he's got to push a button in order to open the lock in the worst-case scenario.
Input
A single line contains integer n (1 ≤ n ≤ 2000) — the number of buttons the lock has.
Output
In a single line print the number of times Manao has to push a button in the worst-case scenario.
Examples
Input
2
Output
3
Input
3
Output
7
Note
Consider the first test sample. Manao can fail his first push and push the wrong button. In this case he will already be able to guess the right one with his second push. And his third push will push the second right button. Thus, in the worst-case scenario he will only need 3 pushes. | instruction | 0 | 2,752 | 19 | 5,504 |
Tags: implementation, math
Correct Solution:
```
def pklk(n):
s=n
if (n==1):
return(n)
if (n==2):
return(3)
for i in range (2,n):
s+=1+i*(n-i)
return (s+1)
n=int(input())
print(pklk(n))
``` | output | 1 | 2,752 | 19 | 5,505 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Manao is trying to open a rather challenging lock. The lock has n buttons on it and to open it, you should press the buttons in a certain order to open the lock. When you push some button, it either stays pressed into the lock (that means that you've guessed correctly and pushed the button that goes next in the sequence), or all pressed buttons return to the initial position. When all buttons are pressed into the lock at once, the lock opens.
Consider an example with three buttons. Let's say that the opening sequence is: {2, 3, 1}. If you first press buttons 1 or 3, the buttons unpress immediately. If you first press button 2, it stays pressed. If you press 1 after 2, all buttons unpress. If you press 3 after 2, buttons 3 and 2 stay pressed. As soon as you've got two pressed buttons, you only need to press button 1 to open the lock.
Manao doesn't know the opening sequence. But he is really smart and he is going to act in the optimal way. Calculate the number of times he's got to push a button in order to open the lock in the worst-case scenario.
Input
A single line contains integer n (1 ≤ n ≤ 2000) — the number of buttons the lock has.
Output
In a single line print the number of times Manao has to push a button in the worst-case scenario.
Examples
Input
2
Output
3
Input
3
Output
7
Note
Consider the first test sample. Manao can fail his first push and push the wrong button. In this case he will already be able to guess the right one with his second push. And his third push will push the second right button. Thus, in the worst-case scenario he will only need 3 pushes. | instruction | 0 | 2,755 | 19 | 5,510 |
Tags: implementation, math
Correct Solution:
```
num = int(input().strip())
print(sum(x*(num-x) for x in range(num))+num)
``` | output | 1 | 2,755 | 19 | 5,511 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Manao is trying to open a rather challenging lock. The lock has n buttons on it and to open it, you should press the buttons in a certain order to open the lock. When you push some button, it either stays pressed into the lock (that means that you've guessed correctly and pushed the button that goes next in the sequence), or all pressed buttons return to the initial position. When all buttons are pressed into the lock at once, the lock opens.
Consider an example with three buttons. Let's say that the opening sequence is: {2, 3, 1}. If you first press buttons 1 or 3, the buttons unpress immediately. If you first press button 2, it stays pressed. If you press 1 after 2, all buttons unpress. If you press 3 after 2, buttons 3 and 2 stay pressed. As soon as you've got two pressed buttons, you only need to press button 1 to open the lock.
Manao doesn't know the opening sequence. But he is really smart and he is going to act in the optimal way. Calculate the number of times he's got to push a button in order to open the lock in the worst-case scenario.
Input
A single line contains integer n (1 ≤ n ≤ 2000) — the number of buttons the lock has.
Output
In a single line print the number of times Manao has to push a button in the worst-case scenario.
Examples
Input
2
Output
3
Input
3
Output
7
Note
Consider the first test sample. Manao can fail his first push and push the wrong button. In this case he will already be able to guess the right one with his second push. And his third push will push the second right button. Thus, in the worst-case scenario he will only need 3 pushes.
Submitted Solution:
```
n=int(input())
z=1
x=n+1
if n==1:
print('1')
else:
for y in range(n-1,1,-1):
x=x+y*z+1;
z=z+1
print(x)
``` | instruction | 0 | 2,760 | 19 | 5,520 |
Yes | output | 1 | 2,760 | 19 | 5,521 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Manao is trying to open a rather challenging lock. The lock has n buttons on it and to open it, you should press the buttons in a certain order to open the lock. When you push some button, it either stays pressed into the lock (that means that you've guessed correctly and pushed the button that goes next in the sequence), or all pressed buttons return to the initial position. When all buttons are pressed into the lock at once, the lock opens.
Consider an example with three buttons. Let's say that the opening sequence is: {2, 3, 1}. If you first press buttons 1 or 3, the buttons unpress immediately. If you first press button 2, it stays pressed. If you press 1 after 2, all buttons unpress. If you press 3 after 2, buttons 3 and 2 stay pressed. As soon as you've got two pressed buttons, you only need to press button 1 to open the lock.
Manao doesn't know the opening sequence. But he is really smart and he is going to act in the optimal way. Calculate the number of times he's got to push a button in order to open the lock in the worst-case scenario.
Input
A single line contains integer n (1 ≤ n ≤ 2000) — the number of buttons the lock has.
Output
In a single line print the number of times Manao has to push a button in the worst-case scenario.
Examples
Input
2
Output
3
Input
3
Output
7
Note
Consider the first test sample. Manao can fail his first push and push the wrong button. In this case he will already be able to guess the right one with his second push. And his third push will push the second right button. Thus, in the worst-case scenario he will only need 3 pushes.
Submitted Solution:
```
n = int(input())
print(sum((n*(i+1)-i*(i+2))for i in range(n)))
``` | instruction | 0 | 2,761 | 19 | 5,522 |
Yes | output | 1 | 2,761 | 19 | 5,523 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Manao is trying to open a rather challenging lock. The lock has n buttons on it and to open it, you should press the buttons in a certain order to open the lock. When you push some button, it either stays pressed into the lock (that means that you've guessed correctly and pushed the button that goes next in the sequence), or all pressed buttons return to the initial position. When all buttons are pressed into the lock at once, the lock opens.
Consider an example with three buttons. Let's say that the opening sequence is: {2, 3, 1}. If you first press buttons 1 or 3, the buttons unpress immediately. If you first press button 2, it stays pressed. If you press 1 after 2, all buttons unpress. If you press 3 after 2, buttons 3 and 2 stay pressed. As soon as you've got two pressed buttons, you only need to press button 1 to open the lock.
Manao doesn't know the opening sequence. But he is really smart and he is going to act in the optimal way. Calculate the number of times he's got to push a button in order to open the lock in the worst-case scenario.
Input
A single line contains integer n (1 ≤ n ≤ 2000) — the number of buttons the lock has.
Output
In a single line print the number of times Manao has to push a button in the worst-case scenario.
Examples
Input
2
Output
3
Input
3
Output
7
Note
Consider the first test sample. Manao can fail his first push and push the wrong button. In this case he will already be able to guess the right one with his second push. And his third push will push the second right button. Thus, in the worst-case scenario he will only need 3 pushes.
Submitted Solution:
```
n=int(input())
def t(n):
t=(n-1)*n/2
return t
def m(n):
x=0
for i in range(0,n):
x+=t(i)+i+1
return x
print(int(m(n)))
``` | instruction | 0 | 2,762 | 19 | 5,524 |
Yes | output | 1 | 2,762 | 19 | 5,525 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Manao is trying to open a rather challenging lock. The lock has n buttons on it and to open it, you should press the buttons in a certain order to open the lock. When you push some button, it either stays pressed into the lock (that means that you've guessed correctly and pushed the button that goes next in the sequence), or all pressed buttons return to the initial position. When all buttons are pressed into the lock at once, the lock opens.
Consider an example with three buttons. Let's say that the opening sequence is: {2, 3, 1}. If you first press buttons 1 or 3, the buttons unpress immediately. If you first press button 2, it stays pressed. If you press 1 after 2, all buttons unpress. If you press 3 after 2, buttons 3 and 2 stay pressed. As soon as you've got two pressed buttons, you only need to press button 1 to open the lock.
Manao doesn't know the opening sequence. But he is really smart and he is going to act in the optimal way. Calculate the number of times he's got to push a button in order to open the lock in the worst-case scenario.
Input
A single line contains integer n (1 ≤ n ≤ 2000) — the number of buttons the lock has.
Output
In a single line print the number of times Manao has to push a button in the worst-case scenario.
Examples
Input
2
Output
3
Input
3
Output
7
Note
Consider the first test sample. Manao can fail his first push and push the wrong button. In this case he will already be able to guess the right one with his second push. And his third push will push the second right button. Thus, in the worst-case scenario he will only need 3 pushes.
Submitted Solution:
```
#!/usr/bin/env python3
n = int(input())
print((n - 1) * n * (n + 1) // 6 + n)
``` | instruction | 0 | 2,763 | 19 | 5,526 |
Yes | output | 1 | 2,763 | 19 | 5,527 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Manao is trying to open a rather challenging lock. The lock has n buttons on it and to open it, you should press the buttons in a certain order to open the lock. When you push some button, it either stays pressed into the lock (that means that you've guessed correctly and pushed the button that goes next in the sequence), or all pressed buttons return to the initial position. When all buttons are pressed into the lock at once, the lock opens.
Consider an example with three buttons. Let's say that the opening sequence is: {2, 3, 1}. If you first press buttons 1 or 3, the buttons unpress immediately. If you first press button 2, it stays pressed. If you press 1 after 2, all buttons unpress. If you press 3 after 2, buttons 3 and 2 stay pressed. As soon as you've got two pressed buttons, you only need to press button 1 to open the lock.
Manao doesn't know the opening sequence. But he is really smart and he is going to act in the optimal way. Calculate the number of times he's got to push a button in order to open the lock in the worst-case scenario.
Input
A single line contains integer n (1 ≤ n ≤ 2000) — the number of buttons the lock has.
Output
In a single line print the number of times Manao has to push a button in the worst-case scenario.
Examples
Input
2
Output
3
Input
3
Output
7
Note
Consider the first test sample. Manao can fail his first push and push the wrong button. In this case he will already be able to guess the right one with his second push. And his third push will push the second right button. Thus, in the worst-case scenario he will only need 3 pushes.
Submitted Solution:
```
def binaryExponentiation(x,n):
res = 1
while n > 0:
if n % 2 == 1:
res = res * x
x = x * x
n = n // 2
return res
h = int(input())
if h == 1:
print(1)
else:
print(binaryExponentiation(2,h)-(h//2))
``` | instruction | 0 | 2,764 | 19 | 5,528 |
No | output | 1 | 2,764 | 19 | 5,529 |
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