message stringlengths 2 57.2k | message_type stringclasses 2 values | message_id int64 0 1 | conversation_id int64 61 108k | cluster float64 22 22 | __index_level_0__ int64 122 217k |
|---|---|---|---|---|---|
Provide tags and a correct Python 3 solution for this coding contest problem.
Let's consider all integers in the range from 1 to n (inclusive).
Among all pairs of distinct integers in this range, find the maximum possible greatest common divisor of integers in pair. Formally, find the maximum value of gcd(a, b), where 1 ≤ a < b ≤ n.
The greatest common divisor, gcd(a, b), of two positive integers a and b is the biggest integer that is a divisor of both a and b.
Input
The first line contains a single integer t (1 ≤ t ≤ 100) — the number of test cases. The description of the test cases follows.
The only line of each test case contains a single integer n (2 ≤ n ≤ 10^6).
Output
For each test case, output the maximum value of gcd(a, b) among all 1 ≤ a < b ≤ n.
Example
Input
2
3
5
Output
1
2
Note
In the first test case, gcd(1, 2) = gcd(2, 3) = gcd(1, 3) = 1.
In the second test case, 2 is the maximum possible value, corresponding to gcd(2, 4). | instruction | 0 | 4,353 | 22 | 8,706 |
Tags: greedy, implementation, math, number theory
Correct Solution:
```
from collections import defaultdict as dd
from collections import deque
import bisect
import heapq
def ri():
return int(input())
def rl():
return list(map(int, input().split()))
def solve():
n = ri()
print (n // 2)
mode = 'T'
if mode == 'T':
t = ri()
for i in range(t):
solve()
else:
solve()
``` | output | 1 | 4,353 | 22 | 8,707 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Let's consider all integers in the range from 1 to n (inclusive).
Among all pairs of distinct integers in this range, find the maximum possible greatest common divisor of integers in pair. Formally, find the maximum value of gcd(a, b), where 1 ≤ a < b ≤ n.
The greatest common divisor, gcd(a, b), of two positive integers a and b is the biggest integer that is a divisor of both a and b.
Input
The first line contains a single integer t (1 ≤ t ≤ 100) — the number of test cases. The description of the test cases follows.
The only line of each test case contains a single integer n (2 ≤ n ≤ 10^6).
Output
For each test case, output the maximum value of gcd(a, b) among all 1 ≤ a < b ≤ n.
Example
Input
2
3
5
Output
1
2
Note
In the first test case, gcd(1, 2) = gcd(2, 3) = gcd(1, 3) = 1.
In the second test case, 2 is the maximum possible value, corresponding to gcd(2, 4). | instruction | 0 | 4,354 | 22 | 8,708 |
Tags: greedy, implementation, math, number theory
Correct Solution:
```
def gcd(n):
if(n%2==0):
return n//2
else:
return gcd(n-1)
t=int(input())
for _ in range(0,t):
n=int(input())
res=gcd(n)
print(res)
``` | output | 1 | 4,354 | 22 | 8,709 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Let's consider all integers in the range from 1 to n (inclusive).
Among all pairs of distinct integers in this range, find the maximum possible greatest common divisor of integers in pair. Formally, find the maximum value of gcd(a, b), where 1 ≤ a < b ≤ n.
The greatest common divisor, gcd(a, b), of two positive integers a and b is the biggest integer that is a divisor of both a and b.
Input
The first line contains a single integer t (1 ≤ t ≤ 100) — the number of test cases. The description of the test cases follows.
The only line of each test case contains a single integer n (2 ≤ n ≤ 10^6).
Output
For each test case, output the maximum value of gcd(a, b) among all 1 ≤ a < b ≤ n.
Example
Input
2
3
5
Output
1
2
Note
In the first test case, gcd(1, 2) = gcd(2, 3) = gcd(1, 3) = 1.
In the second test case, 2 is the maximum possible value, corresponding to gcd(2, 4). | instruction | 0 | 4,355 | 22 | 8,710 |
Tags: greedy, implementation, math, number theory
Correct Solution:
```
for __ in range(int(input())):
n=int(input())
if n%2!=0:
n-=1
n=n//2
print(n)
``` | output | 1 | 4,355 | 22 | 8,711 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Let's consider all integers in the range from 1 to n (inclusive).
Among all pairs of distinct integers in this range, find the maximum possible greatest common divisor of integers in pair. Formally, find the maximum value of gcd(a, b), where 1 ≤ a < b ≤ n.
The greatest common divisor, gcd(a, b), of two positive integers a and b is the biggest integer that is a divisor of both a and b.
Input
The first line contains a single integer t (1 ≤ t ≤ 100) — the number of test cases. The description of the test cases follows.
The only line of each test case contains a single integer n (2 ≤ n ≤ 10^6).
Output
For each test case, output the maximum value of gcd(a, b) among all 1 ≤ a < b ≤ n.
Example
Input
2
3
5
Output
1
2
Note
In the first test case, gcd(1, 2) = gcd(2, 3) = gcd(1, 3) = 1.
In the second test case, 2 is the maximum possible value, corresponding to gcd(2, 4). | instruction | 0 | 4,356 | 22 | 8,712 |
Tags: greedy, implementation, math, number theory
Correct Solution:
```
# @oj: codeforces
# @id: hitwanyang
# @email: 296866643@qq.com
# @date: 2020-06-22 14:44
# @url:https://codeforc.es/contest/1370/problem/A
import sys,os
from io import BytesIO, IOBase
import collections,itertools,bisect,heapq,math,string
from decimal import *
# region fastio
BUFSIZE = 8192
BUFSIZE = 8192
class FastIO(IOBase):
newlines = 0
def __init__(self, file):
self._fd = file.fileno()
self.buffer = BytesIO()
self.writable = "x" in file.mode or "r" not in file.mode
self.write = self.buffer.write if self.writable else None
def read(self):
while True:
b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
if not b:
break
ptr = self.buffer.tell()
self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
self.newlines = 0
return self.buffer.read()
def readline(self):
while self.newlines == 0:
b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
self.newlines = b.count(b"\n") + (not b)
ptr = self.buffer.tell()
self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
self.newlines -= 1
return self.buffer.readline()
def flush(self):
if self.writable:
os.write(self._fd, self.buffer.getvalue())
self.buffer.truncate(0), self.buffer.seek(0)
class IOWrapper(IOBase):
def __init__(self, file):
self.buffer = FastIO(file)
self.flush = self.buffer.flush
self.writable = self.buffer.writable
self.write = lambda s: self.buffer.write(s.encode("ascii"))
self.read = lambda: self.buffer.read().decode("ascii")
self.readline = lambda: self.buffer.readline().decode("ascii")
sys.stdin, sys.stdout = IOWrapper(sys.stdin), IOWrapper(sys.stdout)
input = lambda: sys.stdin.readline().rstrip("\r\n")
# ------------------------------
def main():
t=int(input())
for i in range(t):
n=int(input())
print (n//2)
if __name__ == "__main__":
main()
``` | output | 1 | 4,356 | 22 | 8,713 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Let's consider all integers in the range from 1 to n (inclusive).
Among all pairs of distinct integers in this range, find the maximum possible greatest common divisor of integers in pair. Formally, find the maximum value of gcd(a, b), where 1 ≤ a < b ≤ n.
The greatest common divisor, gcd(a, b), of two positive integers a and b is the biggest integer that is a divisor of both a and b.
Input
The first line contains a single integer t (1 ≤ t ≤ 100) — the number of test cases. The description of the test cases follows.
The only line of each test case contains a single integer n (2 ≤ n ≤ 10^6).
Output
For each test case, output the maximum value of gcd(a, b) among all 1 ≤ a < b ≤ n.
Example
Input
2
3
5
Output
1
2
Note
In the first test case, gcd(1, 2) = gcd(2, 3) = gcd(1, 3) = 1.
In the second test case, 2 is the maximum possible value, corresponding to gcd(2, 4). | instruction | 0 | 4,357 | 22 | 8,714 |
Tags: greedy, implementation, math, number theory
Correct Solution:
```
for nt in range(int(input())):
n = int(input())
print (n//2)
``` | output | 1 | 4,357 | 22 | 8,715 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Let's consider all integers in the range from 1 to n (inclusive).
Among all pairs of distinct integers in this range, find the maximum possible greatest common divisor of integers in pair. Formally, find the maximum value of gcd(a, b), where 1 ≤ a < b ≤ n.
The greatest common divisor, gcd(a, b), of two positive integers a and b is the biggest integer that is a divisor of both a and b.
Input
The first line contains a single integer t (1 ≤ t ≤ 100) — the number of test cases. The description of the test cases follows.
The only line of each test case contains a single integer n (2 ≤ n ≤ 10^6).
Output
For each test case, output the maximum value of gcd(a, b) among all 1 ≤ a < b ≤ n.
Example
Input
2
3
5
Output
1
2
Note
In the first test case, gcd(1, 2) = gcd(2, 3) = gcd(1, 3) = 1.
In the second test case, 2 is the maximum possible value, corresponding to gcd(2, 4). | instruction | 0 | 4,358 | 22 | 8,716 |
Tags: greedy, implementation, math, number theory
Correct Solution:
```
import math
for _ in range(int(input())):
n=int(input())
print(math.floor(n/2))
``` | output | 1 | 4,358 | 22 | 8,717 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Let's consider all integers in the range from 1 to n (inclusive).
Among all pairs of distinct integers in this range, find the maximum possible greatest common divisor of integers in pair. Formally, find the maximum value of gcd(a, b), where 1 ≤ a < b ≤ n.
The greatest common divisor, gcd(a, b), of two positive integers a and b is the biggest integer that is a divisor of both a and b.
Input
The first line contains a single integer t (1 ≤ t ≤ 100) — the number of test cases. The description of the test cases follows.
The only line of each test case contains a single integer n (2 ≤ n ≤ 10^6).
Output
For each test case, output the maximum value of gcd(a, b) among all 1 ≤ a < b ≤ n.
Example
Input
2
3
5
Output
1
2
Note
In the first test case, gcd(1, 2) = gcd(2, 3) = gcd(1, 3) = 1.
In the second test case, 2 is the maximum possible value, corresponding to gcd(2, 4).
Submitted Solution:
```
def task_A():
t = int(input())
for _ in range(t):
n = int(input())
print(n // 2)
def main():
task_A()
if __name__ == '__main__':
main()
``` | instruction | 0 | 4,359 | 22 | 8,718 |
Yes | output | 1 | 4,359 | 22 | 8,719 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Let's consider all integers in the range from 1 to n (inclusive).
Among all pairs of distinct integers in this range, find the maximum possible greatest common divisor of integers in pair. Formally, find the maximum value of gcd(a, b), where 1 ≤ a < b ≤ n.
The greatest common divisor, gcd(a, b), of two positive integers a and b is the biggest integer that is a divisor of both a and b.
Input
The first line contains a single integer t (1 ≤ t ≤ 100) — the number of test cases. The description of the test cases follows.
The only line of each test case contains a single integer n (2 ≤ n ≤ 10^6).
Output
For each test case, output the maximum value of gcd(a, b) among all 1 ≤ a < b ≤ n.
Example
Input
2
3
5
Output
1
2
Note
In the first test case, gcd(1, 2) = gcd(2, 3) = gcd(1, 3) = 1.
In the second test case, 2 is the maximum possible value, corresponding to gcd(2, 4).
Submitted Solution:
```
def main():
t = int(input())
for _ in range(t):
n = int(input())
resposta = 0
for x in range(n, 0, -1):
if not x%2:
resposta = x//2
break
print(resposta)
main()
``` | instruction | 0 | 4,360 | 22 | 8,720 |
Yes | output | 1 | 4,360 | 22 | 8,721 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Let's consider all integers in the range from 1 to n (inclusive).
Among all pairs of distinct integers in this range, find the maximum possible greatest common divisor of integers in pair. Formally, find the maximum value of gcd(a, b), where 1 ≤ a < b ≤ n.
The greatest common divisor, gcd(a, b), of two positive integers a and b is the biggest integer that is a divisor of both a and b.
Input
The first line contains a single integer t (1 ≤ t ≤ 100) — the number of test cases. The description of the test cases follows.
The only line of each test case contains a single integer n (2 ≤ n ≤ 10^6).
Output
For each test case, output the maximum value of gcd(a, b) among all 1 ≤ a < b ≤ n.
Example
Input
2
3
5
Output
1
2
Note
In the first test case, gcd(1, 2) = gcd(2, 3) = gcd(1, 3) = 1.
In the second test case, 2 is the maximum possible value, corresponding to gcd(2, 4).
Submitted Solution:
```
q = int(input())
for i in range (q):
n = int(input())
print(n//2)
``` | instruction | 0 | 4,361 | 22 | 8,722 |
Yes | output | 1 | 4,361 | 22 | 8,723 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Let's consider all integers in the range from 1 to n (inclusive).
Among all pairs of distinct integers in this range, find the maximum possible greatest common divisor of integers in pair. Formally, find the maximum value of gcd(a, b), where 1 ≤ a < b ≤ n.
The greatest common divisor, gcd(a, b), of two positive integers a and b is the biggest integer that is a divisor of both a and b.
Input
The first line contains a single integer t (1 ≤ t ≤ 100) — the number of test cases. The description of the test cases follows.
The only line of each test case contains a single integer n (2 ≤ n ≤ 10^6).
Output
For each test case, output the maximum value of gcd(a, b) among all 1 ≤ a < b ≤ n.
Example
Input
2
3
5
Output
1
2
Note
In the first test case, gcd(1, 2) = gcd(2, 3) = gcd(1, 3) = 1.
In the second test case, 2 is the maximum possible value, corresponding to gcd(2, 4).
Submitted Solution:
```
t = int(input())
n = []
for i in range(t):
n.append(int(input()))
for i in range(len(n)):
if n[i]%2==0:
print(int(n[i] / 2))
else:
print(int((n[i] - 1) / 2))
``` | instruction | 0 | 4,362 | 22 | 8,724 |
Yes | output | 1 | 4,362 | 22 | 8,725 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Let's consider all integers in the range from 1 to n (inclusive).
Among all pairs of distinct integers in this range, find the maximum possible greatest common divisor of integers in pair. Formally, find the maximum value of gcd(a, b), where 1 ≤ a < b ≤ n.
The greatest common divisor, gcd(a, b), of two positive integers a and b is the biggest integer that is a divisor of both a and b.
Input
The first line contains a single integer t (1 ≤ t ≤ 100) — the number of test cases. The description of the test cases follows.
The only line of each test case contains a single integer n (2 ≤ n ≤ 10^6).
Output
For each test case, output the maximum value of gcd(a, b) among all 1 ≤ a < b ≤ n.
Example
Input
2
3
5
Output
1
2
Note
In the first test case, gcd(1, 2) = gcd(2, 3) = gcd(1, 3) = 1.
In the second test case, 2 is the maximum possible value, corresponding to gcd(2, 4).
Submitted Solution:
```
import math
for _ in range(int(input())):
n = int(input())
arr = [0] * n
for i in range(n):
arr[i] = i + 1
high = 0
i = 0
while i < n:
high = max(high, arr[i])
i = i + 1
# Array to store the count of divisors
# i.e. Potential GCDs
divisors = [0] * (high + 1)
# Iterating over every element
i = 0
while i < n:
# Calculating all the divisors
j = 1
while j <= math.sqrt(arr[i]):
# Divisor found
if arr[i] % j == 0:
# Incrementing count for divisor
divisors[j] = divisors[j] + 1
# Element/divisor is also a divisor
# Checking if both divisors are
# not same
if j != arr[i] / j:
divisors[arr[i] // j] = divisors[arr[i] // j] + 1
j = j + 1
i = i + 1
# Checking the highest potential GCD
i = high
while i >= 1:
# If this divisor can divide at least 2
# numbers, it is a GCD of at least 1 pair
if divisors[i] > 1:
print(i)
i = i - 1
``` | instruction | 0 | 4,363 | 22 | 8,726 |
No | output | 1 | 4,363 | 22 | 8,727 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Let's consider all integers in the range from 1 to n (inclusive).
Among all pairs of distinct integers in this range, find the maximum possible greatest common divisor of integers in pair. Formally, find the maximum value of gcd(a, b), where 1 ≤ a < b ≤ n.
The greatest common divisor, gcd(a, b), of two positive integers a and b is the biggest integer that is a divisor of both a and b.
Input
The first line contains a single integer t (1 ≤ t ≤ 100) — the number of test cases. The description of the test cases follows.
The only line of each test case contains a single integer n (2 ≤ n ≤ 10^6).
Output
For each test case, output the maximum value of gcd(a, b) among all 1 ≤ a < b ≤ n.
Example
Input
2
3
5
Output
1
2
Note
In the first test case, gcd(1, 2) = gcd(2, 3) = gcd(1, 3) = 1.
In the second test case, 2 is the maximum possible value, corresponding to gcd(2, 4).
Submitted Solution:
```
t=int(input())
while t:
t=t-1
n=int(input())
for i in range(1,n):
if n%i==0:
c=i
print(c)
``` | instruction | 0 | 4,364 | 22 | 8,728 |
No | output | 1 | 4,364 | 22 | 8,729 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Let's consider all integers in the range from 1 to n (inclusive).
Among all pairs of distinct integers in this range, find the maximum possible greatest common divisor of integers in pair. Formally, find the maximum value of gcd(a, b), where 1 ≤ a < b ≤ n.
The greatest common divisor, gcd(a, b), of two positive integers a and b is the biggest integer that is a divisor of both a and b.
Input
The first line contains a single integer t (1 ≤ t ≤ 100) — the number of test cases. The description of the test cases follows.
The only line of each test case contains a single integer n (2 ≤ n ≤ 10^6).
Output
For each test case, output the maximum value of gcd(a, b) among all 1 ≤ a < b ≤ n.
Example
Input
2
3
5
Output
1
2
Note
In the first test case, gcd(1, 2) = gcd(2, 3) = gcd(1, 3) = 1.
In the second test case, 2 is the maximum possible value, corresponding to gcd(2, 4).
Submitted Solution:
```
#!/usr/bin/env python
import os
import operator
import sys
from io import BytesIO, IOBase
def main():
#for _ in range(int(input())):
# #n=int(input())
# a,b,n=map(int,input().split())
# #arr=[int(k) for k in input().split()]
# count=0
# while True:
# mn=min(a,b)
# mx=max(a,b)
# mn=mn+mx
# count+=1
# if mn>n:
# break
# a=mn
# b=mx
# #print(a,b)
# print(count)
n=int(input())
#if n%2==0:
print(n//2)
BUFSIZE = 8192
class FastIO(IOBase):
newlines = 0
def __init__(self, file):
self._fd = file.fileno()
self.buffer = BytesIO()
self.writable = "x" in file.mode or "r" not in file.mode
self.write = self.buffer.write if self.writable else None
def read(self):
while True:
b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
if not b:
break
ptr = self.buffer.tell()
self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
self.newlines = 0
return self.buffer.read()
def readline(self):
while self.newlines == 0:
b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
self.newlines = b.count(b"\n") + (not b)
ptr = self.buffer.tell()
self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
self.newlines -= 1
return self.buffer.readline()
def flush(self):
if self.writable:
os.write(self._fd, self.buffer.getvalue())
self.buffer.truncate(0), self.buffer.seek(0)
class IOWrapper(IOBase):
def __init__(self, file):
self.buffer = FastIO(file)
self.flush = self.buffer.flush
self.writable = self.buffer.writable
self.write = lambda s: self.buffer.write(s.encode("ascii"))
self.read = lambda: self.buffer.read().decode("ascii")
self.readline = lambda: self.buffer.readline().decode("ascii")
sys.stdin, sys.stdout = IOWrapper(sys.stdin), IOWrapper(sys.stdout)
input = lambda: sys.stdin.readline().rstrip("\r\n")
if __name__ == "__main__":
main()
``` | instruction | 0 | 4,365 | 22 | 8,730 |
No | output | 1 | 4,365 | 22 | 8,731 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Let's consider all integers in the range from 1 to n (inclusive).
Among all pairs of distinct integers in this range, find the maximum possible greatest common divisor of integers in pair. Formally, find the maximum value of gcd(a, b), where 1 ≤ a < b ≤ n.
The greatest common divisor, gcd(a, b), of two positive integers a and b is the biggest integer that is a divisor of both a and b.
Input
The first line contains a single integer t (1 ≤ t ≤ 100) — the number of test cases. The description of the test cases follows.
The only line of each test case contains a single integer n (2 ≤ n ≤ 10^6).
Output
For each test case, output the maximum value of gcd(a, b) among all 1 ≤ a < b ≤ n.
Example
Input
2
3
5
Output
1
2
Note
In the first test case, gcd(1, 2) = gcd(2, 3) = gcd(1, 3) = 1.
In the second test case, 2 is the maximum possible value, corresponding to gcd(2, 4).
Submitted Solution:
```
import math
n=int(input())
for i in range(n):
x=int(input())
print(int(math.sqrt(x)))
``` | instruction | 0 | 4,366 | 22 | 8,732 |
No | output | 1 | 4,366 | 22 | 8,733 |
Provide tags and a correct Python 3 solution for this coding contest problem.
An n × n square matrix is special, if:
* it is binary, that is, each cell contains either a 0, or a 1;
* the number of ones in each row and column equals 2.
You are given n and the first m rows of the matrix. Print the number of special n × n matrices, such that the first m rows coincide with the given ones.
As the required value can be rather large, print the remainder after dividing the value by the given number mod.
Input
The first line of the input contains three integers n, m, mod (2 ≤ n ≤ 500, 0 ≤ m ≤ n, 2 ≤ mod ≤ 109). Then m lines follow, each of them contains n characters — the first rows of the required special matrices. Each of these lines contains exactly two characters '1', the rest characters are '0'. Each column of the given m × n table contains at most two numbers one.
Output
Print the remainder after dividing the required value by number mod.
Examples
Input
3 1 1000
011
Output
2
Input
4 4 100500
0110
1010
0101
1001
Output
1
Note
For the first test the required matrices are:
011
101
110
011
110
101
In the second test the required matrix is already fully given, so the answer is 1. | instruction | 0 | 4,589 | 22 | 9,178 |
Tags: combinatorics, dp
Correct Solution:
```
from math import *
from collections import *
import sys
sys.setrecursionlimit(10**9)
dp = [[-1 for i in range(505)] for j in range(505)]
def memo(row,z,o):
if(row == n):
if(z == 0 and o == 0):
return 1
else:
return 0
if(dp[z][o] != -1): return dp[z][o]
if(z > 1):
dp[z][o] += (z*(z-1)//2)*(memo(row+1,z-2,o+2))
dp[z][o] %= mod
if(z >= 1 and o >= 1):
dp[z][o] += (z*o)*(memo(row+1,z-1,o))
dp[z][o] %= mod
if(o > 1):
dp[z][o] += (o*(o-1)//2)*(memo(row+1,z,o-2))
dp[z][o] %= mod
#print(row,z,o,dp[z][o])
dp[z][o] += 1
dp[z][o] %= mod
return dp[z][o]%mod
n,m,mod = map(int,input().split())
a = []
for i in range(m):
s = list(input())
a.append(s)
#print(a)
ct = [0 for i in range(n)]
for i in range(m):
for j in range(n):
if(a[i][j] == '1'):
ct[j] += 1
z = ct.count(0)
o = ct.count(1)
ans = memo(m,z,o)
print(ans%mod)
``` | output | 1 | 4,589 | 22 | 9,179 |
Provide tags and a correct Python 3 solution for this coding contest problem.
An n × n square matrix is special, if:
* it is binary, that is, each cell contains either a 0, or a 1;
* the number of ones in each row and column equals 2.
You are given n and the first m rows of the matrix. Print the number of special n × n matrices, such that the first m rows coincide with the given ones.
As the required value can be rather large, print the remainder after dividing the value by the given number mod.
Input
The first line of the input contains three integers n, m, mod (2 ≤ n ≤ 500, 0 ≤ m ≤ n, 2 ≤ mod ≤ 109). Then m lines follow, each of them contains n characters — the first rows of the required special matrices. Each of these lines contains exactly two characters '1', the rest characters are '0'. Each column of the given m × n table contains at most two numbers one.
Output
Print the remainder after dividing the required value by number mod.
Examples
Input
3 1 1000
011
Output
2
Input
4 4 100500
0110
1010
0101
1001
Output
1
Note
For the first test the required matrices are:
011
101
110
011
110
101
In the second test the required matrix is already fully given, so the answer is 1. | instruction | 0 | 4,590 | 22 | 9,180 |
Tags: combinatorics, dp
Correct Solution:
```
a,b,mod = list(map(int, input().split()))
g = [2] * a
for i in range(b):
t = input()
for x, y in enumerate(t):
if y == '1':
g[x] -= 1
one = two = 0
for q in g:
if q < 0:
print(0)
exit(0)
if q == 1:
one+=1
if q == 2:
two+=1
mat = [[0]*600 for x in range(600)]
mat[0][0] = 1
#int(one, two)
for j in range(a + 1):
for i in range(a + 1):
if i-2>=0:
mat[i][j] += i*(i-1) // 2 * mat[i-2][j];
#print('in',i,j, mat[i][j], i*(i-1)//2, mat[i-2][j], i-2, mat[0][0])
if j-1>=0:
mat[i][j] += i*j * mat[i][j -1];
if j-2>=0 :
mat[i][j] += j *(j-1)//2 * mat[i+2][j -2];
mat[i][j] %= mod
#print(mat[2][0])
#print(mat[0][2])
print(mat[one][two])
``` | output | 1 | 4,590 | 22 | 9,181 |
Provide tags and a correct Python 3 solution for this coding contest problem.
An n × n square matrix is special, if:
* it is binary, that is, each cell contains either a 0, or a 1;
* the number of ones in each row and column equals 2.
You are given n and the first m rows of the matrix. Print the number of special n × n matrices, such that the first m rows coincide with the given ones.
As the required value can be rather large, print the remainder after dividing the value by the given number mod.
Input
The first line of the input contains three integers n, m, mod (2 ≤ n ≤ 500, 0 ≤ m ≤ n, 2 ≤ mod ≤ 109). Then m lines follow, each of them contains n characters — the first rows of the required special matrices. Each of these lines contains exactly two characters '1', the rest characters are '0'. Each column of the given m × n table contains at most two numbers one.
Output
Print the remainder after dividing the required value by number mod.
Examples
Input
3 1 1000
011
Output
2
Input
4 4 100500
0110
1010
0101
1001
Output
1
Note
For the first test the required matrices are:
011
101
110
011
110
101
In the second test the required matrix is already fully given, so the answer is 1. | instruction | 0 | 4,591 | 22 | 9,182 |
Tags: combinatorics, dp
Correct Solution:
```
# // DP
# // codeforces 489F Special Matrices
n = 0
m = 0
MOD = 0
cap = [0] * 505
ans = [[-1] * 505 for i in range(505)]
def f(one, two):
if one == 0 and two == 0:
return 1
if two > len(ans[one]):
print(str(one) + ' ' + str(two) + ' ' + len(ans[one]))
if ans[one][two] != -1:
return ans[one][two]
temp = 0
if two > 1:
x = two * (two-1) / 2 * f(one+2, two-2)
temp += x % MOD
if one > 1:
x = one * (one-1) / 2 * f(one-2, two)
temp += x % MOD
if two > 0 and one > 0:
x = one * two * f(one, two-1)
temp += x % MOD
temp = temp % MOD
ans[one][two] = temp
return temp
temp = input().split(' ')
n = int(temp[0])
m = int(temp[1])
MOD = int(temp[2])
for i in range(0, m):
cur = ''
cur = input()
for j in range(0, n):
if cur[j] == '1':
cap[j] += 1
n_one = 0;
n_two = 0;
for i in range(0, n):
if cap[i] == 0:
n_two += 1
if cap[i] == 1:
n_one += 1
print(int(f(n_one, n_two)))
# // F. Special Matrices
# // time limit per test
# // 1 second
# // memory limit per test
# // 256 megabytes
# // input
# // standard input
# // output
# // standard output
# // An n × n square matrix is special, if:
# // it is binary, that is, each cell contains either a 0, or a 1;
# // the number of ones in each row and column equals 2.
# // You are given n and the first m rows of the matrix. Print the number of special n × n matrices, such that the first m rows coincide with the given ones.
# // As the required value can be rather large, print the remainder after dividing the value by the given number mod.
# // Input
# // The first line of the input contains three integers n, m, mod (2 ≤ n ≤ 500, 0 ≤ m ≤ n, 2 ≤ mod ≤ 109). Then m lines follow, each of them contains n characters — the first rows of the required special matrices. Each of these lines contains exactly two characters '1', the rest characters are '0'. Each column of the given m × n table contains at most two numbers one.
# // Output
# // Print the remainder after dividing the required value by number mod.
# // Sample test(s)
# // Input
# // 3 1 1000
# // 011
# // Output
# // 2
# // Input
# // 4 4 100500
# // 0110
# // 1010
# // 0101
# // 1001
# // Output
# // 1
# // Note
# // For the first test the required matrices are:
# // 011
# // 101
# // 110
# // 011
# // 110
# // 101
# // In the second test the required matrix is already fully given, so the answer is 1.
``` | output | 1 | 4,591 | 22 | 9,183 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Duff is in love with lovely numbers! A positive integer x is called lovely if and only if there is no such positive integer a > 1 such that a2 is a divisor of x.
<image>
Malek has a number store! In his store, he has only divisors of positive integer n (and he has all of them). As a birthday present, Malek wants to give her a lovely number from his store. He wants this number to be as big as possible.
Malek always had issues in math, so he asked for your help. Please tell him what is the biggest lovely number in his store.
Input
The first and only line of input contains one integer, n (1 ≤ n ≤ 1012).
Output
Print the answer in one line.
Examples
Input
10
Output
10
Input
12
Output
6
Note
In first sample case, there are numbers 1, 2, 5 and 10 in the shop. 10 isn't divisible by any perfect square, so 10 is lovely.
In second sample case, there are numbers 1, 2, 3, 4, 6 and 12 in the shop. 12 is divisible by 4 = 22, so 12 is not lovely, while 6 is indeed lovely. | instruction | 0 | 4,603 | 22 | 9,206 |
Tags: math
Correct Solution:
```
from math import ceil
n = int(input())
n1 = n
p = 1
mas = set()
for i in range(2, ceil(n**.5) + 1):
cnt = 0
while n % i == 0:
n = n//i
mas.add(i)
p *= i
mas.add(n1 // p)
p = 1
for i in mas:
p *= i
print(p)
``` | output | 1 | 4,603 | 22 | 9,207 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Duff is in love with lovely numbers! A positive integer x is called lovely if and only if there is no such positive integer a > 1 such that a2 is a divisor of x.
<image>
Malek has a number store! In his store, he has only divisors of positive integer n (and he has all of them). As a birthday present, Malek wants to give her a lovely number from his store. He wants this number to be as big as possible.
Malek always had issues in math, so he asked for your help. Please tell him what is the biggest lovely number in his store.
Input
The first and only line of input contains one integer, n (1 ≤ n ≤ 1012).
Output
Print the answer in one line.
Examples
Input
10
Output
10
Input
12
Output
6
Note
In first sample case, there are numbers 1, 2, 5 and 10 in the shop. 10 isn't divisible by any perfect square, so 10 is lovely.
In second sample case, there are numbers 1, 2, 3, 4, 6 and 12 in the shop. 12 is divisible by 4 = 22, so 12 is not lovely, while 6 is indeed lovely. | instruction | 0 | 4,604 | 22 | 9,208 |
Tags: math
Correct Solution:
```
from math import *
n = int(input())
for i in range(2,10**6):
while n%(i*i)==0 :
n//=(i)
print(n)
``` | output | 1 | 4,604 | 22 | 9,209 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Duff is in love with lovely numbers! A positive integer x is called lovely if and only if there is no such positive integer a > 1 such that a2 is a divisor of x.
<image>
Malek has a number store! In his store, he has only divisors of positive integer n (and he has all of them). As a birthday present, Malek wants to give her a lovely number from his store. He wants this number to be as big as possible.
Malek always had issues in math, so he asked for your help. Please tell him what is the biggest lovely number in his store.
Input
The first and only line of input contains one integer, n (1 ≤ n ≤ 1012).
Output
Print the answer in one line.
Examples
Input
10
Output
10
Input
12
Output
6
Note
In first sample case, there are numbers 1, 2, 5 and 10 in the shop. 10 isn't divisible by any perfect square, so 10 is lovely.
In second sample case, there are numbers 1, 2, 3, 4, 6 and 12 in the shop. 12 is divisible by 4 = 22, so 12 is not lovely, while 6 is indeed lovely. | instruction | 0 | 4,605 | 22 | 9,210 |
Tags: math
Correct Solution:
```
import math
n = int(input())
m = n
m = math.sqrt(m)
m = math.floor(m)
i = 2
x = 1
while i<=m:
if (n % i*i)==0:
while (n % i)==0:
n = n//i
n = n*i
m = n
m = math.sqrt(m)
m = math.floor(m)
i = i+1
print(n)
``` | output | 1 | 4,605 | 22 | 9,211 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Duff is in love with lovely numbers! A positive integer x is called lovely if and only if there is no such positive integer a > 1 such that a2 is a divisor of x.
<image>
Malek has a number store! In his store, he has only divisors of positive integer n (and he has all of them). As a birthday present, Malek wants to give her a lovely number from his store. He wants this number to be as big as possible.
Malek always had issues in math, so he asked for your help. Please tell him what is the biggest lovely number in his store.
Input
The first and only line of input contains one integer, n (1 ≤ n ≤ 1012).
Output
Print the answer in one line.
Examples
Input
10
Output
10
Input
12
Output
6
Note
In first sample case, there are numbers 1, 2, 5 and 10 in the shop. 10 isn't divisible by any perfect square, so 10 is lovely.
In second sample case, there are numbers 1, 2, 3, 4, 6 and 12 in the shop. 12 is divisible by 4 = 22, so 12 is not lovely, while 6 is indeed lovely. | instruction | 0 | 4,606 | 22 | 9,212 |
Tags: math
Correct Solution:
```
import math
n = int(input())
def factors(n):
return set(x for tup in ([i, n//i] for i in range(1, int(n**0.5)+1) if n % i == 0) for x in tup)
for factor in sorted(factors(n), reverse=True):
failed = False
for f in factors(factor):
if f != 1 and f == int(math.sqrt(f))**2:
failed = True
break
if not failed:
print(factor)
break
``` | output | 1 | 4,606 | 22 | 9,213 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Duff is in love with lovely numbers! A positive integer x is called lovely if and only if there is no such positive integer a > 1 such that a2 is a divisor of x.
<image>
Malek has a number store! In his store, he has only divisors of positive integer n (and he has all of them). As a birthday present, Malek wants to give her a lovely number from his store. He wants this number to be as big as possible.
Malek always had issues in math, so he asked for your help. Please tell him what is the biggest lovely number in his store.
Input
The first and only line of input contains one integer, n (1 ≤ n ≤ 1012).
Output
Print the answer in one line.
Examples
Input
10
Output
10
Input
12
Output
6
Note
In first sample case, there are numbers 1, 2, 5 and 10 in the shop. 10 isn't divisible by any perfect square, so 10 is lovely.
In second sample case, there are numbers 1, 2, 3, 4, 6 and 12 in the shop. 12 is divisible by 4 = 22, so 12 is not lovely, while 6 is indeed lovely. | instruction | 0 | 4,607 | 22 | 9,214 |
Tags: math
Correct Solution:
```
from copy import copy
n = int(input())
factors = set()
new = copy(n)
for i in range(2, int(n**(1/2))+1):
#print(i)
while new % i == 0:
factors.add(i)
new //= i
if new != 1:
factors.add(new)
ans = 1
for i in factors:
ans *= i
print(ans)
``` | output | 1 | 4,607 | 22 | 9,215 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Duff is in love with lovely numbers! A positive integer x is called lovely if and only if there is no such positive integer a > 1 such that a2 is a divisor of x.
<image>
Malek has a number store! In his store, he has only divisors of positive integer n (and he has all of them). As a birthday present, Malek wants to give her a lovely number from his store. He wants this number to be as big as possible.
Malek always had issues in math, so he asked for your help. Please tell him what is the biggest lovely number in his store.
Input
The first and only line of input contains one integer, n (1 ≤ n ≤ 1012).
Output
Print the answer in one line.
Examples
Input
10
Output
10
Input
12
Output
6
Note
In first sample case, there are numbers 1, 2, 5 and 10 in the shop. 10 isn't divisible by any perfect square, so 10 is lovely.
In second sample case, there are numbers 1, 2, 3, 4, 6 and 12 in the shop. 12 is divisible by 4 = 22, so 12 is not lovely, while 6 is indeed lovely. | instruction | 0 | 4,608 | 22 | 9,216 |
Tags: math
Correct Solution:
```
import sys
#sys.stdin = open("input.txt")
#sys.stdout = open("output.txt", "w")
n = int(input())
di = [1]
i = 2
while n > 1:
if i*i > n:
break
if n % i == 0:
di += [i]
while n % i == 0 and n > 1:
n //= i
i += 1
if n != 1:
di += [n]
ans = 1
for item in di:
ans *= item
print(ans)
``` | output | 1 | 4,608 | 22 | 9,217 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Duff is in love with lovely numbers! A positive integer x is called lovely if and only if there is no such positive integer a > 1 such that a2 is a divisor of x.
<image>
Malek has a number store! In his store, he has only divisors of positive integer n (and he has all of them). As a birthday present, Malek wants to give her a lovely number from his store. He wants this number to be as big as possible.
Malek always had issues in math, so he asked for your help. Please tell him what is the biggest lovely number in his store.
Input
The first and only line of input contains one integer, n (1 ≤ n ≤ 1012).
Output
Print the answer in one line.
Examples
Input
10
Output
10
Input
12
Output
6
Note
In first sample case, there are numbers 1, 2, 5 and 10 in the shop. 10 isn't divisible by any perfect square, so 10 is lovely.
In second sample case, there are numbers 1, 2, 3, 4, 6 and 12 in the shop. 12 is divisible by 4 = 22, so 12 is not lovely, while 6 is indeed lovely. | instruction | 0 | 4,609 | 22 | 9,218 |
Tags: math
Correct Solution:
```
import math
n=int(input())
y=0
if n==1:
print(1)
exit(0)
while (n**(0.5))%1==0:
n=int(n**(0.5))
#print(n)
for i in range(2,10**6+1):
x=math.log(n,i)
#print(x)
if n%i==0 :
j=int(x)+1
while(j>=2):
if n%(i**j)==0:
y+=1
#print(y)
j-=1
n/=(i**(y))
y=0
print(int(n))
``` | output | 1 | 4,609 | 22 | 9,219 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Duff is in love with lovely numbers! A positive integer x is called lovely if and only if there is no such positive integer a > 1 such that a2 is a divisor of x.
<image>
Malek has a number store! In his store, he has only divisors of positive integer n (and he has all of them). As a birthday present, Malek wants to give her a lovely number from his store. He wants this number to be as big as possible.
Malek always had issues in math, so he asked for your help. Please tell him what is the biggest lovely number in his store.
Input
The first and only line of input contains one integer, n (1 ≤ n ≤ 1012).
Output
Print the answer in one line.
Examples
Input
10
Output
10
Input
12
Output
6
Note
In first sample case, there are numbers 1, 2, 5 and 10 in the shop. 10 isn't divisible by any perfect square, so 10 is lovely.
In second sample case, there are numbers 1, 2, 3, 4, 6 and 12 in the shop. 12 is divisible by 4 = 22, so 12 is not lovely, while 6 is indeed lovely. | instruction | 0 | 4,610 | 22 | 9,220 |
Tags: math
Correct Solution:
```
# Python program to print prime factors
import math
from collections import Counter
# A function to print all prime factors of
# a given number n
def primeFactors(n):
primes = Counter()
# Print the number of two's that divide n
while n % 2 == 0:
primes[2] += 1
n = n / 2
# n must be odd at this point
# so a skip of 2 ( i = i + 2) can be used
for i in range(3,int(math.sqrt(n))+1,2):
# while i divides n , print i ad divide n
while n % i== 0:
primes[i] += 1
n = n / i
# Condition if n is a prime
# number greater than 2
if n > 2:
primes[int(n)] += 1
return primes
# Driver Program to test above function
n = int(input())
c = primeFactors(n)
total = 1
for n in c.keys():
total *= n
print(total)
# This code is contributed by Harshit Agrawal
``` | output | 1 | 4,610 | 22 | 9,221 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Duff is in love with lovely numbers! A positive integer x is called lovely if and only if there is no such positive integer a > 1 such that a2 is a divisor of x.
<image>
Malek has a number store! In his store, he has only divisors of positive integer n (and he has all of them). As a birthday present, Malek wants to give her a lovely number from his store. He wants this number to be as big as possible.
Malek always had issues in math, so he asked for your help. Please tell him what is the biggest lovely number in his store.
Input
The first and only line of input contains one integer, n (1 ≤ n ≤ 1012).
Output
Print the answer in one line.
Examples
Input
10
Output
10
Input
12
Output
6
Note
In first sample case, there are numbers 1, 2, 5 and 10 in the shop. 10 isn't divisible by any perfect square, so 10 is lovely.
In second sample case, there are numbers 1, 2, 3, 4, 6 and 12 in the shop. 12 is divisible by 4 = 22, so 12 is not lovely, while 6 is indeed lovely.
Submitted Solution:
```
n = int(input())
i=2
while i*i <= n:
while n%(i*i)==0:
n=n//i
i+=1
print(n)
``` | instruction | 0 | 4,611 | 22 | 9,222 |
Yes | output | 1 | 4,611 | 22 | 9,223 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Duff is in love with lovely numbers! A positive integer x is called lovely if and only if there is no such positive integer a > 1 such that a2 is a divisor of x.
<image>
Malek has a number store! In his store, he has only divisors of positive integer n (and he has all of them). As a birthday present, Malek wants to give her a lovely number from his store. He wants this number to be as big as possible.
Malek always had issues in math, so he asked for your help. Please tell him what is the biggest lovely number in his store.
Input
The first and only line of input contains one integer, n (1 ≤ n ≤ 1012).
Output
Print the answer in one line.
Examples
Input
10
Output
10
Input
12
Output
6
Note
In first sample case, there are numbers 1, 2, 5 and 10 in the shop. 10 isn't divisible by any perfect square, so 10 is lovely.
In second sample case, there are numbers 1, 2, 3, 4, 6 and 12 in the shop. 12 is divisible by 4 = 22, so 12 is not lovely, while 6 is indeed lovely.
Submitted Solution:
```
import math
n=int(input())
squareFreePart=1
while(n>1):
nothingFound=True
for p in range(2,int(math.sqrt(n))+1):
if(n%p==0):
nothingFound=False
while(n%p==0):
n=n//p
squareFreePart*=p
break
if (nothingFound):
squareFreePart*=n
break
print(squareFreePart)
``` | instruction | 0 | 4,612 | 22 | 9,224 |
Yes | output | 1 | 4,612 | 22 | 9,225 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Duff is in love with lovely numbers! A positive integer x is called lovely if and only if there is no such positive integer a > 1 such that a2 is a divisor of x.
<image>
Malek has a number store! In his store, he has only divisors of positive integer n (and he has all of them). As a birthday present, Malek wants to give her a lovely number from his store. He wants this number to be as big as possible.
Malek always had issues in math, so he asked for your help. Please tell him what is the biggest lovely number in his store.
Input
The first and only line of input contains one integer, n (1 ≤ n ≤ 1012).
Output
Print the answer in one line.
Examples
Input
10
Output
10
Input
12
Output
6
Note
In first sample case, there are numbers 1, 2, 5 and 10 in the shop. 10 isn't divisible by any perfect square, so 10 is lovely.
In second sample case, there are numbers 1, 2, 3, 4, 6 and 12 in the shop. 12 is divisible by 4 = 22, so 12 is not lovely, while 6 is indeed lovely.
Submitted Solution:
```
n = int(input())
i = 2
resposta = 1
while i * i <= n:
if n % i == 0:
resposta *= i
while n % i == 0:
n //= i
i += 1
if n > 1:
resposta *= n
print(resposta)
``` | instruction | 0 | 4,613 | 22 | 9,226 |
Yes | output | 1 | 4,613 | 22 | 9,227 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Duff is in love with lovely numbers! A positive integer x is called lovely if and only if there is no such positive integer a > 1 such that a2 is a divisor of x.
<image>
Malek has a number store! In his store, he has only divisors of positive integer n (and he has all of them). As a birthday present, Malek wants to give her a lovely number from his store. He wants this number to be as big as possible.
Malek always had issues in math, so he asked for your help. Please tell him what is the biggest lovely number in his store.
Input
The first and only line of input contains one integer, n (1 ≤ n ≤ 1012).
Output
Print the answer in one line.
Examples
Input
10
Output
10
Input
12
Output
6
Note
In first sample case, there are numbers 1, 2, 5 and 10 in the shop. 10 isn't divisible by any perfect square, so 10 is lovely.
In second sample case, there are numbers 1, 2, 3, 4, 6 and 12 in the shop. 12 is divisible by 4 = 22, so 12 is not lovely, while 6 is indeed lovely.
Submitted Solution:
```
n = int(input())
ans = 1
i = 2
while i * i <= n:
if n % i == 0:
while n % i == 0:
n //= i
ans *= i
i += 1
if n > 1:
ans *= n
print(ans)
``` | instruction | 0 | 4,614 | 22 | 9,228 |
Yes | output | 1 | 4,614 | 22 | 9,229 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Duff is in love with lovely numbers! A positive integer x is called lovely if and only if there is no such positive integer a > 1 such that a2 is a divisor of x.
<image>
Malek has a number store! In his store, he has only divisors of positive integer n (and he has all of them). As a birthday present, Malek wants to give her a lovely number from his store. He wants this number to be as big as possible.
Malek always had issues in math, so he asked for your help. Please tell him what is the biggest lovely number in his store.
Input
The first and only line of input contains one integer, n (1 ≤ n ≤ 1012).
Output
Print the answer in one line.
Examples
Input
10
Output
10
Input
12
Output
6
Note
In first sample case, there are numbers 1, 2, 5 and 10 in the shop. 10 isn't divisible by any perfect square, so 10 is lovely.
In second sample case, there are numbers 1, 2, 3, 4, 6 and 12 in the shop. 12 is divisible by 4 = 22, so 12 is not lovely, while 6 is indeed lovely.
Submitted Solution:
```
import math
n=int(input())
y=0
if n==1:
print(1)
exit(0)
while (n**(0.5))%1==0:
n=int(n**(0.5))
#print(n)
for i in range(2,int(n**0.5)+1):
x=math.log(n,i)
if n%i==0 :
for j in range(2,int(x+1)):
if n%(i**j)==0:
y+=1
#print(y)
n/=(i**(y))
y=0
print(int(n))
``` | instruction | 0 | 4,615 | 22 | 9,230 |
No | output | 1 | 4,615 | 22 | 9,231 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Duff is in love with lovely numbers! A positive integer x is called lovely if and only if there is no such positive integer a > 1 such that a2 is a divisor of x.
<image>
Malek has a number store! In his store, he has only divisors of positive integer n (and he has all of them). As a birthday present, Malek wants to give her a lovely number from his store. He wants this number to be as big as possible.
Malek always had issues in math, so he asked for your help. Please tell him what is the biggest lovely number in his store.
Input
The first and only line of input contains one integer, n (1 ≤ n ≤ 1012).
Output
Print the answer in one line.
Examples
Input
10
Output
10
Input
12
Output
6
Note
In first sample case, there are numbers 1, 2, 5 and 10 in the shop. 10 isn't divisible by any perfect square, so 10 is lovely.
In second sample case, there are numbers 1, 2, 3, 4, 6 and 12 in the shop. 12 is divisible by 4 = 22, so 12 is not lovely, while 6 is indeed lovely.
Submitted Solution:
```
n = int(input())
d = n
s = 2
result=True
while d!=1:
if n%d==0:
result = True
s=2
while s**2<d:
if (d%(s**2)==0):
result=False
break
else:
s += 1
#if s**2>d:
#result=True
if result:
break
d -= 1
print(d)
``` | instruction | 0 | 4,616 | 22 | 9,232 |
No | output | 1 | 4,616 | 22 | 9,233 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Duff is in love with lovely numbers! A positive integer x is called lovely if and only if there is no such positive integer a > 1 such that a2 is a divisor of x.
<image>
Malek has a number store! In his store, he has only divisors of positive integer n (and he has all of them). As a birthday present, Malek wants to give her a lovely number from his store. He wants this number to be as big as possible.
Malek always had issues in math, so he asked for your help. Please tell him what is the biggest lovely number in his store.
Input
The first and only line of input contains one integer, n (1 ≤ n ≤ 1012).
Output
Print the answer in one line.
Examples
Input
10
Output
10
Input
12
Output
6
Note
In first sample case, there are numbers 1, 2, 5 and 10 in the shop. 10 isn't divisible by any perfect square, so 10 is lovely.
In second sample case, there are numbers 1, 2, 3, 4, 6 and 12 in the shop. 12 is divisible by 4 = 22, so 12 is not lovely, while 6 is indeed lovely.
Submitted Solution:
```
from math import sqrt
n = int(input())
for i in range(2, int(sqrt(n))+1):
if n%(i**2)==0:
print(int(n/(i**2)))
exit()
print(n)
``` | instruction | 0 | 4,617 | 22 | 9,234 |
No | output | 1 | 4,617 | 22 | 9,235 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Duff is in love with lovely numbers! A positive integer x is called lovely if and only if there is no such positive integer a > 1 such that a2 is a divisor of x.
<image>
Malek has a number store! In his store, he has only divisors of positive integer n (and he has all of them). As a birthday present, Malek wants to give her a lovely number from his store. He wants this number to be as big as possible.
Malek always had issues in math, so he asked for your help. Please tell him what is the biggest lovely number in his store.
Input
The first and only line of input contains one integer, n (1 ≤ n ≤ 1012).
Output
Print the answer in one line.
Examples
Input
10
Output
10
Input
12
Output
6
Note
In first sample case, there are numbers 1, 2, 5 and 10 in the shop. 10 isn't divisible by any perfect square, so 10 is lovely.
In second sample case, there are numbers 1, 2, 3, 4, 6 and 12 in the shop. 12 is divisible by 4 = 22, so 12 is not lovely, while 6 is indeed lovely.
Submitted Solution:
```
def getDivisors(number):
div = set()
for i in range(1, (number // 2) + 1):
if(number % i == 0):
div.add(i)
div.add(number // i)
div = list(div)
div.sort(reverse = True)
return div
def isLovely(number):
divisors = getDivisors(number)
for i in range(len(divisors)):
j = 2
while(pow(j, 2) <= number):
if((pow(j,2)) in divisors):
return False
j += 1
return True
number = int(input())
divisors = getDivisors(number)
for i in range(len(divisors)):
divisor = divisors[i]
if(isLovely(divisor)):
print(divisor)
break
``` | instruction | 0 | 4,618 | 22 | 9,236 |
No | output | 1 | 4,618 | 22 | 9,237 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Mahmoud has an array a consisting of n integers. He asked Ehab to find another array b of the same length such that:
* b is lexicographically greater than or equal to a.
* bi ≥ 2.
* b is pairwise coprime: for every 1 ≤ i < j ≤ n, bi and bj are coprime, i. e. GCD(bi, bj) = 1, where GCD(w, z) is the greatest common divisor of w and z.
Ehab wants to choose a special array so he wants the lexicographically minimal array between all the variants. Can you find it?
An array x is lexicographically greater than an array y if there exists an index i such than xi > yi and xj = yj for all 1 ≤ j < i. An array x is equal to an array y if xi = yi for all 1 ≤ i ≤ n.
Input
The first line contains an integer n (1 ≤ n ≤ 105), the number of elements in a and b.
The second line contains n integers a1, a2, ..., an (2 ≤ ai ≤ 105), the elements of a.
Output
Output n space-separated integers, the i-th of them representing bi.
Examples
Input
5
2 3 5 4 13
Output
2 3 5 7 11
Input
3
10 3 7
Output
10 3 7
Note
Note that in the second sample, the array is already pairwise coprime so we printed it. | instruction | 0 | 4,783 | 22 | 9,566 |
Tags: constructive algorithms, greedy, math, number theory
Correct Solution:
```
import atexit
import io
import sys
# Buffering IO
_INPUT_LINES = sys.stdin.read().splitlines()
input = iter(_INPUT_LINES).__next__
_OUTPUT_BUFFER = io.StringIO()
sys.stdout = _OUTPUT_BUFFER
@atexit.register
def write():
sys.__stdout__.write(_OUTPUT_BUFFER.getvalue())
ppp = ('2 3 5 7 11 13 17 19 23 29 '
+ '31 37 41 43 47 53 59 61 67 71 '
+ '73 79 83 89 97 101 103 107 109 113 '
+'127 131 137 139 149 151 157 163 167 173 '
+'179 181 191 193 197 199 211 223 227 229 '
+'233 239 241 251 257 263 269 271 277 281 '
+'283 293 307 311 313 317 ')
pp = [int(x) for x in ppp.split()]
xx = [False] * 1500000
def f(aa):
t = []
for p in pp:
if aa % p == 0:
while aa%p == 0:
aa = aa//p
t.append(p)
if aa == 1:
break
if aa != 1:
t.append(aa)
for tt in t:
for i in range(tt, 1500000, tt):
xx[i]=True
def main():
n = input()
a = [int(x) for x in input().split()]
b = []
for aa in a:
if xx[aa] == False:
b.append(aa)
f(aa)
else:
kk = aa + 1
while xx[kk] == True:
kk += 1
b.append(kk)
f(kk)
break
t = 2
while len(b) < len(a):
while xx[t] == True:
t+=1
b.append(t)
f(t)
print(' '.join(str(x) for x in b))
if __name__ == '__main__':
main()
``` | output | 1 | 4,783 | 22 | 9,567 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Mahmoud has an array a consisting of n integers. He asked Ehab to find another array b of the same length such that:
* b is lexicographically greater than or equal to a.
* bi ≥ 2.
* b is pairwise coprime: for every 1 ≤ i < j ≤ n, bi and bj are coprime, i. e. GCD(bi, bj) = 1, where GCD(w, z) is the greatest common divisor of w and z.
Ehab wants to choose a special array so he wants the lexicographically minimal array between all the variants. Can you find it?
An array x is lexicographically greater than an array y if there exists an index i such than xi > yi and xj = yj for all 1 ≤ j < i. An array x is equal to an array y if xi = yi for all 1 ≤ i ≤ n.
Input
The first line contains an integer n (1 ≤ n ≤ 105), the number of elements in a and b.
The second line contains n integers a1, a2, ..., an (2 ≤ ai ≤ 105), the elements of a.
Output
Output n space-separated integers, the i-th of them representing bi.
Examples
Input
5
2 3 5 4 13
Output
2 3 5 7 11
Input
3
10 3 7
Output
10 3 7
Note
Note that in the second sample, the array is already pairwise coprime so we printed it. | instruction | 0 | 4,784 | 22 | 9,568 |
Tags: constructive algorithms, greedy, math, number theory
Correct Solution:
```
m=2*10**6
prime=[0 for i in range(m)]
n=int(input())
arr=list(map(int,input().split()))
s=set(arr)
i=0
flag=0
for i in range(n):
jump =arr[i]
if prime[jump] ==1:
for k in range(jump,m):
if prime[k] ==0:
arr[i] = k
flag=1
break
s=set()
l=2
jump =arr[i]
while l*l <=arr[i]:
while jump %l ==0:
jump //=l
s.add(l)
l+=1
if jump >1:
s.add(jump)
for p in s:
for j in range(p,m,p):
prime[j] =1
if flag==1:
break
i+=1
for k in range(2,m):
if i ==n:
break
if prime[k] ==0:
arr[i] =k
for l in range(k,m,k):
prime[l] =1
i+=1
print(*arr)
``` | output | 1 | 4,784 | 22 | 9,569 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Mahmoud has an array a consisting of n integers. He asked Ehab to find another array b of the same length such that:
* b is lexicographically greater than or equal to a.
* bi ≥ 2.
* b is pairwise coprime: for every 1 ≤ i < j ≤ n, bi and bj are coprime, i. e. GCD(bi, bj) = 1, where GCD(w, z) is the greatest common divisor of w and z.
Ehab wants to choose a special array so he wants the lexicographically minimal array between all the variants. Can you find it?
An array x is lexicographically greater than an array y if there exists an index i such than xi > yi and xj = yj for all 1 ≤ j < i. An array x is equal to an array y if xi = yi for all 1 ≤ i ≤ n.
Input
The first line contains an integer n (1 ≤ n ≤ 105), the number of elements in a and b.
The second line contains n integers a1, a2, ..., an (2 ≤ ai ≤ 105), the elements of a.
Output
Output n space-separated integers, the i-th of them representing bi.
Examples
Input
5
2 3 5 4 13
Output
2 3 5 7 11
Input
3
10 3 7
Output
10 3 7
Note
Note that in the second sample, the array is already pairwise coprime so we printed it. | instruction | 0 | 4,785 | 22 | 9,570 |
Tags: constructive algorithms, greedy, math, number theory
Correct Solution:
```
# -*- coding: UTF-8 -*-
MAX_NUM = 2000000
prime_str = ('2 3 5 7 11 13 17 19 23 29 '
+ '31 37 41 43 47 53 59 61 67 71 '
+ '73 79 83 89 97 101 103 107 109 113 '
+ '127 131 137 139 149 151 157 163 167 173 '
+ '179 181 191 193 197 199 211 223 227 229 '
+ '233 239 241 251 257 263 269 271 277 281 '
+ '283 293 307 311 313 317 '
)
prime_list = [int(p) for p in prime_str.split()]
used = [False] * MAX_NUM
n = int(input())
a = list(map(int, input().split()))
def record(x):
t = []
for p in prime_list:
if x % p == 0:
while x % p == 0:
x = x // p
t.append(p)
if x == 1:
break
if x != 1:
t.append(x)
for ti in t:
for i in range(ti, MAX_NUM, ti):
used[i] = True
b = []
for ai in a:
if not used[ai]:
b.append(ai)
record(ai)
else:
tmp = ai + 1
while used[tmp]:
tmp += 1
b.append(tmp)
record(tmp)
break
tmp = 2
while len(b) < len(a):
while used[tmp]:
tmp += 1
b.append(tmp)
record(tmp)
print(' '.join(str(x) for x in b))
``` | output | 1 | 4,785 | 22 | 9,571 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Mahmoud has an array a consisting of n integers. He asked Ehab to find another array b of the same length such that:
* b is lexicographically greater than or equal to a.
* bi ≥ 2.
* b is pairwise coprime: for every 1 ≤ i < j ≤ n, bi and bj are coprime, i. e. GCD(bi, bj) = 1, where GCD(w, z) is the greatest common divisor of w and z.
Ehab wants to choose a special array so he wants the lexicographically minimal array between all the variants. Can you find it?
An array x is lexicographically greater than an array y if there exists an index i such than xi > yi and xj = yj for all 1 ≤ j < i. An array x is equal to an array y if xi = yi for all 1 ≤ i ≤ n.
Input
The first line contains an integer n (1 ≤ n ≤ 105), the number of elements in a and b.
The second line contains n integers a1, a2, ..., an (2 ≤ ai ≤ 105), the elements of a.
Output
Output n space-separated integers, the i-th of them representing bi.
Examples
Input
5
2 3 5 4 13
Output
2 3 5 7 11
Input
3
10 3 7
Output
10 3 7
Note
Note that in the second sample, the array is already pairwise coprime so we printed it. | instruction | 0 | 4,786 | 22 | 9,572 |
Tags: constructive algorithms, greedy, math, number theory
Correct Solution:
```
MAX_NUM = 2000000
prime_str = ('2 3 5 7 11 13 17 19 23 29 '
+ '31 37 41 43 47 53 59 61 67 71 '
+ '73 79 83 89 97 101 103 107 109 113 '
+ '127 131 137 139 149 151 157 163 167 173 '
+ '179 181 191 193 197 199 211 223 227 229 '
+ '233 239 241 251 257 263 269 271 277 281 '
+ '283 293 307 311 313 317 '
)
prime_list = [int(p) for p in prime_str.split()]
used = [False] * MAX_NUM
n = int(input())
a = list(map(int, input().split()))
def record(x):
t = []
for p in prime_list:
if x % p == 0:
while x % p == 0:
x = x // p
t.append(p)
if x == 1:
break
if x != 1:
t.append(x)
for ti in t:
for i in range(ti, MAX_NUM, ti):
used[i] = True
b = []
for ai in a:
if not used[ai]:
b.append(ai)
record(ai)
else:
temp = ai + 1
while used[temp]:
temp += 1
b.append(temp)
record(temp)
break
temp = 2
while len(b) < len(a):
while used[temp]:
temp += 1
b.append(temp)
record(temp)
print(' '.join(str(x) for x in b))
``` | output | 1 | 4,786 | 22 | 9,573 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Mahmoud has an array a consisting of n integers. He asked Ehab to find another array b of the same length such that:
* b is lexicographically greater than or equal to a.
* bi ≥ 2.
* b is pairwise coprime: for every 1 ≤ i < j ≤ n, bi and bj are coprime, i. e. GCD(bi, bj) = 1, where GCD(w, z) is the greatest common divisor of w and z.
Ehab wants to choose a special array so he wants the lexicographically minimal array between all the variants. Can you find it?
An array x is lexicographically greater than an array y if there exists an index i such than xi > yi and xj = yj for all 1 ≤ j < i. An array x is equal to an array y if xi = yi for all 1 ≤ i ≤ n.
Input
The first line contains an integer n (1 ≤ n ≤ 105), the number of elements in a and b.
The second line contains n integers a1, a2, ..., an (2 ≤ ai ≤ 105), the elements of a.
Output
Output n space-separated integers, the i-th of them representing bi.
Examples
Input
5
2 3 5 4 13
Output
2 3 5 7 11
Input
3
10 3 7
Output
10 3 7
Note
Note that in the second sample, the array is already pairwise coprime so we printed it. | instruction | 0 | 4,787 | 22 | 9,574 |
Tags: constructive algorithms, greedy, math, number theory
Correct Solution:
```
"""Codeforces P959D. Mahmoud and Ehab and another array construction task
(http://codeforces.com/problemset/problem/959/D)
Problem tags: constructive algorithms, greedy, number theory
Hint: Use sieve to keep the list of numbers which are coprime with every number
in the array. When a new elem is add to the array, the sieve is updated for
the prime factors of the new elem. The length of sieve should be larger than
n-th prime, which is 1,299,709 when n is 10^6. (This code uses 150000 for
the sieve size.)
Time Complexity: O(nlog^2(n))
"""
import atexit
import io
import sys
# Buffering IO
_INPUT_LINES = sys.stdin.read().splitlines()
input = iter(_INPUT_LINES).__next__
_OUTPUT_BUFFER = io.StringIO()
sys.stdout = _OUTPUT_BUFFER
@atexit.register
def write():
sys.__stdout__.write(_OUTPUT_BUFFER.getvalue())
def prime_list(n):
""" Returns a list of primes < n """
sieve = [True] * n
for i in range(3, int(n ** 0.5) + 1, 2):
if sieve[i]:
sieve[i*i::2*i] = [False] * ((n - i * i - 1) // (2 * i) + 1)
return [2] + [i for i in range(3, n, 2) if sieve[i]]
def prime_factors(n):
if (not hasattr(prime_factors, "primes") or
prime_factors.primes[-1] ** 2 < n):
prime_factors.primes = prime_list(max(5000, int(n ** 0.5) + 1))
res = []
for p in prime_factors.primes:
if p * p > n:
break
count = 0
while n % p == 0:
n //= p
count += 1
if count:
res.append((p, count))
if n == 1:
break
if n != 1:
res.append((n, 1))
return res
def update_available(n, available):
pf = prime_factors(n)
for p, _ in pf:
if available[p]:
available[p::p] = [False] * ((len(available) - 1) // p)
def main():
n = int(input())
a = [int(x) for x in input().split()]
b = []
available = [True] * 1500000
for a_num in a:
if available[a_num] == True:
b.append(a_num)
update_available(a_num, available)
else:
b_num = available.index(True, a_num)
b.append(b_num)
update_available(b_num, available)
break
b_num = 2
while len(b) < n:
b_num = available.index(True, b_num)
b.append(b_num)
update_available(b_num, available)
print(' '.join(str(x) for x in b))
if __name__ == '__main__':
main()
``` | output | 1 | 4,787 | 22 | 9,575 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Mahmoud has an array a consisting of n integers. He asked Ehab to find another array b of the same length such that:
* b is lexicographically greater than or equal to a.
* bi ≥ 2.
* b is pairwise coprime: for every 1 ≤ i < j ≤ n, bi and bj are coprime, i. e. GCD(bi, bj) = 1, where GCD(w, z) is the greatest common divisor of w and z.
Ehab wants to choose a special array so he wants the lexicographically minimal array between all the variants. Can you find it?
An array x is lexicographically greater than an array y if there exists an index i such than xi > yi and xj = yj for all 1 ≤ j < i. An array x is equal to an array y if xi = yi for all 1 ≤ i ≤ n.
Input
The first line contains an integer n (1 ≤ n ≤ 105), the number of elements in a and b.
The second line contains n integers a1, a2, ..., an (2 ≤ ai ≤ 105), the elements of a.
Output
Output n space-separated integers, the i-th of them representing bi.
Examples
Input
5
2 3 5 4 13
Output
2 3 5 7 11
Input
3
10 3 7
Output
10 3 7
Note
Note that in the second sample, the array is already pairwise coprime so we printed it.
Submitted Solution:
```
max_primes = 2*10**6
def get_primes(n):
""" Создание списка простых чисел меньших n
:param n: верхняя границаб до которой ищем простые числа
:return: отсортированный список простых чисе от 2 до n
"""
numbers = set(range(n, 1, -1))
primes = []
while numbers:
p = numbers.pop()
primes.append(p)
numbers.difference_update(set(range(p*2, n+1, p)))
primes_list = list(primes)
primes_list.sort()
return primes_list
def gcd (a,b):
if (b == 0):
return a
else:
return gcd (b, a % b)
def nextel(s):
for i in range(s,max_primes):
next_prime = primes[i]
for j in b:
if gcd(next_prime, j ) >1:
break
else:
return next_prime
primes = get_primes(max_primes)
n = int(input())
arr = list(map(int, input().split()))
b = [max(2, arr[0])]
bigger = b[0] > arr[0]
start = 0
for el in arr[1:]:
if bigger:
next_best = nextel(start)
b.append(next_best)
start += 1
else:
k = start
while True:
next_best = nextel(k)
if next_best >= el:
break
else:
k +=1
b.append(next_best)
bigger = next_best > el
# print(primes[:10])
print(*b)
``` | instruction | 0 | 4,788 | 22 | 9,576 |
No | output | 1 | 4,788 | 22 | 9,577 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Mahmoud has an array a consisting of n integers. He asked Ehab to find another array b of the same length such that:
* b is lexicographically greater than or equal to a.
* bi ≥ 2.
* b is pairwise coprime: for every 1 ≤ i < j ≤ n, bi and bj are coprime, i. e. GCD(bi, bj) = 1, where GCD(w, z) is the greatest common divisor of w and z.
Ehab wants to choose a special array so he wants the lexicographically minimal array between all the variants. Can you find it?
An array x is lexicographically greater than an array y if there exists an index i such than xi > yi and xj = yj for all 1 ≤ j < i. An array x is equal to an array y if xi = yi for all 1 ≤ i ≤ n.
Input
The first line contains an integer n (1 ≤ n ≤ 105), the number of elements in a and b.
The second line contains n integers a1, a2, ..., an (2 ≤ ai ≤ 105), the elements of a.
Output
Output n space-separated integers, the i-th of them representing bi.
Examples
Input
5
2 3 5 4 13
Output
2 3 5 7 11
Input
3
10 3 7
Output
10 3 7
Note
Note that in the second sample, the array is already pairwise coprime so we printed it.
Submitted Solution:
```
def IsPrime(n):
d = 2
while d * d <= n and n % d != 0:
d += 1
return d * d > n
prime = []
for i in range(100000):
if IsPrime(i):
prime.append(i)
prime.pop(0)
prime.pop(0)
def Factor(n):
Ans = []
d = 2
while d * d <= n:
if n % d == 0:
Ans.append(d)
n //= d
else:
d += 1
if n > 1:
Ans.append(n)
return Ans
ans = []
n = int(input())
s = input().split()
nums = []
for i in range(n):
nums.append(int(s[i]))
dels = []
delssprev = []
gi = 0
for i in nums:
dels += (Factor(i))
delss = set(dels)
if len(delss) < len(dels):
gi = i
break
delssprev = delss
ans.append(i)
for i in prime:
if i > gi and i not in delssprev:
ans.append(i)
delssprev.add(i)
break
ost = n - len(ans)
if delssprev:
for i in delssprev:
prime.pop(prime.index(i))
for i in range(ost):
ans.append(prime.pop(0))
sans = ''
for i in ans:
sans += str(i) + ' '
print(sans)
``` | instruction | 0 | 4,789 | 22 | 9,578 |
No | output | 1 | 4,789 | 22 | 9,579 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Mahmoud has an array a consisting of n integers. He asked Ehab to find another array b of the same length such that:
* b is lexicographically greater than or equal to a.
* bi ≥ 2.
* b is pairwise coprime: for every 1 ≤ i < j ≤ n, bi and bj are coprime, i. e. GCD(bi, bj) = 1, where GCD(w, z) is the greatest common divisor of w and z.
Ehab wants to choose a special array so he wants the lexicographically minimal array between all the variants. Can you find it?
An array x is lexicographically greater than an array y if there exists an index i such than xi > yi and xj = yj for all 1 ≤ j < i. An array x is equal to an array y if xi = yi for all 1 ≤ i ≤ n.
Input
The first line contains an integer n (1 ≤ n ≤ 105), the number of elements in a and b.
The second line contains n integers a1, a2, ..., an (2 ≤ ai ≤ 105), the elements of a.
Output
Output n space-separated integers, the i-th of them representing bi.
Examples
Input
5
2 3 5 4 13
Output
2 3 5 7 11
Input
3
10 3 7
Output
10 3 7
Note
Note that in the second sample, the array is already pairwise coprime so we printed it.
Submitted Solution:
```
def gcd(a,b):
if a>b:
a,b=b,a
if a==0:
return(b)
return(gcd(b%a,a))
n=int(input())
a=list(map(int,input().split()))
b=[str(a[0])]
g=a[0]
m=2
bol1=True
for i in range(1,n):
ai=a[i]
if bol1:
j=ai+1-ai%2
while gcd(g,j)!=1:
j+=2
else:
j=m
bol=True
while (j<ai and bol1) or gcd(g,j)!=1:
if j==2:
j=3
else:
j+=2
bol=bol and gcd(g,j)==1
if bol:
m=j
bol1=j==ai
b.append(str(j))
g*=j
print(' '.join(b))
``` | instruction | 0 | 4,790 | 22 | 9,580 |
No | output | 1 | 4,790 | 22 | 9,581 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Mahmoud has an array a consisting of n integers. He asked Ehab to find another array b of the same length such that:
* b is lexicographically greater than or equal to a.
* bi ≥ 2.
* b is pairwise coprime: for every 1 ≤ i < j ≤ n, bi and bj are coprime, i. e. GCD(bi, bj) = 1, where GCD(w, z) is the greatest common divisor of w and z.
Ehab wants to choose a special array so he wants the lexicographically minimal array between all the variants. Can you find it?
An array x is lexicographically greater than an array y if there exists an index i such than xi > yi and xj = yj for all 1 ≤ j < i. An array x is equal to an array y if xi = yi for all 1 ≤ i ≤ n.
Input
The first line contains an integer n (1 ≤ n ≤ 105), the number of elements in a and b.
The second line contains n integers a1, a2, ..., an (2 ≤ ai ≤ 105), the elements of a.
Output
Output n space-separated integers, the i-th of them representing bi.
Examples
Input
5
2 3 5 4 13
Output
2 3 5 7 11
Input
3
10 3 7
Output
10 3 7
Note
Note that in the second sample, the array is already pairwise coprime so we printed it.
Submitted Solution:
```
m = 300500
n = int(input())
b = map(int, input().split())
r = []
a = [0] * m
def gf(n):
d = 2
while d * d <= n:
f = 1
while n % d is 0:
if f:
yield d
f = 0
n //= d
d += 1
if n > 1:
yield n
def f(x):
r.append(x)
for y in gf(x):
for i in range(y, m, y):
a[i] = 1
for x in b:
if a[x]:
break
f(x)
if len(r) < n:
for i in range(x + 1, m):
if not a[i]:
f(i)
break
k = 2
for i in range(len(r), n):
for j in range(k, m):
if not a[j]:
f(j)
k = j + 1
break
print(*r)
``` | instruction | 0 | 4,791 | 22 | 9,582 |
No | output | 1 | 4,791 | 22 | 9,583 |
Provide a correct Python 3 solution for this coding contest problem.
Find \displaystyle{\sum_{a=1}^{K}\sum_{b=1}^{K}\sum_{c=1}^{K} \gcd(a,b,c)}.
Here \gcd(a,b,c) denotes the greatest common divisor of a, b, and c.
Constraints
* 1 \leq K \leq 200
* K is an integer.
Input
Input is given from Standard Input in the following format:
K
Output
Print the value of \displaystyle{\sum_{a=1}^{K}\sum_{b=1}^{K}\sum_{c=1}^{K} \gcd(a,b,c)}.
Examples
Input
2
Output
9
Input
200
Output
10813692 | instruction | 0 | 4,825 | 22 | 9,650 |
"Correct Solution:
```
import math
a = int(input())
b = 0
for i in range(1,a+1):
for j in range(1,a+1):
for k in range(1,a+1):
b+=math.gcd(math.gcd(i,j),k)
print(b)
``` | output | 1 | 4,825 | 22 | 9,651 |
Provide a correct Python 3 solution for this coding contest problem.
Find \displaystyle{\sum_{a=1}^{K}\sum_{b=1}^{K}\sum_{c=1}^{K} \gcd(a,b,c)}.
Here \gcd(a,b,c) denotes the greatest common divisor of a, b, and c.
Constraints
* 1 \leq K \leq 200
* K is an integer.
Input
Input is given from Standard Input in the following format:
K
Output
Print the value of \displaystyle{\sum_{a=1}^{K}\sum_{b=1}^{K}\sum_{c=1}^{K} \gcd(a,b,c)}.
Examples
Input
2
Output
9
Input
200
Output
10813692 | instruction | 0 | 4,826 | 22 | 9,652 |
"Correct Solution:
```
from math import gcd
r = range(1, int(input()) + 1)
print(sum(gcd(gcd(a, b), c) for a in r for b in r for c in r))
``` | output | 1 | 4,826 | 22 | 9,653 |
Provide a correct Python 3 solution for this coding contest problem.
Find \displaystyle{\sum_{a=1}^{K}\sum_{b=1}^{K}\sum_{c=1}^{K} \gcd(a,b,c)}.
Here \gcd(a,b,c) denotes the greatest common divisor of a, b, and c.
Constraints
* 1 \leq K \leq 200
* K is an integer.
Input
Input is given from Standard Input in the following format:
K
Output
Print the value of \displaystyle{\sum_{a=1}^{K}\sum_{b=1}^{K}\sum_{c=1}^{K} \gcd(a,b,c)}.
Examples
Input
2
Output
9
Input
200
Output
10813692 | instruction | 0 | 4,827 | 22 | 9,654 |
"Correct Solution:
```
import math
K = int(input())
ans = 0
for a in range(1,K+1):
for b in range(1,K+1):
for c in range(1,K+1):
ans += math.gcd(math.gcd(a,b),c)
print(ans)
``` | output | 1 | 4,827 | 22 | 9,655 |
Provide a correct Python 3 solution for this coding contest problem.
Find \displaystyle{\sum_{a=1}^{K}\sum_{b=1}^{K}\sum_{c=1}^{K} \gcd(a,b,c)}.
Here \gcd(a,b,c) denotes the greatest common divisor of a, b, and c.
Constraints
* 1 \leq K \leq 200
* K is an integer.
Input
Input is given from Standard Input in the following format:
K
Output
Print the value of \displaystyle{\sum_{a=1}^{K}\sum_{b=1}^{K}\sum_{c=1}^{K} \gcd(a,b,c)}.
Examples
Input
2
Output
9
Input
200
Output
10813692 | instruction | 0 | 4,828 | 22 | 9,656 |
"Correct Solution:
```
from math import gcd
n = int(input())
sum = 0
for i in range(1,n+1):
for j in range(1,n+1):
for k in range(1,n+1):
sum += gcd(gcd(i,j),k)
print(sum)
``` | output | 1 | 4,828 | 22 | 9,657 |
Provide a correct Python 3 solution for this coding contest problem.
Find \displaystyle{\sum_{a=1}^{K}\sum_{b=1}^{K}\sum_{c=1}^{K} \gcd(a,b,c)}.
Here \gcd(a,b,c) denotes the greatest common divisor of a, b, and c.
Constraints
* 1 \leq K \leq 200
* K is an integer.
Input
Input is given from Standard Input in the following format:
K
Output
Print the value of \displaystyle{\sum_{a=1}^{K}\sum_{b=1}^{K}\sum_{c=1}^{K} \gcd(a,b,c)}.
Examples
Input
2
Output
9
Input
200
Output
10813692 | instruction | 0 | 4,829 | 22 | 9,658 |
"Correct Solution:
```
from math import gcd
K = int(input())
print(sum(gcd(gcd(a, b), c) for c in range(1, K + 1) for b in range(1, K + 1) for a in range(1, K + 1)))
``` | output | 1 | 4,829 | 22 | 9,659 |
Provide a correct Python 3 solution for this coding contest problem.
Find \displaystyle{\sum_{a=1}^{K}\sum_{b=1}^{K}\sum_{c=1}^{K} \gcd(a,b,c)}.
Here \gcd(a,b,c) denotes the greatest common divisor of a, b, and c.
Constraints
* 1 \leq K \leq 200
* K is an integer.
Input
Input is given from Standard Input in the following format:
K
Output
Print the value of \displaystyle{\sum_{a=1}^{K}\sum_{b=1}^{K}\sum_{c=1}^{K} \gcd(a,b,c)}.
Examples
Input
2
Output
9
Input
200
Output
10813692 | instruction | 0 | 4,830 | 22 | 9,660 |
"Correct Solution:
```
from math import gcd
s=int(input())
a=0
for i in range(1,s+1):
for j in range(1,s+1):
for k in range(1,s+1):
a+=gcd(gcd(i,j),k)
print(a)
``` | output | 1 | 4,830 | 22 | 9,661 |
Provide a correct Python 3 solution for this coding contest problem.
Find \displaystyle{\sum_{a=1}^{K}\sum_{b=1}^{K}\sum_{c=1}^{K} \gcd(a,b,c)}.
Here \gcd(a,b,c) denotes the greatest common divisor of a, b, and c.
Constraints
* 1 \leq K \leq 200
* K is an integer.
Input
Input is given from Standard Input in the following format:
K
Output
Print the value of \displaystyle{\sum_{a=1}^{K}\sum_{b=1}^{K}\sum_{c=1}^{K} \gcd(a,b,c)}.
Examples
Input
2
Output
9
Input
200
Output
10813692 | instruction | 0 | 4,831 | 22 | 9,662 |
"Correct Solution:
```
n = int(input())
l = 0
import math
for a in range(1,n+1):
for b in range(1,n+1):
for c in range(1,n+1):
l+=math.gcd(a,math.gcd(b,c))
print(l)
``` | output | 1 | 4,831 | 22 | 9,663 |
Provide a correct Python 3 solution for this coding contest problem.
Find \displaystyle{\sum_{a=1}^{K}\sum_{b=1}^{K}\sum_{c=1}^{K} \gcd(a,b,c)}.
Here \gcd(a,b,c) denotes the greatest common divisor of a, b, and c.
Constraints
* 1 \leq K \leq 200
* K is an integer.
Input
Input is given from Standard Input in the following format:
K
Output
Print the value of \displaystyle{\sum_{a=1}^{K}\sum_{b=1}^{K}\sum_{c=1}^{K} \gcd(a,b,c)}.
Examples
Input
2
Output
9
Input
200
Output
10813692 | instruction | 0 | 4,832 | 22 | 9,664 |
"Correct Solution:
```
from math import gcd
a = 0
K = int(input())
for i in range(1, K+1):
for j in range(1, K+1):
for l in range(1, K+1):
a += gcd(i, gcd(j, l))
print(a)
``` | output | 1 | 4,832 | 22 | 9,665 |
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