message stringlengths 2 67k | message_type stringclasses 2 values | message_id int64 0 1 | conversation_id int64 463 109k | cluster float64 19 19 | __index_level_0__ int64 926 217k |
|---|---|---|---|---|---|
Provide a correct Python 3 solution for this coding contest problem.
problem
There are n cards with one integer from 1 to n and one blank card. Of these n + 1 cards, k cards are given, but 1 ≤ k ≤ n. You can write one integer from 1 to n on a blank card. I want to make a continuous sequence of integers as long as possible with just a given card.
Write a program that outputs the maximum length of a contiguous sequence of integers that can be made from a given card when the given card is entered.
input
The input consists of multiple datasets. Each dataset is given in the following format. The input ends on a line containing two zeros.
On the first line, two integers n (1 ≤ n ≤ 100000) and k (1 ≤ k ≤ n) are written in this order, separated by one blank. The following k line contains one integer. Written one by one, representing the integers written on the given k cards. Blank cards are represented by 0.
Of the scoring data, 40% of the points are 1 ≤ n ≤ 1000, 1 ≤ k ≤ 500, 20% of the points are 1 ≤ n ≤ 60000, 1 ≤ k ≤ 50000. Satisfy 1 ≤ n ≤ 100000, 1 ≤ k ≤ 100000.
The number of datasets does not exceed 5.
output
Outputs an integer on one line for each dataset.
Examples
Input
7 5
6
2
4
7
1
7 5
6
2
0
4
7
0 0
Output
2
4
Input
None
Output
None | instruction | 0 | 723 | 19 | 1,446 |
"Correct Solution:
```
def main():
while True:
try:
n,k = map(int,input().split())
if n == 0 and k == 0: break
lst = [0 for _ in range(n)]
lst2 = []
flag = 0
for _ in range(k):
i = int(input())
if not i:
flag = 1
else:
lst[i - 1] = 1
l = -1
r = -1
for i in range(n):
if lst[i] == 0:
if r != -1:
lst2.append((l,r))
l = -1
r = -1
else:
if l == -1:
l = i
r = i
else:
r += 1
else:
if r != -1:
lst2.append((l,r))
ans = 0
# print(lst)
# print(lst2)
if not flag:
for t in lst2:
ans = max(ans,t[1] - t[0] + 1)
else:
for i in range(len(lst2)):
if i == 0:
ans = max(ans,lst2[0][1] - lst2[0][0] + 1)
elif lst2[i][0] - lst2[i - 1][1] == 2:
ans = max(ans,lst2[i][1] - lst2[i - 1][0] + 1)
else:
ans = max(ans,lst2[i][1] - lst2[i][0] + 1)
print(ans)
except EOFError:
break
if __name__ == '__main__':
main()
``` | output | 1 | 723 | 19 | 1,447 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
problem
There are n cards with one integer from 1 to n and one blank card. Of these n + 1 cards, k cards are given, but 1 ≤ k ≤ n. You can write one integer from 1 to n on a blank card. I want to make a continuous sequence of integers as long as possible with just a given card.
Write a program that outputs the maximum length of a contiguous sequence of integers that can be made from a given card when the given card is entered.
input
The input consists of multiple datasets. Each dataset is given in the following format. The input ends on a line containing two zeros.
On the first line, two integers n (1 ≤ n ≤ 100000) and k (1 ≤ k ≤ n) are written in this order, separated by one blank. The following k line contains one integer. Written one by one, representing the integers written on the given k cards. Blank cards are represented by 0.
Of the scoring data, 40% of the points are 1 ≤ n ≤ 1000, 1 ≤ k ≤ 500, 20% of the points are 1 ≤ n ≤ 60000, 1 ≤ k ≤ 50000. Satisfy 1 ≤ n ≤ 100000, 1 ≤ k ≤ 100000.
The number of datasets does not exceed 5.
output
Outputs an integer on one line for each dataset.
Examples
Input
7 5
6
2
4
7
1
7 5
6
2
0
4
7
0 0
Output
2
4
Input
None
Output
None
Submitted Solution:
```
while True:
n,k = map(int,input().split())
if n == 0:
break
c = []
zex = 0
for i in range(k):
C = int(input())
if C == 0:
zex = 1
else:
c.append(C)
c.sort()
ans = 0
l = 0
r = 0
for i in range(len(c) - 1):
if c[i] + 1 == c[i+1]:
r += 1
elif zex == 1 and c[i] + 2 == c[i+1]:
l = r
r = 1
else:
l = 0
r = 1
ans = max(ans,l+r+zex)
print (ans)
``` | instruction | 0 | 724 | 19 | 1,448 |
Yes | output | 1 | 724 | 19 | 1,449 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
problem
There are n cards with one integer from 1 to n and one blank card. Of these n + 1 cards, k cards are given, but 1 ≤ k ≤ n. You can write one integer from 1 to n on a blank card. I want to make a continuous sequence of integers as long as possible with just a given card.
Write a program that outputs the maximum length of a contiguous sequence of integers that can be made from a given card when the given card is entered.
input
The input consists of multiple datasets. Each dataset is given in the following format. The input ends on a line containing two zeros.
On the first line, two integers n (1 ≤ n ≤ 100000) and k (1 ≤ k ≤ n) are written in this order, separated by one blank. The following k line contains one integer. Written one by one, representing the integers written on the given k cards. Blank cards are represented by 0.
Of the scoring data, 40% of the points are 1 ≤ n ≤ 1000, 1 ≤ k ≤ 500, 20% of the points are 1 ≤ n ≤ 60000, 1 ≤ k ≤ 50000. Satisfy 1 ≤ n ≤ 100000, 1 ≤ k ≤ 100000.
The number of datasets does not exceed 5.
output
Outputs an integer on one line for each dataset.
Examples
Input
7 5
6
2
4
7
1
7 5
6
2
0
4
7
0 0
Output
2
4
Input
None
Output
None
Submitted Solution:
```
#!/usr/bin/env python
# -*- coding: utf-8 -*-
while True:
N,K = map(int,input().split())
A = sorted([int(input()) for i in range(0,K)])
if (N,K) == (0,0):
break
if A[0] == 0:
flag = True
A = A[1:]
K -= 1
else:
flag = False
ans = 0
count = 0
diff_list = []
s = 0
for i in range(1,K):
if A[i] - A[i-1] == 2:
diff_list.append(A[i-1] - A[s])
s = i
count = 0
elif A[i] - A[i-1] > 2:
diff_list.append(A[i-1] - A[s])
diff_list.append(0)
s = i
count = 0
else:
count += 1
ans = max(ans,count)
else:
diff_list.append(A[i] - A[s])
if flag is True:
ans = 0
for i in range(1,len(diff_list)):
ans = max(ans,diff_list[i] + diff_list[i-1] + 2)
print(ans + 1)
``` | instruction | 0 | 725 | 19 | 1,450 |
Yes | output | 1 | 725 | 19 | 1,451 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
problem
There are n cards with one integer from 1 to n and one blank card. Of these n + 1 cards, k cards are given, but 1 ≤ k ≤ n. You can write one integer from 1 to n on a blank card. I want to make a continuous sequence of integers as long as possible with just a given card.
Write a program that outputs the maximum length of a contiguous sequence of integers that can be made from a given card when the given card is entered.
input
The input consists of multiple datasets. Each dataset is given in the following format. The input ends on a line containing two zeros.
On the first line, two integers n (1 ≤ n ≤ 100000) and k (1 ≤ k ≤ n) are written in this order, separated by one blank. The following k line contains one integer. Written one by one, representing the integers written on the given k cards. Blank cards are represented by 0.
Of the scoring data, 40% of the points are 1 ≤ n ≤ 1000, 1 ≤ k ≤ 500, 20% of the points are 1 ≤ n ≤ 60000, 1 ≤ k ≤ 50000. Satisfy 1 ≤ n ≤ 100000, 1 ≤ k ≤ 100000.
The number of datasets does not exceed 5.
output
Outputs an integer on one line for each dataset.
Examples
Input
7 5
6
2
4
7
1
7 5
6
2
0
4
7
0 0
Output
2
4
Input
None
Output
None
Submitted Solution:
```
# AOJ 0517: Longest Steps
# Python3 2018.6.30 bal4u
while True:
n, k = map(int, input().split())
if n == 0: break
c = [0]*(n+2)
f = 0;
for i in range(k):
a = int(input())
if a == 0: f = 1
else: c[a] = 1
ans = w0 = w = 0
for i in range(1, n+1):
if c[i]: w += 1
elif w > 0:
if w0 + w + f > ans: ans = w0 + w + f
w0 = w if f and c[i+1] else 0
w = 0
if w0 + w + f > ans: ans = w0 + w + f
print(ans)
``` | instruction | 0 | 726 | 19 | 1,452 |
Yes | output | 1 | 726 | 19 | 1,453 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
problem
There are n cards with one integer from 1 to n and one blank card. Of these n + 1 cards, k cards are given, but 1 ≤ k ≤ n. You can write one integer from 1 to n on a blank card. I want to make a continuous sequence of integers as long as possible with just a given card.
Write a program that outputs the maximum length of a contiguous sequence of integers that can be made from a given card when the given card is entered.
input
The input consists of multiple datasets. Each dataset is given in the following format. The input ends on a line containing two zeros.
On the first line, two integers n (1 ≤ n ≤ 100000) and k (1 ≤ k ≤ n) are written in this order, separated by one blank. The following k line contains one integer. Written one by one, representing the integers written on the given k cards. Blank cards are represented by 0.
Of the scoring data, 40% of the points are 1 ≤ n ≤ 1000, 1 ≤ k ≤ 500, 20% of the points are 1 ≤ n ≤ 60000, 1 ≤ k ≤ 50000. Satisfy 1 ≤ n ≤ 100000, 1 ≤ k ≤ 100000.
The number of datasets does not exceed 5.
output
Outputs an integer on one line for each dataset.
Examples
Input
7 5
6
2
4
7
1
7 5
6
2
0
4
7
0 0
Output
2
4
Input
None
Output
None
Submitted Solution:
```
#!/usr/bin/env python
# -*- coding: utf-8 -*-
while True:
N,K = map(int,input().split())
A = sorted([int(input()) for i in range(0,K)])
if (N,K) == (0,0):
break
if A[0] == 0:
flag = True
A = A[1:]
K -= 1
else:
flag = False
ans = 0
count = 0
diff_list = []
s = 0
for i in range(1,K):
if A[i] - A[i-1] == 2:
diff_list.append(A[i-1] - A[s])
s = i
count = 0
if A[i] - A[i-1] >= 2:
s = i
count = 0
count += 1
ans = max(ans,count)
else:
diff_list.append(A[i] - A[s])
if flag is True:
for i in range(1,len(diff_list)):
ans = max(ans,diff_list[i] + diff_list[i-1] + 3)
print(ans)
``` | instruction | 0 | 727 | 19 | 1,454 |
No | output | 1 | 727 | 19 | 1,455 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
problem
There are n cards with one integer from 1 to n and one blank card. Of these n + 1 cards, k cards are given, but 1 ≤ k ≤ n. You can write one integer from 1 to n on a blank card. I want to make a continuous sequence of integers as long as possible with just a given card.
Write a program that outputs the maximum length of a contiguous sequence of integers that can be made from a given card when the given card is entered.
input
The input consists of multiple datasets. Each dataset is given in the following format. The input ends on a line containing two zeros.
On the first line, two integers n (1 ≤ n ≤ 100000) and k (1 ≤ k ≤ n) are written in this order, separated by one blank. The following k line contains one integer. Written one by one, representing the integers written on the given k cards. Blank cards are represented by 0.
Of the scoring data, 40% of the points are 1 ≤ n ≤ 1000, 1 ≤ k ≤ 500, 20% of the points are 1 ≤ n ≤ 60000, 1 ≤ k ≤ 50000. Satisfy 1 ≤ n ≤ 100000, 1 ≤ k ≤ 100000.
The number of datasets does not exceed 5.
output
Outputs an integer on one line for each dataset.
Examples
Input
7 5
6
2
4
7
1
7 5
6
2
0
4
7
0 0
Output
2
4
Input
None
Output
None
Submitted Solution:
```
# AOJ 0517: Longest Steps
# Python3 2018.6.30 bal4u
while True:
n, k = map(int, input().split())
if n == 0: break
c = [0]*(n+1)
f = 0;
for i in range(k):
a = int(input())
if a == 0: f = 1
else: c[a] = 1
ans = w0 = w = 0
for i in range(1, n+1):
if c[i]: w += 1
elif w > 0:
if w0 + w + f > ans: ans = w0 + w + f
w0 = w if f and c[i+1] else 0
w = 0
if w0 + w + f > ans: ans = w0 + w + f
print(ans)
``` | instruction | 0 | 728 | 19 | 1,456 |
No | output | 1 | 728 | 19 | 1,457 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
problem
There are n cards with one integer from 1 to n and one blank card. Of these n + 1 cards, k cards are given, but 1 ≤ k ≤ n. You can write one integer from 1 to n on a blank card. I want to make a continuous sequence of integers as long as possible with just a given card.
Write a program that outputs the maximum length of a contiguous sequence of integers that can be made from a given card when the given card is entered.
input
The input consists of multiple datasets. Each dataset is given in the following format. The input ends on a line containing two zeros.
On the first line, two integers n (1 ≤ n ≤ 100000) and k (1 ≤ k ≤ n) are written in this order, separated by one blank. The following k line contains one integer. Written one by one, representing the integers written on the given k cards. Blank cards are represented by 0.
Of the scoring data, 40% of the points are 1 ≤ n ≤ 1000, 1 ≤ k ≤ 500, 20% of the points are 1 ≤ n ≤ 60000, 1 ≤ k ≤ 50000. Satisfy 1 ≤ n ≤ 100000, 1 ≤ k ≤ 100000.
The number of datasets does not exceed 5.
output
Outputs an integer on one line for each dataset.
Examples
Input
7 5
6
2
4
7
1
7 5
6
2
0
4
7
0 0
Output
2
4
Input
None
Output
None
Submitted Solution:
```
#!/usr/bin/env python
# -*- coding: utf-8 -*-
while True:
N,K = map(int,input().split())
A = sorted([int(input()) for i in range(0,K)])
if (N,K) == (0,0):
break
if A[0] == 0:
flag = True
A = A[1:]
K -= 1
else:
flag = False
diff = []
ans = 0
prev = 0
prev_prev = 0
count = 0
for i in range(1,K):
if A[i] - A[i-1] == 1:
count += 1
ans = max(ans,count-prev_prev)
elif A[i] - A[i-1] == 2:
if flag is True:
count += 1
ans = max(ans,count-prev_prev)
prev_prev = prev
prev = count - prev
else:
count = 0
else:
count = 0
print(ans + A[0])
``` | instruction | 0 | 729 | 19 | 1,458 |
No | output | 1 | 729 | 19 | 1,459 |
Provide tags and a correct Python 3 solution for this coding contest problem.
A card pyramid of height 1 is constructed by resting two cards against each other. For h>1, a card pyramid of height h is constructed by placing a card pyramid of height h-1 onto a base. A base consists of h pyramids of height 1, and h-1 cards on top. For example, card pyramids of heights 1, 2, and 3 look as follows:
<image>
You start with n cards and build the tallest pyramid that you can. If there are some cards remaining, you build the tallest pyramid possible with the remaining cards. You repeat this process until it is impossible to build another pyramid. In the end, how many pyramids will you have constructed?
Input
Each test consists of multiple test cases. The first line contains a single integer t (1≤ t≤ 1000) — the number of test cases. Next t lines contain descriptions of test cases.
Each test case contains a single integer n (1≤ n≤ 10^9) — the number of cards.
It is guaranteed that the sum of n over all test cases does not exceed 10^9.
Output
For each test case output a single integer — the number of pyramids you will have constructed in the end.
Example
Input
5
3
14
15
24
1
Output
1
2
1
3
0
Note
In the first test, you construct a pyramid of height 1 with 2 cards. There is 1 card remaining, which is not enough to build a pyramid.
In the second test, you build two pyramids, each of height 2, with no cards remaining.
In the third test, you build one pyramid of height 3, with no cards remaining.
In the fourth test, you build one pyramid of height 3 with 9 cards remaining. Then you build a pyramid of height 2 with 2 cards remaining. Then you build a final pyramid of height 1 with no cards remaining.
In the fifth test, one card is not enough to build any pyramids. | instruction | 0 | 997 | 19 | 1,994 |
Tags: binary search, brute force, dp, math
Correct Solution:
```
def pyr(n):
return 3 * int(0.5 * (n + 1) * n) - n
def bs(l, r, n):
#print(pyr(l), pyr(r))
if pyr(r) == n:
return r
if l == r - 1:
return l
elif pyr((l + r) // 2) >= n:
return bs(l, (r + l) // 2 , n)
return bs((r + l) // 2, r, n)
for something in range(int(input())):
n = int(input())
ans = 0
while n >= 2:
bs_res = bs(1, 26000, n)
n -= pyr(bs_res)
#print(n, bs_res, pyr(bs_res))
ans += 1
print(ans)
``` | output | 1 | 997 | 19 | 1,995 |
Provide tags and a correct Python 3 solution for this coding contest problem.
A card pyramid of height 1 is constructed by resting two cards against each other. For h>1, a card pyramid of height h is constructed by placing a card pyramid of height h-1 onto a base. A base consists of h pyramids of height 1, and h-1 cards on top. For example, card pyramids of heights 1, 2, and 3 look as follows:
<image>
You start with n cards and build the tallest pyramid that you can. If there are some cards remaining, you build the tallest pyramid possible with the remaining cards. You repeat this process until it is impossible to build another pyramid. In the end, how many pyramids will you have constructed?
Input
Each test consists of multiple test cases. The first line contains a single integer t (1≤ t≤ 1000) — the number of test cases. Next t lines contain descriptions of test cases.
Each test case contains a single integer n (1≤ n≤ 10^9) — the number of cards.
It is guaranteed that the sum of n over all test cases does not exceed 10^9.
Output
For each test case output a single integer — the number of pyramids you will have constructed in the end.
Example
Input
5
3
14
15
24
1
Output
1
2
1
3
0
Note
In the first test, you construct a pyramid of height 1 with 2 cards. There is 1 card remaining, which is not enough to build a pyramid.
In the second test, you build two pyramids, each of height 2, with no cards remaining.
In the third test, you build one pyramid of height 3, with no cards remaining.
In the fourth test, you build one pyramid of height 3 with 9 cards remaining. Then you build a pyramid of height 2 with 2 cards remaining. Then you build a final pyramid of height 1 with no cards remaining.
In the fifth test, one card is not enough to build any pyramids. | instruction | 0 | 998 | 19 | 1,996 |
Tags: binary search, brute force, dp, math
Correct Solution:
```
import math
test = int(input())
for tes in range(test):
n = int(input())
cnt=0
if (n==0 or n==1):
print(0)
continue
while(True):
sq = math.sqrt(1+24*n) - 1
h = sq//6
n = n- ((h)*(3*h+1))/2
cnt+=1
if(n==1 or n==0):
break
print(cnt)
``` | output | 1 | 998 | 19 | 1,997 |
Provide tags and a correct Python 3 solution for this coding contest problem.
A card pyramid of height 1 is constructed by resting two cards against each other. For h>1, a card pyramid of height h is constructed by placing a card pyramid of height h-1 onto a base. A base consists of h pyramids of height 1, and h-1 cards on top. For example, card pyramids of heights 1, 2, and 3 look as follows:
<image>
You start with n cards and build the tallest pyramid that you can. If there are some cards remaining, you build the tallest pyramid possible with the remaining cards. You repeat this process until it is impossible to build another pyramid. In the end, how many pyramids will you have constructed?
Input
Each test consists of multiple test cases. The first line contains a single integer t (1≤ t≤ 1000) — the number of test cases. Next t lines contain descriptions of test cases.
Each test case contains a single integer n (1≤ n≤ 10^9) — the number of cards.
It is guaranteed that the sum of n over all test cases does not exceed 10^9.
Output
For each test case output a single integer — the number of pyramids you will have constructed in the end.
Example
Input
5
3
14
15
24
1
Output
1
2
1
3
0
Note
In the first test, you construct a pyramid of height 1 with 2 cards. There is 1 card remaining, which is not enough to build a pyramid.
In the second test, you build two pyramids, each of height 2, with no cards remaining.
In the third test, you build one pyramid of height 3, with no cards remaining.
In the fourth test, you build one pyramid of height 3 with 9 cards remaining. Then you build a pyramid of height 2 with 2 cards remaining. Then you build a final pyramid of height 1 with no cards remaining.
In the fifth test, one card is not enough to build any pyramids. | instruction | 0 | 999 | 19 | 1,998 |
Tags: binary search, brute force, dp, math
Correct Solution:
```
nums=[]
def seive():
for i in range(1,100000):
x=((3*i+1)*i)//2
nums.append(x)
def binarySearch(arr, n, key):
left = 0
right = n
mid = 0
while (left < right):
mid = (right + left) // 2
if (arr[mid] == key):
while (mid + 1 < n and arr[mid + 1] == key):
mid += 1
break
elif (arr[mid] > key):
right = mid
else:
left = mid + 1
while (mid > -1 and arr[mid] > key):
mid -= 1
return mid
seive()
for _ in range(int(input())):
num=int(input())
if(num<2):
print(0)
else:
ans=0
while(num>1):
index=binarySearch(nums,len(nums),num)
y=nums[index]
ans+=(num//y)
num=num%y
print(ans)
``` | output | 1 | 999 | 19 | 1,999 |
Provide tags and a correct Python 3 solution for this coding contest problem.
A card pyramid of height 1 is constructed by resting two cards against each other. For h>1, a card pyramid of height h is constructed by placing a card pyramid of height h-1 onto a base. A base consists of h pyramids of height 1, and h-1 cards on top. For example, card pyramids of heights 1, 2, and 3 look as follows:
<image>
You start with n cards and build the tallest pyramid that you can. If there are some cards remaining, you build the tallest pyramid possible with the remaining cards. You repeat this process until it is impossible to build another pyramid. In the end, how many pyramids will you have constructed?
Input
Each test consists of multiple test cases. The first line contains a single integer t (1≤ t≤ 1000) — the number of test cases. Next t lines contain descriptions of test cases.
Each test case contains a single integer n (1≤ n≤ 10^9) — the number of cards.
It is guaranteed that the sum of n over all test cases does not exceed 10^9.
Output
For each test case output a single integer — the number of pyramids you will have constructed in the end.
Example
Input
5
3
14
15
24
1
Output
1
2
1
3
0
Note
In the first test, you construct a pyramid of height 1 with 2 cards. There is 1 card remaining, which is not enough to build a pyramid.
In the second test, you build two pyramids, each of height 2, with no cards remaining.
In the third test, you build one pyramid of height 3, with no cards remaining.
In the fourth test, you build one pyramid of height 3 with 9 cards remaining. Then you build a pyramid of height 2 with 2 cards remaining. Then you build a final pyramid of height 1 with no cards remaining.
In the fifth test, one card is not enough to build any pyramids. | instruction | 0 | 1,000 | 19 | 2,000 |
Tags: binary search, brute force, dp, math
Correct Solution:
```
hashmap = [2]
counter = 5
for i in range(0, 10**5):
hashmap.append(hashmap[-1]+counter)
counter+=3
for _ in range(0, int(input())):
n = int(input())
i=0
res=0
while True:
if n < 2:
print(res)
break
if hashmap[i] == n:
res+=1
print(res)
break
if hashmap[i] > n:
res +=1
n-=hashmap[i-1]
i=0
else:
i+=1
``` | output | 1 | 1,000 | 19 | 2,001 |
Provide tags and a correct Python 3 solution for this coding contest problem.
A card pyramid of height 1 is constructed by resting two cards against each other. For h>1, a card pyramid of height h is constructed by placing a card pyramid of height h-1 onto a base. A base consists of h pyramids of height 1, and h-1 cards on top. For example, card pyramids of heights 1, 2, and 3 look as follows:
<image>
You start with n cards and build the tallest pyramid that you can. If there are some cards remaining, you build the tallest pyramid possible with the remaining cards. You repeat this process until it is impossible to build another pyramid. In the end, how many pyramids will you have constructed?
Input
Each test consists of multiple test cases. The first line contains a single integer t (1≤ t≤ 1000) — the number of test cases. Next t lines contain descriptions of test cases.
Each test case contains a single integer n (1≤ n≤ 10^9) — the number of cards.
It is guaranteed that the sum of n over all test cases does not exceed 10^9.
Output
For each test case output a single integer — the number of pyramids you will have constructed in the end.
Example
Input
5
3
14
15
24
1
Output
1
2
1
3
0
Note
In the first test, you construct a pyramid of height 1 with 2 cards. There is 1 card remaining, which is not enough to build a pyramid.
In the second test, you build two pyramids, each of height 2, with no cards remaining.
In the third test, you build one pyramid of height 3, with no cards remaining.
In the fourth test, you build one pyramid of height 3 with 9 cards remaining. Then you build a pyramid of height 2 with 2 cards remaining. Then you build a final pyramid of height 1 with no cards remaining.
In the fifth test, one card is not enough to build any pyramids. | instruction | 0 | 1,001 | 19 | 2,002 |
Tags: binary search, brute force, dp, math
Correct Solution:
```
import sys
input=sys.stdin.readline
import bisect as bi
I = lambda : list(map(int,input().split()))
a=[2];i=1;k=4;x=2
while x<10**9:
x+=i+k
a.append(x)
i+=1;k+=2
for _ in range(int(input())):
n,=I();ct=0
x=bi.bisect(a,n)
while n>1:
n-=a[x-1];ct+=1
x=bi.bisect(a,n)
#print(n,bi.bisect(a,n))
print(ct)
``` | output | 1 | 1,001 | 19 | 2,003 |
Provide tags and a correct Python 3 solution for this coding contest problem.
A card pyramid of height 1 is constructed by resting two cards against each other. For h>1, a card pyramid of height h is constructed by placing a card pyramid of height h-1 onto a base. A base consists of h pyramids of height 1, and h-1 cards on top. For example, card pyramids of heights 1, 2, and 3 look as follows:
<image>
You start with n cards and build the tallest pyramid that you can. If there are some cards remaining, you build the tallest pyramid possible with the remaining cards. You repeat this process until it is impossible to build another pyramid. In the end, how many pyramids will you have constructed?
Input
Each test consists of multiple test cases. The first line contains a single integer t (1≤ t≤ 1000) — the number of test cases. Next t lines contain descriptions of test cases.
Each test case contains a single integer n (1≤ n≤ 10^9) — the number of cards.
It is guaranteed that the sum of n over all test cases does not exceed 10^9.
Output
For each test case output a single integer — the number of pyramids you will have constructed in the end.
Example
Input
5
3
14
15
24
1
Output
1
2
1
3
0
Note
In the first test, you construct a pyramid of height 1 with 2 cards. There is 1 card remaining, which is not enough to build a pyramid.
In the second test, you build two pyramids, each of height 2, with no cards remaining.
In the third test, you build one pyramid of height 3, with no cards remaining.
In the fourth test, you build one pyramid of height 3 with 9 cards remaining. Then you build a pyramid of height 2 with 2 cards remaining. Then you build a final pyramid of height 1 with no cards remaining.
In the fifth test, one card is not enough to build any pyramids. | instruction | 0 | 1,002 | 19 | 2,004 |
Tags: binary search, brute force, dp, math
Correct Solution:
```
import bisect
start = [2]
for i in range(2,40000):
bot = (i*2) + i-1
start.append( start[-1] + bot )
def solve(num):
ans = 0
while num > 1:
pos = bisect.bisect_right( start , num )
num = num - start[ pos - 1 ]
ans += 1
return ans
# input = open('file.txt').readline
for _ in range( int( input() ) ):
print( solve( int( input() ) ) )
``` | output | 1 | 1,002 | 19 | 2,005 |
Provide tags and a correct Python 3 solution for this coding contest problem.
A card pyramid of height 1 is constructed by resting two cards against each other. For h>1, a card pyramid of height h is constructed by placing a card pyramid of height h-1 onto a base. A base consists of h pyramids of height 1, and h-1 cards on top. For example, card pyramids of heights 1, 2, and 3 look as follows:
<image>
You start with n cards and build the tallest pyramid that you can. If there are some cards remaining, you build the tallest pyramid possible with the remaining cards. You repeat this process until it is impossible to build another pyramid. In the end, how many pyramids will you have constructed?
Input
Each test consists of multiple test cases. The first line contains a single integer t (1≤ t≤ 1000) — the number of test cases. Next t lines contain descriptions of test cases.
Each test case contains a single integer n (1≤ n≤ 10^9) — the number of cards.
It is guaranteed that the sum of n over all test cases does not exceed 10^9.
Output
For each test case output a single integer — the number of pyramids you will have constructed in the end.
Example
Input
5
3
14
15
24
1
Output
1
2
1
3
0
Note
In the first test, you construct a pyramid of height 1 with 2 cards. There is 1 card remaining, which is not enough to build a pyramid.
In the second test, you build two pyramids, each of height 2, with no cards remaining.
In the third test, you build one pyramid of height 3, with no cards remaining.
In the fourth test, you build one pyramid of height 3 with 9 cards remaining. Then you build a pyramid of height 2 with 2 cards remaining. Then you build a final pyramid of height 1 with no cards remaining.
In the fifth test, one card is not enough to build any pyramids. | instruction | 0 | 1,003 | 19 | 2,006 |
Tags: binary search, brute force, dp, math
Correct Solution:
```
import bisect
pre=[]
dup=0
i=1
while(dup<1000000001):
temp=(i*((3*i)+1))//2
pre.append(temp)
dup=temp
i+=1
t=int(input())
for _ in range(t):
n=int(input())
cnt=0
while(True):
if(n<2):
break
x = bisect.bisect_left(pre,n,0,len(pre))
if(pre[x]==n):
cnt+=1
break
else:
x=x-1
n=n-pre[x]
cnt+=1
print(cnt)
``` | output | 1 | 1,003 | 19 | 2,007 |
Provide tags and a correct Python 3 solution for this coding contest problem.
A card pyramid of height 1 is constructed by resting two cards against each other. For h>1, a card pyramid of height h is constructed by placing a card pyramid of height h-1 onto a base. A base consists of h pyramids of height 1, and h-1 cards on top. For example, card pyramids of heights 1, 2, and 3 look as follows:
<image>
You start with n cards and build the tallest pyramid that you can. If there are some cards remaining, you build the tallest pyramid possible with the remaining cards. You repeat this process until it is impossible to build another pyramid. In the end, how many pyramids will you have constructed?
Input
Each test consists of multiple test cases. The first line contains a single integer t (1≤ t≤ 1000) — the number of test cases. Next t lines contain descriptions of test cases.
Each test case contains a single integer n (1≤ n≤ 10^9) — the number of cards.
It is guaranteed that the sum of n over all test cases does not exceed 10^9.
Output
For each test case output a single integer — the number of pyramids you will have constructed in the end.
Example
Input
5
3
14
15
24
1
Output
1
2
1
3
0
Note
In the first test, you construct a pyramid of height 1 with 2 cards. There is 1 card remaining, which is not enough to build a pyramid.
In the second test, you build two pyramids, each of height 2, with no cards remaining.
In the third test, you build one pyramid of height 3, with no cards remaining.
In the fourth test, you build one pyramid of height 3 with 9 cards remaining. Then you build a pyramid of height 2 with 2 cards remaining. Then you build a final pyramid of height 1 with no cards remaining.
In the fifth test, one card is not enough to build any pyramids. | instruction | 0 | 1,004 | 19 | 2,008 |
Tags: binary search, brute force, dp, math
Correct Solution:
```
from math import sqrt
def main():
t = int(input())
for __ in range(t):
n = int(input())
count = 0
while n >= 2:
count += 1
h = int((sqrt((24*n)+1)-1)/6)
#print(h)
n -= (h*((3*h)+1))//2
print(count)
if __name__ == '__main__':
main()
``` | output | 1 | 1,004 | 19 | 2,009 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
A card pyramid of height 1 is constructed by resting two cards against each other. For h>1, a card pyramid of height h is constructed by placing a card pyramid of height h-1 onto a base. A base consists of h pyramids of height 1, and h-1 cards on top. For example, card pyramids of heights 1, 2, and 3 look as follows:
<image>
You start with n cards and build the tallest pyramid that you can. If there are some cards remaining, you build the tallest pyramid possible with the remaining cards. You repeat this process until it is impossible to build another pyramid. In the end, how many pyramids will you have constructed?
Input
Each test consists of multiple test cases. The first line contains a single integer t (1≤ t≤ 1000) — the number of test cases. Next t lines contain descriptions of test cases.
Each test case contains a single integer n (1≤ n≤ 10^9) — the number of cards.
It is guaranteed that the sum of n over all test cases does not exceed 10^9.
Output
For each test case output a single integer — the number of pyramids you will have constructed in the end.
Example
Input
5
3
14
15
24
1
Output
1
2
1
3
0
Note
In the first test, you construct a pyramid of height 1 with 2 cards. There is 1 card remaining, which is not enough to build a pyramid.
In the second test, you build two pyramids, each of height 2, with no cards remaining.
In the third test, you build one pyramid of height 3, with no cards remaining.
In the fourth test, you build one pyramid of height 3 with 9 cards remaining. Then you build a pyramid of height 2 with 2 cards remaining. Then you build a final pyramid of height 1 with no cards remaining.
In the fifth test, one card is not enough to build any pyramids.
Submitted Solution:
```
import sys
import math
input = lambda : sys.stdin.readline().strip()
t = int(input())
def cards(h):
return (3*h**2+h)//2
while t:
t-=1
n = int(input())
ans = 0
h = 1
while cards(h+1)<=n:
h+=1
while n>0 and h>0:
if cards(h)<=n:
n-=cards(h)
ans+=1
else:
h-=1
print(ans)
``` | instruction | 0 | 1,005 | 19 | 2,010 |
Yes | output | 1 | 1,005 | 19 | 2,011 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
A card pyramid of height 1 is constructed by resting two cards against each other. For h>1, a card pyramid of height h is constructed by placing a card pyramid of height h-1 onto a base. A base consists of h pyramids of height 1, and h-1 cards on top. For example, card pyramids of heights 1, 2, and 3 look as follows:
<image>
You start with n cards and build the tallest pyramid that you can. If there are some cards remaining, you build the tallest pyramid possible with the remaining cards. You repeat this process until it is impossible to build another pyramid. In the end, how many pyramids will you have constructed?
Input
Each test consists of multiple test cases. The first line contains a single integer t (1≤ t≤ 1000) — the number of test cases. Next t lines contain descriptions of test cases.
Each test case contains a single integer n (1≤ n≤ 10^9) — the number of cards.
It is guaranteed that the sum of n over all test cases does not exceed 10^9.
Output
For each test case output a single integer — the number of pyramids you will have constructed in the end.
Example
Input
5
3
14
15
24
1
Output
1
2
1
3
0
Note
In the first test, you construct a pyramid of height 1 with 2 cards. There is 1 card remaining, which is not enough to build a pyramid.
In the second test, you build two pyramids, each of height 2, with no cards remaining.
In the third test, you build one pyramid of height 3, with no cards remaining.
In the fourth test, you build one pyramid of height 3 with 9 cards remaining. Then you build a pyramid of height 2 with 2 cards remaining. Then you build a final pyramid of height 1 with no cards remaining.
In the fifth test, one card is not enough to build any pyramids.
Submitted Solution:
```
t = int(input())
for asd in range(t):
n = int(input())
out = 0
while(n > 1):
f=2
count = 1
num = f
while(f <= n):
count += 1
num = f
f = f+((3*count) -1)
n = n - num
# print(num)
out = out+1
# print(f)
print(out)
# print("a")
``` | instruction | 0 | 1,006 | 19 | 2,012 |
Yes | output | 1 | 1,006 | 19 | 2,013 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
A card pyramid of height 1 is constructed by resting two cards against each other. For h>1, a card pyramid of height h is constructed by placing a card pyramid of height h-1 onto a base. A base consists of h pyramids of height 1, and h-1 cards on top. For example, card pyramids of heights 1, 2, and 3 look as follows:
<image>
You start with n cards and build the tallest pyramid that you can. If there are some cards remaining, you build the tallest pyramid possible with the remaining cards. You repeat this process until it is impossible to build another pyramid. In the end, how many pyramids will you have constructed?
Input
Each test consists of multiple test cases. The first line contains a single integer t (1≤ t≤ 1000) — the number of test cases. Next t lines contain descriptions of test cases.
Each test case contains a single integer n (1≤ n≤ 10^9) — the number of cards.
It is guaranteed that the sum of n over all test cases does not exceed 10^9.
Output
For each test case output a single integer — the number of pyramids you will have constructed in the end.
Example
Input
5
3
14
15
24
1
Output
1
2
1
3
0
Note
In the first test, you construct a pyramid of height 1 with 2 cards. There is 1 card remaining, which is not enough to build a pyramid.
In the second test, you build two pyramids, each of height 2, with no cards remaining.
In the third test, you build one pyramid of height 3, with no cards remaining.
In the fourth test, you build one pyramid of height 3 with 9 cards remaining. Then you build a pyramid of height 2 with 2 cards remaining. Then you build a final pyramid of height 1 with no cards remaining.
In the fifth test, one card is not enough to build any pyramids.
Submitted Solution:
```
#importing bisect
import bisect
# defining input == t
t = int(input())
# Logical Execution
pyramid_heights = [2]
pyramid_height = 2
# sum
addition = 5
# comparison
while pyramid_height < 1000000000:
pyramid_height = pyramid_height + addition
# sum of += 3
addition += 3
pyramid_heights.append(pyramid_height)
# again while execution
while t !=0:
height = int(input())
#print answer
ans = 0
pos = (bisect.bisect_left(pyramid_heights, height))
# execution 2
while height >= 0:
# execution of if
if height == 0:
break
if height < pyramid_heights[0]:
break
else:
if height - pyramid_heights[pos] >= 0:
height = height - pyramid_heights[pos]
ans += 1
else:
pos -= 1
# printing of 2nd answer ts
print(ans)
t -= 1
``` | instruction | 0 | 1,007 | 19 | 2,014 |
Yes | output | 1 | 1,007 | 19 | 2,015 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
A card pyramid of height 1 is constructed by resting two cards against each other. For h>1, a card pyramid of height h is constructed by placing a card pyramid of height h-1 onto a base. A base consists of h pyramids of height 1, and h-1 cards on top. For example, card pyramids of heights 1, 2, and 3 look as follows:
<image>
You start with n cards and build the tallest pyramid that you can. If there are some cards remaining, you build the tallest pyramid possible with the remaining cards. You repeat this process until it is impossible to build another pyramid. In the end, how many pyramids will you have constructed?
Input
Each test consists of multiple test cases. The first line contains a single integer t (1≤ t≤ 1000) — the number of test cases. Next t lines contain descriptions of test cases.
Each test case contains a single integer n (1≤ n≤ 10^9) — the number of cards.
It is guaranteed that the sum of n over all test cases does not exceed 10^9.
Output
For each test case output a single integer — the number of pyramids you will have constructed in the end.
Example
Input
5
3
14
15
24
1
Output
1
2
1
3
0
Note
In the first test, you construct a pyramid of height 1 with 2 cards. There is 1 card remaining, which is not enough to build a pyramid.
In the second test, you build two pyramids, each of height 2, with no cards remaining.
In the third test, you build one pyramid of height 3, with no cards remaining.
In the fourth test, you build one pyramid of height 3 with 9 cards remaining. Then you build a pyramid of height 2 with 2 cards remaining. Then you build a final pyramid of height 1 with no cards remaining.
In the fifth test, one card is not enough to build any pyramids.
Submitted Solution:
```
import bisect
t=int(input())
const=[(3*(i+1)**2+i+1)//2 for i in range(33000)]
for i in range(t):
n=int(input())
cnt=0
while n>=2:
d=bisect.bisect_right(const,n)
n-=const[d-1]
cnt+=1
print(cnt)
``` | instruction | 0 | 1,008 | 19 | 2,016 |
Yes | output | 1 | 1,008 | 19 | 2,017 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
A card pyramid of height 1 is constructed by resting two cards against each other. For h>1, a card pyramid of height h is constructed by placing a card pyramid of height h-1 onto a base. A base consists of h pyramids of height 1, and h-1 cards on top. For example, card pyramids of heights 1, 2, and 3 look as follows:
<image>
You start with n cards and build the tallest pyramid that you can. If there are some cards remaining, you build the tallest pyramid possible with the remaining cards. You repeat this process until it is impossible to build another pyramid. In the end, how many pyramids will you have constructed?
Input
Each test consists of multiple test cases. The first line contains a single integer t (1≤ t≤ 1000) — the number of test cases. Next t lines contain descriptions of test cases.
Each test case contains a single integer n (1≤ n≤ 10^9) — the number of cards.
It is guaranteed that the sum of n over all test cases does not exceed 10^9.
Output
For each test case output a single integer — the number of pyramids you will have constructed in the end.
Example
Input
5
3
14
15
24
1
Output
1
2
1
3
0
Note
In the first test, you construct a pyramid of height 1 with 2 cards. There is 1 card remaining, which is not enough to build a pyramid.
In the second test, you build two pyramids, each of height 2, with no cards remaining.
In the third test, you build one pyramid of height 3, with no cards remaining.
In the fourth test, you build one pyramid of height 3 with 9 cards remaining. Then you build a pyramid of height 2 with 2 cards remaining. Then you build a final pyramid of height 1 with no cards remaining.
In the fifth test, one card is not enough to build any pyramids.
Submitted Solution:
```
n=int(input())
a=[]
for i in range(n):
a.append(int(input()))
k=5
p=2
d=0
for i in range(n):
if a[i]>=2:
while a[i]>=0:
while a[i]>=p:
p+=k
k+=3
p-=3
a[i]-=p
d+=1
k=5
p=2
a[i]=d
d=0
else:
a[i]=0
for i in range(n):
print(a[i])
``` | instruction | 0 | 1,009 | 19 | 2,018 |
No | output | 1 | 1,009 | 19 | 2,019 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
A card pyramid of height 1 is constructed by resting two cards against each other. For h>1, a card pyramid of height h is constructed by placing a card pyramid of height h-1 onto a base. A base consists of h pyramids of height 1, and h-1 cards on top. For example, card pyramids of heights 1, 2, and 3 look as follows:
<image>
You start with n cards and build the tallest pyramid that you can. If there are some cards remaining, you build the tallest pyramid possible with the remaining cards. You repeat this process until it is impossible to build another pyramid. In the end, how many pyramids will you have constructed?
Input
Each test consists of multiple test cases. The first line contains a single integer t (1≤ t≤ 1000) — the number of test cases. Next t lines contain descriptions of test cases.
Each test case contains a single integer n (1≤ n≤ 10^9) — the number of cards.
It is guaranteed that the sum of n over all test cases does not exceed 10^9.
Output
For each test case output a single integer — the number of pyramids you will have constructed in the end.
Example
Input
5
3
14
15
24
1
Output
1
2
1
3
0
Note
In the first test, you construct a pyramid of height 1 with 2 cards. There is 1 card remaining, which is not enough to build a pyramid.
In the second test, you build two pyramids, each of height 2, with no cards remaining.
In the third test, you build one pyramid of height 3, with no cards remaining.
In the fourth test, you build one pyramid of height 3 with 9 cards remaining. Then you build a pyramid of height 2 with 2 cards remaining. Then you build a final pyramid of height 1 with no cards remaining.
In the fifth test, one card is not enough to build any pyramids.
Submitted Solution:
```
for _ in range(int(input())):
n = int(input())
dp = [0, 2]
i = 1
while dp[i] < n:
i+=1
dp.append(dp[i-1] +3*i - 1)
#i-=1
ans = 0
for j in range(i,-1,-1):
if dp[j] <=n:
n-=dp[j]
ans+=1
if n <= 1:
break
print(ans)
``` | instruction | 0 | 1,010 | 19 | 2,020 |
No | output | 1 | 1,010 | 19 | 2,021 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
A card pyramid of height 1 is constructed by resting two cards against each other. For h>1, a card pyramid of height h is constructed by placing a card pyramid of height h-1 onto a base. A base consists of h pyramids of height 1, and h-1 cards on top. For example, card pyramids of heights 1, 2, and 3 look as follows:
<image>
You start with n cards and build the tallest pyramid that you can. If there are some cards remaining, you build the tallest pyramid possible with the remaining cards. You repeat this process until it is impossible to build another pyramid. In the end, how many pyramids will you have constructed?
Input
Each test consists of multiple test cases. The first line contains a single integer t (1≤ t≤ 1000) — the number of test cases. Next t lines contain descriptions of test cases.
Each test case contains a single integer n (1≤ n≤ 10^9) — the number of cards.
It is guaranteed that the sum of n over all test cases does not exceed 10^9.
Output
For each test case output a single integer — the number of pyramids you will have constructed in the end.
Example
Input
5
3
14
15
24
1
Output
1
2
1
3
0
Note
In the first test, you construct a pyramid of height 1 with 2 cards. There is 1 card remaining, which is not enough to build a pyramid.
In the second test, you build two pyramids, each of height 2, with no cards remaining.
In the third test, you build one pyramid of height 3, with no cards remaining.
In the fourth test, you build one pyramid of height 3 with 9 cards remaining. Then you build a pyramid of height 2 with 2 cards remaining. Then you build a final pyramid of height 1 with no cards remaining.
In the fifth test, one card is not enough to build any pyramids.
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")
a=[]
import bisect
for i in range(10**4):
s=(i*(i+1)//2)*3-i
a.append(s)
#print(a)
for _ in range(int(input())):
c=0
n=int(input())
while n>=2:
q=bisect.bisect_right(a,n)
n=n-a[q-1]
c+=1
print(c)
``` | instruction | 0 | 1,011 | 19 | 2,022 |
No | output | 1 | 1,011 | 19 | 2,023 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
A card pyramid of height 1 is constructed by resting two cards against each other. For h>1, a card pyramid of height h is constructed by placing a card pyramid of height h-1 onto a base. A base consists of h pyramids of height 1, and h-1 cards on top. For example, card pyramids of heights 1, 2, and 3 look as follows:
<image>
You start with n cards and build the tallest pyramid that you can. If there are some cards remaining, you build the tallest pyramid possible with the remaining cards. You repeat this process until it is impossible to build another pyramid. In the end, how many pyramids will you have constructed?
Input
Each test consists of multiple test cases. The first line contains a single integer t (1≤ t≤ 1000) — the number of test cases. Next t lines contain descriptions of test cases.
Each test case contains a single integer n (1≤ n≤ 10^9) — the number of cards.
It is guaranteed that the sum of n over all test cases does not exceed 10^9.
Output
For each test case output a single integer — the number of pyramids you will have constructed in the end.
Example
Input
5
3
14
15
24
1
Output
1
2
1
3
0
Note
In the first test, you construct a pyramid of height 1 with 2 cards. There is 1 card remaining, which is not enough to build a pyramid.
In the second test, you build two pyramids, each of height 2, with no cards remaining.
In the third test, you build one pyramid of height 3, with no cards remaining.
In the fourth test, you build one pyramid of height 3 with 9 cards remaining. Then you build a pyramid of height 2 with 2 cards remaining. Then you build a final pyramid of height 1 with no cards remaining.
In the fifth test, one card is not enough to build any pyramids.
Submitted Solution:
```
a = [0, 2]
def triangle(h):
cards = 0
if len(a) > h:
cards = a[h]
else:
cards = triangle(h - 1) + 2 * h + h - 1
a.insert(h, cards)
return cards
k = int(input("Enter value "))
p = []
for i in range(0,k):
p.insert(i, int(input()))
def max(n):
m=0
while triangle(m)<=n:
m+=1
return n-triangle(m-1)
def number(b):
count=0
while b>=2:
b=max(b)
count+=1
return count
for s in range(0,k):
print(number(p[s]))
``` | instruction | 0 | 1,012 | 19 | 2,024 |
No | output | 1 | 1,012 | 19 | 2,025 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Two beavers, Timur and Marsel, play the following game.
There are n logs, each of exactly m meters in length. The beavers move in turns. For each move a beaver chooses a log and gnaws it into some number (more than one) of equal parts, the length of each one is expressed by an integer and is no less than k meters. Each resulting part is also a log which can be gnawed in future by any beaver. The beaver that can't make a move loses. Thus, the other beaver wins.
Timur makes the first move. The players play in the optimal way. Determine the winner.
Input
The first line contains three integers n, m, k (1 ≤ n, m, k ≤ 109).
Output
Print "Timur", if Timur wins, or "Marsel", if Marsel wins. You should print everything without the quotes.
Examples
Input
1 15 4
Output
Timur
Input
4 9 5
Output
Marsel
Note
In the first sample the beavers only have one log, of 15 meters in length. Timur moves first. The only move he can do is to split the log into 3 parts each 5 meters in length. Then Marsel moves but he can't split any of the resulting logs, as k = 4. Thus, the winner is Timur.
In the second example the beavers have 4 logs 9 meters in length. Timur can't split any of them, so that the resulting parts possessed the length of not less than 5 meters, that's why he loses instantly. | instruction | 0 | 1,373 | 19 | 2,746 |
Tags: dp, games, number theory
Correct Solution:
```
#!/usr/bin/env python3
def main():
n, m, k = (int(t) for t in input().split())
if n % 2 == 0:
print("Marsel")
return
if k == 1 and m > k:
print("Timur")
return
t = 2
while t * t <= m:
if m % t == 0:
if m // t >= k:
print("Timur")
return
print("Marsel")
return
t += 1
print("Marsel")
return
main()
``` | output | 1 | 1,373 | 19 | 2,747 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Two beavers, Timur and Marsel, play the following game.
There are n logs, each of exactly m meters in length. The beavers move in turns. For each move a beaver chooses a log and gnaws it into some number (more than one) of equal parts, the length of each one is expressed by an integer and is no less than k meters. Each resulting part is also a log which can be gnawed in future by any beaver. The beaver that can't make a move loses. Thus, the other beaver wins.
Timur makes the first move. The players play in the optimal way. Determine the winner.
Input
The first line contains three integers n, m, k (1 ≤ n, m, k ≤ 109).
Output
Print "Timur", if Timur wins, or "Marsel", if Marsel wins. You should print everything without the quotes.
Examples
Input
1 15 4
Output
Timur
Input
4 9 5
Output
Marsel
Note
In the first sample the beavers only have one log, of 15 meters in length. Timur moves first. The only move he can do is to split the log into 3 parts each 5 meters in length. Then Marsel moves but he can't split any of the resulting logs, as k = 4. Thus, the winner is Timur.
In the second example the beavers have 4 logs 9 meters in length. Timur can't split any of them, so that the resulting parts possessed the length of not less than 5 meters, that's why he loses instantly. | instruction | 0 | 1,374 | 19 | 2,748 |
Tags: dp, games, number theory
Correct Solution:
```
x=input()
l=x.split()
n=int(l[0])
m=int(l[1])
k=int(l[2])
def func_2(m,k):
if k==1 and m!=1:
return True
s=int(m**.5)
for i in range(2,s+1):
if not m%i:
if i>=k or m/i>=k:
return True
return False
if func_2(m,k):
p=n
else :
p=0
if p%2==0:
print('Marsel')
else :
print('Timur')
``` | output | 1 | 1,374 | 19 | 2,749 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Two beavers, Timur and Marsel, play the following game.
There are n logs, each of exactly m meters in length. The beavers move in turns. For each move a beaver chooses a log and gnaws it into some number (more than one) of equal parts, the length of each one is expressed by an integer and is no less than k meters. Each resulting part is also a log which can be gnawed in future by any beaver. The beaver that can't make a move loses. Thus, the other beaver wins.
Timur makes the first move. The players play in the optimal way. Determine the winner.
Input
The first line contains three integers n, m, k (1 ≤ n, m, k ≤ 109).
Output
Print "Timur", if Timur wins, or "Marsel", if Marsel wins. You should print everything without the quotes.
Examples
Input
1 15 4
Output
Timur
Input
4 9 5
Output
Marsel
Note
In the first sample the beavers only have one log, of 15 meters in length. Timur moves first. The only move he can do is to split the log into 3 parts each 5 meters in length. Then Marsel moves but he can't split any of the resulting logs, as k = 4. Thus, the winner is Timur.
In the second example the beavers have 4 logs 9 meters in length. Timur can't split any of them, so that the resulting parts possessed the length of not less than 5 meters, that's why he loses instantly. | instruction | 0 | 1,375 | 19 | 2,750 |
Tags: dp, games, number theory
Correct Solution:
```
n, m, k = map(int, input().split())
if n % 2 == 0:
print('Marsel')
else:
divisors = set()
i = 1
while i * i <= m:
if m % i == 0:
divisors.add(i)
divisors.add(m // i)
i += 1
ans = 10 ** 18
for x in divisors:
if x >= k and x != m:
ans = min(ans, x)
if ans < 10 ** 18:
print('Timur')
else:
print('Marsel')
``` | output | 1 | 1,375 | 19 | 2,751 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Two beavers, Timur and Marsel, play the following game.
There are n logs, each of exactly m meters in length. The beavers move in turns. For each move a beaver chooses a log and gnaws it into some number (more than one) of equal parts, the length of each one is expressed by an integer and is no less than k meters. Each resulting part is also a log which can be gnawed in future by any beaver. The beaver that can't make a move loses. Thus, the other beaver wins.
Timur makes the first move. The players play in the optimal way. Determine the winner.
Input
The first line contains three integers n, m, k (1 ≤ n, m, k ≤ 109).
Output
Print "Timur", if Timur wins, or "Marsel", if Marsel wins. You should print everything without the quotes.
Examples
Input
1 15 4
Output
Timur
Input
4 9 5
Output
Marsel
Note
In the first sample the beavers only have one log, of 15 meters in length. Timur moves first. The only move he can do is to split the log into 3 parts each 5 meters in length. Then Marsel moves but he can't split any of the resulting logs, as k = 4. Thus, the winner is Timur.
In the second example the beavers have 4 logs 9 meters in length. Timur can't split any of them, so that the resulting parts possessed the length of not less than 5 meters, that's why he loses instantly. | instruction | 0 | 1,376 | 19 | 2,752 |
Tags: dp, games, number theory
Correct Solution:
```
from sys import stdin, stdout
def check(m, k):
for i in range(2, int(m ** 0.5) + 1):
if not m % i and (i >= k or m // i >= k):
return 1
else:
return 0
n, m, k = map(int, stdin.readline().split())
if m < 2 * k or (k != 1 and not check(m, k)):
stdout.write('Marsel')
elif n % 2:
stdout.write('Timur')
else:
stdout.write('Marsel')
``` | output | 1 | 1,376 | 19 | 2,753 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Two beavers, Timur and Marsel, play the following game.
There are n logs, each of exactly m meters in length. The beavers move in turns. For each move a beaver chooses a log and gnaws it into some number (more than one) of equal parts, the length of each one is expressed by an integer and is no less than k meters. Each resulting part is also a log which can be gnawed in future by any beaver. The beaver that can't make a move loses. Thus, the other beaver wins.
Timur makes the first move. The players play in the optimal way. Determine the winner.
Input
The first line contains three integers n, m, k (1 ≤ n, m, k ≤ 109).
Output
Print "Timur", if Timur wins, or "Marsel", if Marsel wins. You should print everything without the quotes.
Examples
Input
1 15 4
Output
Timur
Input
4 9 5
Output
Marsel
Note
In the first sample the beavers only have one log, of 15 meters in length. Timur moves first. The only move he can do is to split the log into 3 parts each 5 meters in length. Then Marsel moves but he can't split any of the resulting logs, as k = 4. Thus, the winner is Timur.
In the second example the beavers have 4 logs 9 meters in length. Timur can't split any of them, so that the resulting parts possessed the length of not less than 5 meters, that's why he loses instantly. | instruction | 0 | 1,377 | 19 | 2,754 |
Tags: dp, games, number theory
Correct Solution:
```
from collections import Counter
nn,mm,kk=[int(i) for i in input().split()]
if nn%2==0:
print('Marsel')
exit(0)
def get_ls(n):
result = []
i = 2
while i < n:
if n % i == 0:
n /= i
result.append(i)
else:
i += 1
result.append(int(n))
return result
#print(mm)
if mm%499999993==0:
mm=mm//499999993
ls = get_ls(mm)
ls.append(499999993)
mm*=499999993
elif mm%166666649==0:
#print('***')
mm=mm//166666649
ls = get_ls(mm)
ls.append(166666649)
mm*=166666649
elif mm%999999937==0:
#print('***')
mm=mm//999999937
ls = get_ls(mm)
ls.append(999999937)
mm*=999999937
elif mm%14925373==0:
#print('***')
mm=mm//14925373
ls = get_ls(mm)
ls.append(14925373)
mm*=14925373
elif mm%10204081==0:
#print('***')
mm=mm//10204081
ls = get_ls(mm)
ls.append(10204081)
mm*=10204081
else:
ls = get_ls(mm)
#print(ls)
kkk = dict(Counter(ls)).items()
d = [k for k, _ in kkk]
m = [v for _, v in kkk]
k = [0 for _ in range(len(set(ls)))]
ln = range(len(m))
dels=[]
try:
while True:
r = 1
for i1, i2 in zip(d, k):
r *= i1 ** i2
dels.append(r)
k[0] += 1
for i in ln:
if k[i] > m[i]:
k[i] = 0
k[i+1] += 1
except IndexError:
pass
for i in dels:
#print(i,kk,mm)
if kk<=i<mm:
print('Timur')
exit(0)
print('Marsel')
``` | output | 1 | 1,377 | 19 | 2,755 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Two beavers, Timur and Marsel, play the following game.
There are n logs, each of exactly m meters in length. The beavers move in turns. For each move a beaver chooses a log and gnaws it into some number (more than one) of equal parts, the length of each one is expressed by an integer and is no less than k meters. Each resulting part is also a log which can be gnawed in future by any beaver. The beaver that can't make a move loses. Thus, the other beaver wins.
Timur makes the first move. The players play in the optimal way. Determine the winner.
Input
The first line contains three integers n, m, k (1 ≤ n, m, k ≤ 109).
Output
Print "Timur", if Timur wins, or "Marsel", if Marsel wins. You should print everything without the quotes.
Examples
Input
1 15 4
Output
Timur
Input
4 9 5
Output
Marsel
Note
In the first sample the beavers only have one log, of 15 meters in length. Timur moves first. The only move he can do is to split the log into 3 parts each 5 meters in length. Then Marsel moves but he can't split any of the resulting logs, as k = 4. Thus, the winner is Timur.
In the second example the beavers have 4 logs 9 meters in length. Timur can't split any of them, so that the resulting parts possessed the length of not less than 5 meters, that's why he loses instantly. | instruction | 0 | 1,378 | 19 | 2,756 |
Tags: dp, games, number theory
Correct Solution:
```
import sys
from array import array # noqa: F401
def input():
return sys.stdin.buffer.readline().decode('utf-8')
def get_primes(n: int):
from itertools import chain
from array import array
primes = [2, 3]
is_prime = (array('b', (0, 0, 1, 1, 0, 1, 0)) +
array('b', (1, 0, 0, 0, 1, 0)) * ((n - 1) // 6))
for i in chain.from_iterable((range(5, n + 1, 6), range(7, n + 1, 6))):
if is_prime[i]:
primes.append(i)
for j in range(i * 3, n + 1, i * 2):
is_prime[j] = 0
return is_prime, primes
n, m, k = map(int, input().split())
if m == 1:
print('Marsel')
exit()
_, primes = get_primes(32000)
primes.append(m)
for p in primes:
if m % p == 0 and m // p >= k:
print('Timur' if n & 1 else 'Marsel')
exit()
print('Marsel')
``` | output | 1 | 1,378 | 19 | 2,757 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Two beavers, Timur and Marsel, play the following game.
There are n logs, each of exactly m meters in length. The beavers move in turns. For each move a beaver chooses a log and gnaws it into some number (more than one) of equal parts, the length of each one is expressed by an integer and is no less than k meters. Each resulting part is also a log which can be gnawed in future by any beaver. The beaver that can't make a move loses. Thus, the other beaver wins.
Timur makes the first move. The players play in the optimal way. Determine the winner.
Input
The first line contains three integers n, m, k (1 ≤ n, m, k ≤ 109).
Output
Print "Timur", if Timur wins, or "Marsel", if Marsel wins. You should print everything without the quotes.
Examples
Input
1 15 4
Output
Timur
Input
4 9 5
Output
Marsel
Note
In the first sample the beavers only have one log, of 15 meters in length. Timur moves first. The only move he can do is to split the log into 3 parts each 5 meters in length. Then Marsel moves but he can't split any of the resulting logs, as k = 4. Thus, the winner is Timur.
In the second example the beavers have 4 logs 9 meters in length. Timur can't split any of them, so that the resulting parts possessed the length of not less than 5 meters, that's why he loses instantly. | instruction | 0 | 1,379 | 19 | 2,758 |
Tags: dp, games, number theory
Correct Solution:
```
def check(a, b, c):
return (b <= a and a < c)
def can(n, m, k):
if n % 2 == 0:
return False
d = 1
while d*d <= m:
if m % d == 0 and (check(d, k, m) or check(m/d, k, m)):
return True
d += 1
return False
n, m, k = map(int, input().split(' '))
print ('Timur' if can(n, m, k) else 'Marsel')
``` | output | 1 | 1,379 | 19 | 2,759 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Two beavers, Timur and Marsel, play the following game.
There are n logs, each of exactly m meters in length. The beavers move in turns. For each move a beaver chooses a log and gnaws it into some number (more than one) of equal parts, the length of each one is expressed by an integer and is no less than k meters. Each resulting part is also a log which can be gnawed in future by any beaver. The beaver that can't make a move loses. Thus, the other beaver wins.
Timur makes the first move. The players play in the optimal way. Determine the winner.
Input
The first line contains three integers n, m, k (1 ≤ n, m, k ≤ 109).
Output
Print "Timur", if Timur wins, or "Marsel", if Marsel wins. You should print everything without the quotes.
Examples
Input
1 15 4
Output
Timur
Input
4 9 5
Output
Marsel
Note
In the first sample the beavers only have one log, of 15 meters in length. Timur moves first. The only move he can do is to split the log into 3 parts each 5 meters in length. Then Marsel moves but he can't split any of the resulting logs, as k = 4. Thus, the winner is Timur.
In the second example the beavers have 4 logs 9 meters in length. Timur can't split any of them, so that the resulting parts possessed the length of not less than 5 meters, that's why he loses instantly. | instruction | 0 | 1,380 | 19 | 2,760 |
Tags: dp, games, number theory
Correct Solution:
```
def IsPrime(n):
d = 2
if n != 1:
while n % d != 0:
d += 1
return d == n
p = False
n, m, k = [int(i) for i in input().split()]
if m==2 and k==1 :
if n%2!=0:
print('Timur')
else:print('Marsel')
quit()
elif m<=k:
print('Marsel')
quit()
if n%2!=0 and m%k==0:
print('Timur')
quit()
if m==999999937 :
print('Marsel')
quit()
if k!=1 and k!=100:
for i in range(2,round(m**0.5)+1):
if m % i == 0 and m//i>k:
p = True
if p==False and k!=1 and k!=100:
print('Marsel')
quit()
if IsPrime(m):
print('Marsel')
elif m % 2 == 0 or m % 2 != 0:
if n % 2 != 0:
print('Timur')
else:
print('Marsel')
``` | output | 1 | 1,380 | 19 | 2,761 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Two beavers, Timur and Marsel, play the following game.
There are n logs, each of exactly m meters in length. The beavers move in turns. For each move a beaver chooses a log and gnaws it into some number (more than one) of equal parts, the length of each one is expressed by an integer and is no less than k meters. Each resulting part is also a log which can be gnawed in future by any beaver. The beaver that can't make a move loses. Thus, the other beaver wins.
Timur makes the first move. The players play in the optimal way. Determine the winner.
Input
The first line contains three integers n, m, k (1 ≤ n, m, k ≤ 109).
Output
Print "Timur", if Timur wins, or "Marsel", if Marsel wins. You should print everything without the quotes.
Examples
Input
1 15 4
Output
Timur
Input
4 9 5
Output
Marsel
Note
In the first sample the beavers only have one log, of 15 meters in length. Timur moves first. The only move he can do is to split the log into 3 parts each 5 meters in length. Then Marsel moves but he can't split any of the resulting logs, as k = 4. Thus, the winner is Timur.
In the second example the beavers have 4 logs 9 meters in length. Timur can't split any of them, so that the resulting parts possessed the length of not less than 5 meters, that's why he loses instantly.
Submitted Solution:
```
from sys import stdin, stdout
def check(m, k):
for i in range(2, int(m ** 0.5) + 1):
if not m % i and (i >= k or m // i >= k):
return 1
else:
return 0
n, m, k = map(int, stdin.readline().split())
if m < 2 * k or (k != 1 and not check(m, k)):
stdout.write('Marsel')
elif n % 2:
stdout.write('Timur')
else:
stdout.write('Marsel')
# Made By Mostafa_Khaled
``` | instruction | 0 | 1,381 | 19 | 2,762 |
Yes | output | 1 | 1,381 | 19 | 2,763 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Two beavers, Timur and Marsel, play the following game.
There are n logs, each of exactly m meters in length. The beavers move in turns. For each move a beaver chooses a log and gnaws it into some number (more than one) of equal parts, the length of each one is expressed by an integer and is no less than k meters. Each resulting part is also a log which can be gnawed in future by any beaver. The beaver that can't make a move loses. Thus, the other beaver wins.
Timur makes the first move. The players play in the optimal way. Determine the winner.
Input
The first line contains three integers n, m, k (1 ≤ n, m, k ≤ 109).
Output
Print "Timur", if Timur wins, or "Marsel", if Marsel wins. You should print everything without the quotes.
Examples
Input
1 15 4
Output
Timur
Input
4 9 5
Output
Marsel
Note
In the first sample the beavers only have one log, of 15 meters in length. Timur moves first. The only move he can do is to split the log into 3 parts each 5 meters in length. Then Marsel moves but he can't split any of the resulting logs, as k = 4. Thus, the winner is Timur.
In the second example the beavers have 4 logs 9 meters in length. Timur can't split any of them, so that the resulting parts possessed the length of not less than 5 meters, that's why he loses instantly.
Submitted Solution:
```
n, m, k = map(int, input().split())
if n % 2 == 0:
print("Marsel")
exit(0)
if m % 2 == 0 and m // 2 >= k:
print("Timur")
exit(0)
if k == 1:
if m > 1:
print("Timur")
else:
print("Marsel")
exit(0)
root = int(m ** 0.5)
for d in range(2, root + 1):
if m % d == 0 and m / d >= k:
print("Timur")
exit(0)
print("Marsel")
``` | instruction | 0 | 1,382 | 19 | 2,764 |
Yes | output | 1 | 1,382 | 19 | 2,765 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Two beavers, Timur and Marsel, play the following game.
There are n logs, each of exactly m meters in length. The beavers move in turns. For each move a beaver chooses a log and gnaws it into some number (more than one) of equal parts, the length of each one is expressed by an integer and is no less than k meters. Each resulting part is also a log which can be gnawed in future by any beaver. The beaver that can't make a move loses. Thus, the other beaver wins.
Timur makes the first move. The players play in the optimal way. Determine the winner.
Input
The first line contains three integers n, m, k (1 ≤ n, m, k ≤ 109).
Output
Print "Timur", if Timur wins, or "Marsel", if Marsel wins. You should print everything without the quotes.
Examples
Input
1 15 4
Output
Timur
Input
4 9 5
Output
Marsel
Note
In the first sample the beavers only have one log, of 15 meters in length. Timur moves first. The only move he can do is to split the log into 3 parts each 5 meters in length. Then Marsel moves but he can't split any of the resulting logs, as k = 4. Thus, the winner is Timur.
In the second example the beavers have 4 logs 9 meters in length. Timur can't split any of them, so that the resulting parts possessed the length of not less than 5 meters, that's why he loses instantly.
Submitted Solution:
```
n,m,k=map(int,input().split())
if n%2==0:
print("Marsel")
else:
for z in range(2,int(m**0.5)+2):
if m%z==0 and m//z>=k:
print("Timur")
break
else:
if k==1 and m>1:
print("Timur")
else:
print("Marsel")
``` | instruction | 0 | 1,383 | 19 | 2,766 |
Yes | output | 1 | 1,383 | 19 | 2,767 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Two beavers, Timur and Marsel, play the following game.
There are n logs, each of exactly m meters in length. The beavers move in turns. For each move a beaver chooses a log and gnaws it into some number (more than one) of equal parts, the length of each one is expressed by an integer and is no less than k meters. Each resulting part is also a log which can be gnawed in future by any beaver. The beaver that can't make a move loses. Thus, the other beaver wins.
Timur makes the first move. The players play in the optimal way. Determine the winner.
Input
The first line contains three integers n, m, k (1 ≤ n, m, k ≤ 109).
Output
Print "Timur", if Timur wins, or "Marsel", if Marsel wins. You should print everything without the quotes.
Examples
Input
1 15 4
Output
Timur
Input
4 9 5
Output
Marsel
Note
In the first sample the beavers only have one log, of 15 meters in length. Timur moves first. The only move he can do is to split the log into 3 parts each 5 meters in length. Then Marsel moves but he can't split any of the resulting logs, as k = 4. Thus, the winner is Timur.
In the second example the beavers have 4 logs 9 meters in length. Timur can't split any of them, so that the resulting parts possessed the length of not less than 5 meters, that's why he loses instantly.
Submitted Solution:
```
import math
def check(m, k):
if k == 1 and m != 1: return True
for i in range(2, math.floor(math.pow(m, 0.5)) + 1):
if (m % i == 0) and (m / i) >= k:
return True
return False
n, m, k = map(int, input().split(" "))
if (n % 2 != 0) and check(m, k):
print("Timur")
if (n % 2 == 0) or not check(m, k):
print("Marsel")
``` | instruction | 0 | 1,384 | 19 | 2,768 |
Yes | output | 1 | 1,384 | 19 | 2,769 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Two beavers, Timur and Marsel, play the following game.
There are n logs, each of exactly m meters in length. The beavers move in turns. For each move a beaver chooses a log and gnaws it into some number (more than one) of equal parts, the length of each one is expressed by an integer and is no less than k meters. Each resulting part is also a log which can be gnawed in future by any beaver. The beaver that can't make a move loses. Thus, the other beaver wins.
Timur makes the first move. The players play in the optimal way. Determine the winner.
Input
The first line contains three integers n, m, k (1 ≤ n, m, k ≤ 109).
Output
Print "Timur", if Timur wins, or "Marsel", if Marsel wins. You should print everything without the quotes.
Examples
Input
1 15 4
Output
Timur
Input
4 9 5
Output
Marsel
Note
In the first sample the beavers only have one log, of 15 meters in length. Timur moves first. The only move he can do is to split the log into 3 parts each 5 meters in length. Then Marsel moves but he can't split any of the resulting logs, as k = 4. Thus, the winner is Timur.
In the second example the beavers have 4 logs 9 meters in length. Timur can't split any of them, so that the resulting parts possessed the length of not less than 5 meters, that's why he loses instantly.
Submitted Solution:
```
n,m,k=map(int,input().split())
if n%2==0:
print("Marsel")
else:
for z in range(k,m+1):
if m%z==0:
print("Timur")
break
else:
print("Marsel")
``` | instruction | 0 | 1,385 | 19 | 2,770 |
No | output | 1 | 1,385 | 19 | 2,771 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Two beavers, Timur and Marsel, play the following game.
There are n logs, each of exactly m meters in length. The beavers move in turns. For each move a beaver chooses a log and gnaws it into some number (more than one) of equal parts, the length of each one is expressed by an integer and is no less than k meters. Each resulting part is also a log which can be gnawed in future by any beaver. The beaver that can't make a move loses. Thus, the other beaver wins.
Timur makes the first move. The players play in the optimal way. Determine the winner.
Input
The first line contains three integers n, m, k (1 ≤ n, m, k ≤ 109).
Output
Print "Timur", if Timur wins, or "Marsel", if Marsel wins. You should print everything without the quotes.
Examples
Input
1 15 4
Output
Timur
Input
4 9 5
Output
Marsel
Note
In the first sample the beavers only have one log, of 15 meters in length. Timur moves first. The only move he can do is to split the log into 3 parts each 5 meters in length. Then Marsel moves but he can't split any of the resulting logs, as k = 4. Thus, the winner is Timur.
In the second example the beavers have 4 logs 9 meters in length. Timur can't split any of them, so that the resulting parts possessed the length of not less than 5 meters, that's why he loses instantly.
Submitted Solution:
```
n,m,k=[int(i) for i in input().split()]
b='Timur'
for i in range(m//k,k-1,-1):
if m%i==0:
m//=i
b='Marsel'
if n%2!=0 :
print(b)
elif b=='Timur':
print('Marsel')
else: print('Timur')
``` | instruction | 0 | 1,386 | 19 | 2,772 |
No | output | 1 | 1,386 | 19 | 2,773 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Two beavers, Timur and Marsel, play the following game.
There are n logs, each of exactly m meters in length. The beavers move in turns. For each move a beaver chooses a log and gnaws it into some number (more than one) of equal parts, the length of each one is expressed by an integer and is no less than k meters. Each resulting part is also a log which can be gnawed in future by any beaver. The beaver that can't make a move loses. Thus, the other beaver wins.
Timur makes the first move. The players play in the optimal way. Determine the winner.
Input
The first line contains three integers n, m, k (1 ≤ n, m, k ≤ 109).
Output
Print "Timur", if Timur wins, or "Marsel", if Marsel wins. You should print everything without the quotes.
Examples
Input
1 15 4
Output
Timur
Input
4 9 5
Output
Marsel
Note
In the first sample the beavers only have one log, of 15 meters in length. Timur moves first. The only move he can do is to split the log into 3 parts each 5 meters in length. Then Marsel moves but he can't split any of the resulting logs, as k = 4. Thus, the winner is Timur.
In the second example the beavers have 4 logs 9 meters in length. Timur can't split any of them, so that the resulting parts possessed the length of not less than 5 meters, that's why he loses instantly.
Submitted Solution:
```
def IsPrime(n):
d = 2
if n != 1:
while n % d != 0:
d += 1
return d == n
p = False
n, m, k = [int(i) for i in input().split()]
if m==2 and k==1:
print('Timur')
quit()
for i in range(m // 2, k - 1, -1):
if m % i == 0:
p = True
if p==False:
print('Marsel')
quit()
if IsPrime(m):
print('Marsel')
elif k >= m:
print('Marsel')
elif m % 2 == 0 or m % 2 != 0:
if n % 2 != 0:
print('Timur')
else:
print('Marsel')
``` | instruction | 0 | 1,387 | 19 | 2,774 |
No | output | 1 | 1,387 | 19 | 2,775 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Two beavers, Timur and Marsel, play the following game.
There are n logs, each of exactly m meters in length. The beavers move in turns. For each move a beaver chooses a log and gnaws it into some number (more than one) of equal parts, the length of each one is expressed by an integer and is no less than k meters. Each resulting part is also a log which can be gnawed in future by any beaver. The beaver that can't make a move loses. Thus, the other beaver wins.
Timur makes the first move. The players play in the optimal way. Determine the winner.
Input
The first line contains three integers n, m, k (1 ≤ n, m, k ≤ 109).
Output
Print "Timur", if Timur wins, or "Marsel", if Marsel wins. You should print everything without the quotes.
Examples
Input
1 15 4
Output
Timur
Input
4 9 5
Output
Marsel
Note
In the first sample the beavers only have one log, of 15 meters in length. Timur moves first. The only move he can do is to split the log into 3 parts each 5 meters in length. Then Marsel moves but he can't split any of the resulting logs, as k = 4. Thus, the winner is Timur.
In the second example the beavers have 4 logs 9 meters in length. Timur can't split any of them, so that the resulting parts possessed the length of not less than 5 meters, that's why he loses instantly.
Submitted Solution:
```
def can(n, m, k):
if n % 2 == 0:
return False
d = 2
while d <= m:
if m % d == 0 and (d >= k or m/d >= k):
return True
if d * d > m:
break
d += 1
return False
n, m, k = map(int, input().split(' '))
print ('Timur' if can(n, m, k) else 'Marsel')
``` | instruction | 0 | 1,388 | 19 | 2,776 |
No | output | 1 | 1,388 | 19 | 2,777 |
Provide tags and a correct Python 3 solution for this coding contest problem.
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. | instruction | 0 | 2,183 | 19 | 4,366 |
Tags: games, greedy, implementation
Correct Solution:
```
from collections import Counter
n = int(input())
c = Counter([int(x) for x in input().split()])
flag = 0
for key in c.keys():
if c[key] % 2 != 0:
flag = 1
break
print("Conan" if flag else "Agasa")
``` | output | 1 | 2,183 | 19 | 4,367 |
Provide tags and a correct Python 3 solution for this coding contest problem.
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. | instruction | 0 | 2,184 | 19 | 4,368 |
Tags: games, greedy, implementation
Correct Solution:
```
n = int(input())
a = list(map(int,input().split()))
d = dict()
for i in a:
if i in d:
d[i] += 1
else:
d[i] = 1
import collections
nd = collections.OrderedDict(sorted(d.items(), key = lambda t : t[0], reverse = True))
for i in nd:
if nd[i] % 2 == 1:
print('Conan')
break
else:
print('Agasa')
``` | output | 1 | 2,184 | 19 | 4,369 |
Provide tags and a correct Python 3 solution for this coding contest problem.
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. | instruction | 0 | 2,185 | 19 | 4,370 |
Tags: games, greedy, implementation
Correct Solution:
```
n = int(input())
nums = [int(x) for x in input().split()]
nums.sort()
nums.reverse()
last_num = nums[0]
count = 0
for num in nums:
if num == last_num:
count += 1
else:
if count % 2 == 1:
print('Conan')
break;
else:
last_num = num
count = 1
else:
if count % 2 == 1:
print('Conan')
else:
print('Agasa')
``` | output | 1 | 2,185 | 19 | 4,371 |
Provide tags and a correct Python 3 solution for this coding contest problem.
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. | instruction | 0 | 2,186 | 19 | 4,372 |
Tags: games, greedy, implementation
Correct Solution:
```
def read():
return list(map(int,input().split()))
n=int(input())
a=read()
b={}
for i in a:
if i in b:
b[i]+=1
else:
b[i]=1
for i in b:
if b[i]%2==1:
print('Conan')
exit()
print('Agasa')
``` | output | 1 | 2,186 | 19 | 4,373 |
Provide tags and a correct Python 3 solution for this coding contest problem.
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. | instruction | 0 | 2,187 | 19 | 4,374 |
Tags: games, greedy, implementation
Correct Solution:
```
from collections import Counter
n = int(input())
cards = Counter(map(int, input().split()))
for card, amt in cards.items():
if amt % 2:
print('Conan')
break
else:
print('Agasa')
``` | output | 1 | 2,187 | 19 | 4,375 |
Provide tags and a correct Python 3 solution for this coding contest problem.
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. | instruction | 0 | 2,188 | 19 | 4,376 |
Tags: games, greedy, implementation
Correct 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")
``` | output | 1 | 2,188 | 19 | 4,377 |
Provide tags and a correct Python 3 solution for this coding contest problem.
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. | instruction | 0 | 2,189 | 19 | 4,378 |
Tags: games, greedy, implementation
Correct Solution:
```
from collections import Counter
n = int(input())
print(('Agasa', 'Conan')[1 in [i % 2 for i in Counter(list(map(int, input().split()))).values()]])
``` | output | 1 | 2,189 | 19 | 4,379 |
Provide tags and a correct Python 3 solution for this coding contest problem.
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. | instruction | 0 | 2,190 | 19 | 4,380 |
Tags: games, greedy, implementation
Correct Solution:
```
from collections import Counter
n = int(input())
a = [int(i) for i in input().strip().split()]
c = Counter(a)
conan = False
a.sort(reverse=True)
for i in set(a):
if c[i] % 2 == 1:
conan = True
break
print("Conan" if conan else "Agasa")
``` | output | 1 | 2,190 | 19 | 4,381 |
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 = sorted(list(map(int, input().split())))
last = a[0]
cnt = 1
x = []
for i in range(1, n):
if a[i] != last:
x.append(cnt)
last = a[i]
cnt = 0
cnt += 1
x.append(cnt)
x = x[::-1]
for i in x:
if i%2==1:
print('Conan')
exit(0)
print('Agasa')
``` | instruction | 0 | 2,191 | 19 | 4,382 |
Yes | output | 1 | 2,191 | 19 | 4,383 |
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())
b=[0]*100001
a=list(map(int,input().split()))
for i in a:
b[i]+=1
for i in b:
if i%2==1:
print('Conan')
exit()
print('Agasa')
``` | instruction | 0 | 2,192 | 19 | 4,384 |
Yes | output | 1 | 2,192 | 19 | 4,385 |
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 = [int(i) for i in input().split()]
m = [0] * (10 ** 5 + 2)
for i in a:
m[i] += 1
for i in range(10 ** 5 + 2):
if m[i] % 2 != 0:
print("Conan")
exit()
print("Agasa")
``` | instruction | 0 | 2,193 | 19 | 4,386 |
Yes | output | 1 | 2,193 | 19 | 4,387 |
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