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 |
|---|---|---|---|---|---|
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Some days ago, I learned the concept of LCM (least common multiple). I've played with it for several times and I want to make a big number with it.
But I also don't want to use many numbers, so I'll choose three positive integers (they don't have to be distinct) which are not greater than n. Can you help me to find the maximum possible least common multiple of these three integers?
Input
The first line contains an integer n (1 ≤ n ≤ 106) — the n mentioned in the statement.
Output
Print a single integer — the maximum possible LCM of three not necessarily distinct positive integers that are not greater than n.
Examples
Input
9
Output
504
Input
7
Output
210
Note
The least common multiple of some positive integers is the least positive integer which is multiple for each of them.
The result may become very large, 32-bit integer won't be enough. So using 64-bit integers is recommended.
For the last example, we can chose numbers 7, 6, 5 and the LCM of them is 7·6·5 = 210. It is the maximum value we can get.
Submitted Solution:
```
def main():
n = int(input())
print(n if n < 3 else ((n - 1) * (n * (n - 2) if n & 1 else (n - 3) * (n if n % 3 else n - 2))))
if __name__ == '__main__':
main()
``` | instruction | 0 | 72,797 | 22 | 145,594 |
Yes | output | 1 | 72,797 | 22 | 145,595 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Some days ago, I learned the concept of LCM (least common multiple). I've played with it for several times and I want to make a big number with it.
But I also don't want to use many numbers, so I'll choose three positive integers (they don't have to be distinct) which are not greater than n. Can you help me to find the maximum possible least common multiple of these three integers?
Input
The first line contains an integer n (1 ≤ n ≤ 106) — the n mentioned in the statement.
Output
Print a single integer — the maximum possible LCM of three not necessarily distinct positive integers that are not greater than n.
Examples
Input
9
Output
504
Input
7
Output
210
Note
The least common multiple of some positive integers is the least positive integer which is multiple for each of them.
The result may become very large, 32-bit integer won't be enough. So using 64-bit integers is recommended.
For the last example, we can chose numbers 7, 6, 5 and the LCM of them is 7·6·5 = 210. It is the maximum value we can get.
Submitted Solution:
```
n=int(input())
a=[1,2]
if n<=2:
print(a[n-1])
elif n&1:
print(n*(n-1)*(n-2))
else:
if n%3!=0:
print((n-3)*(n)*(n-1))
else:
print(((n-2)*(n-1)*(n-3)))
``` | instruction | 0 | 72,798 | 22 | 145,596 |
Yes | output | 1 | 72,798 | 22 | 145,597 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Some days ago, I learned the concept of LCM (least common multiple). I've played with it for several times and I want to make a big number with it.
But I also don't want to use many numbers, so I'll choose three positive integers (they don't have to be distinct) which are not greater than n. Can you help me to find the maximum possible least common multiple of these three integers?
Input
The first line contains an integer n (1 ≤ n ≤ 106) — the n mentioned in the statement.
Output
Print a single integer — the maximum possible LCM of three not necessarily distinct positive integers that are not greater than n.
Examples
Input
9
Output
504
Input
7
Output
210
Note
The least common multiple of some positive integers is the least positive integer which is multiple for each of them.
The result may become very large, 32-bit integer won't be enough. So using 64-bit integers is recommended.
For the last example, we can chose numbers 7, 6, 5 and the LCM of them is 7·6·5 = 210. It is the maximum value we can get.
Submitted Solution:
```
def SieveOfEratosthenes(n):
lst=list()
prime = [True for i in range(n+1)]
p = 2
while (p * p <= n):
# If prime[p] is not changed, then it is a prime
if (prime[p] == True):
# Update all multiples of p
for i in range(p * p, n+1, p):
prime[i] = False
p += 1
for p in range(2, n+1):
if prime[p]:
lst.append(p),
return lst
def gcd(a,b):
if a == 0:
return b
return gcd(b % a, a)
def lcm(a,b):
return (a / gcd(a,b))* b
n=int(input())
if n==1:
print(1)
elif n==2:
print(2)
elif n==3:
print(6)
else:
a = n-2
lst1=list()
x=SieveOfEratosthenes(a)
c=max(x)
for i in range(c,n-1):
c2=n*(n-1)
c1=lcm(c2, i)
lst1.append(c1)
print(int(max(lst1)))
``` | instruction | 0 | 72,799 | 22 | 145,598 |
No | output | 1 | 72,799 | 22 | 145,599 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Some days ago, I learned the concept of LCM (least common multiple). I've played with it for several times and I want to make a big number with it.
But I also don't want to use many numbers, so I'll choose three positive integers (they don't have to be distinct) which are not greater than n. Can you help me to find the maximum possible least common multiple of these three integers?
Input
The first line contains an integer n (1 ≤ n ≤ 106) — the n mentioned in the statement.
Output
Print a single integer — the maximum possible LCM of three not necessarily distinct positive integers that are not greater than n.
Examples
Input
9
Output
504
Input
7
Output
210
Note
The least common multiple of some positive integers is the least positive integer which is multiple for each of them.
The result may become very large, 32-bit integer won't be enough. So using 64-bit integers is recommended.
For the last example, we can chose numbers 7, 6, 5 and the LCM of them is 7·6·5 = 210. It is the maximum value we can get.
Submitted Solution:
```
n=int(input())
if n==1:
print(1)
exit(0)
if n==2:
print(2)
exit(0)
if n%2:
print(n*(n-1)*(n-2))
else:
x=((n*(n-1)*(n-2))//2)
y=((n-1)*(n-2)*(n-3))
print(max(x,y))
``` | instruction | 0 | 72,800 | 22 | 145,600 |
No | output | 1 | 72,800 | 22 | 145,601 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Some days ago, I learned the concept of LCM (least common multiple). I've played with it for several times and I want to make a big number with it.
But I also don't want to use many numbers, so I'll choose three positive integers (they don't have to be distinct) which are not greater than n. Can you help me to find the maximum possible least common multiple of these three integers?
Input
The first line contains an integer n (1 ≤ n ≤ 106) — the n mentioned in the statement.
Output
Print a single integer — the maximum possible LCM of three not necessarily distinct positive integers that are not greater than n.
Examples
Input
9
Output
504
Input
7
Output
210
Note
The least common multiple of some positive integers is the least positive integer which is multiple for each of them.
The result may become very large, 32-bit integer won't be enough. So using 64-bit integers is recommended.
For the last example, we can chose numbers 7, 6, 5 and the LCM of them is 7·6·5 = 210. It is the maximum value we can get.
Submitted Solution:
```
n = int(input())
lcm = n*(n-1)*(n-2)
if n >3:
print(lcm)
elif n ==1:
print('1')
else:
print('2')
``` | instruction | 0 | 72,801 | 22 | 145,602 |
No | output | 1 | 72,801 | 22 | 145,603 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Some days ago, I learned the concept of LCM (least common multiple). I've played with it for several times and I want to make a big number with it.
But I also don't want to use many numbers, so I'll choose three positive integers (they don't have to be distinct) which are not greater than n. Can you help me to find the maximum possible least common multiple of these three integers?
Input
The first line contains an integer n (1 ≤ n ≤ 106) — the n mentioned in the statement.
Output
Print a single integer — the maximum possible LCM of three not necessarily distinct positive integers that are not greater than n.
Examples
Input
9
Output
504
Input
7
Output
210
Note
The least common multiple of some positive integers is the least positive integer which is multiple for each of them.
The result may become very large, 32-bit integer won't be enough. So using 64-bit integers is recommended.
For the last example, we can chose numbers 7, 6, 5 and the LCM of them is 7·6·5 = 210. It is the maximum value we can get.
Submitted Solution:
```
if __name__ == '__main__':
n = int(input().strip())
if n == 1:
print(1)
elif n == 2:
print(2)
elif n == 3:
print(6)
else:
if n & 1:
print(n * (n - 1) * (n - 2))
else:
ma = 0
for i in range(max(0, n - 50), n - 2):
ma = max(ma, i * (i + 1) * (i + 2))
print(ma)
``` | instruction | 0 | 72,802 | 22 | 145,604 |
No | output | 1 | 72,802 | 22 | 145,605 |
Provide a correct Python 3 solution for this coding contest problem.
You are given N positive integers a_1, a_2, ..., a_N.
For a non-negative integer m, let f(m) = (m\ mod\ a_1) + (m\ mod\ a_2) + ... + (m\ mod\ a_N).
Here, X\ mod\ Y denotes the remainder of the division of X by Y.
Find the maximum value of f.
Constraints
* All values in input are integers.
* 2 \leq N \leq 3000
* 2 \leq a_i \leq 10^5
Input
Input is given from Standard Input in the following format:
N
a_1 a_2 ... a_N
Output
Print the maximum value of f.
Examples
Input
3
3 4 6
Output
10
Input
5
7 46 11 20 11
Output
90
Input
7
994 518 941 851 647 2 581
Output
4527 | instruction | 0 | 73,141 | 22 | 146,282 |
"Correct Solution:
```
N = int(input())
a = [int(n) for n in input().split()]
print(sum(a)-N)
``` | output | 1 | 73,141 | 22 | 146,283 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given N positive integers a_1, a_2, ..., a_N.
For a non-negative integer m, let f(m) = (m\ mod\ a_1) + (m\ mod\ a_2) + ... + (m\ mod\ a_N).
Here, X\ mod\ Y denotes the remainder of the division of X by Y.
Find the maximum value of f.
Constraints
* All values in input are integers.
* 2 \leq N \leq 3000
* 2 \leq a_i \leq 10^5
Input
Input is given from Standard Input in the following format:
N
a_1 a_2 ... a_N
Output
Print the maximum value of f.
Examples
Input
3
3 4 6
Output
10
Input
5
7 46 11 20 11
Output
90
Input
7
994 518 941 851 647 2 581
Output
4527
Submitted Solution:
```
def gcd(x,y):
x,y = max(x,y),min(x,y)
while(y>0):
x,y = y,x%y
print(x)
def lcm(a,b):
return(int(a*b/gcd(a,b)))
n = int(input())
a = list(map(int,input().split()))
least_common_multiple = 1
for i in range(n):
least_common_multiple = lcm(least_common_multiple,a[i])
ans = 0
for i in range(n):
ans += (least_common_multiple-1)%a[i]
print(ans)
``` | instruction | 0 | 73,149 | 22 | 146,298 |
No | output | 1 | 73,149 | 22 | 146,299 |
Provide a correct Python 3 solution for this coding contest problem.
D: The Diversity of Prime Factorization
Problem
Ebi-chan has the FACTORIZATION MACHINE, which can factorize natural numbers M (greater than 1) in O ($ \ log $ M) time! But unfortunately, the machine could display only digits and white spaces.
In general, we consider the factorization of M as p_1 ^ {e_1} \ times p_2 ^ {e_2} \ times ... \ times p_K ^ {e_K} where (1) i <j implies p_i <p_j and (2) p_i is prime. Now, she gives M to the machine, and the machine displays according to the following rules in ascending order with respect to i:
* If e_i = 1, then displays p_i,
* otherwise, displays p_i e_i.
For example, if she gives either `22` or` 2048`, then `2 11` is displayed. If either` 24` or `54`, then` 2 3 3`.
Okay, Ebi-chan has written down the output of the machine, but she notices that she has forgotten to write down the input! Now, your task is to count how many natural numbers result in a noted output. Note that Ebi-chan has mistaken writing and no input could result in the output.
The answer could be too large, so, you must output it modulo 10 ^ 9 + 7 (prime number).
Input
N
q_1 q_2 $ \ cdots $ q_N
In the first line, the number of the output of the machine is given. In the second line, the output of the machine is given.
Constraints
* 1 \ leq N \ leq 10 ^ 5
* 2 \ leq q_i \ leq 10 ^ 6 (1 \ leq i \ leq N)
Output
Print the number of the natural numbers that result in the given output of the machine.
Sample Input 1
3
2 3 3
Sample Output for Input 1
2
24 = 2 ^ 3 \ times 3 and 54 = 2 \ times 3 ^ 3 satisfy the condition.
Sample Input 2
3
2 3 4
Sample Output 2 for Input 2
1
Only 162 = 2 \ times 3 ^ 4 satisfies the condition. Note that 4 is not prime.
Sample Input 3
3
3 5 2
Sample Output for Input 3
1
Since 2 <3 <5, only 75 = 3 \ times 5 ^ 2 satisfies the condition.
Sample Input 4
1
Four
Sample Output for Input 4
0
Ebi-chan should have written down it more carefully.
Example
Input
3
2 3 3
Output
2 | instruction | 0 | 73,270 | 22 | 146,540 |
"Correct Solution:
```
from collections import defaultdict
MAX = 1000000
ROOT = 1000
MOD = 1000000007
is_prime = [True] * (MAX + 1)
is_prime[0] = is_prime[1] = False
for i in range(2, ROOT + 1):
if is_prime[i]:
for j in range(i * i, MAX + 1, i):
is_prime[j] = False
n = int(input())
qlst = list(map(int, input().split()))
total1 = 0#next is kisuu or sisuu
total2 = 1#next is kisuu only(pre is index)
last_prime = 0
dic = {}
dic[(last_prime, 0)] = total1
dic[(last_prime, 1)] = total2
for q in qlst:
new_dic = defaultdict(int)
for k, v in dic.items():
last_prime, t = k
if is_prime[q]:
if t == 0:
if last_prime < q:
new_dic[(q, 0)] = (new_dic[(q, 0)] + v) % MOD
new_dic[(last_prime, 1)] = (new_dic[(last_prime, 1)] + v) % MOD
else:
new_dic[(last_prime, 1)] = (new_dic[(last_prime, 1)] + v) % MOD
else:
if last_prime < q:
new_dic[(q, 0)] = (new_dic[(q, 0)] + v) % MOD
if not is_prime[q]:
if t == 0:
new_dic[(last_prime, 1)] = (new_dic[(last_prime, 1)] + v) % MOD
dic = new_dic
print(sum(dic.values()) % MOD)
``` | output | 1 | 73,270 | 22 | 146,541 |
Provide a correct Python 3 solution for this coding contest problem.
A prime number is a natural number which has exactly two distinct natural number divisors: 1 and itself. For example, the first four prime numbers are: 2, 3, 5 and 7.
Write a program which reads a list of N integers and prints the number of prime numbers in the list.
Constraints
1 ≤ N ≤ 10000
2 ≤ an element of the list ≤ 108
Input
The first line contains an integer N, the number of elements in the list.
N numbers are given in the following lines.
Output
Print the number of prime numbers in the given list.
Examples
Input
5
2
3
4
5
6
Output
3
Input
11
7
8
9
10
11
12
13
14
15
16
17
Output
4 | instruction | 0 | 73,271 | 22 | 146,542 |
"Correct Solution:
```
x = int(input())
count = 0
for i in range(0, x):
a = int(input())
for j in range ( 2, a ):
c = int(a)
if a % j == 0:
count += 1
break;
if j * j > c:
break;
print(x-count)
``` | output | 1 | 73,271 | 22 | 146,543 |
Provide a correct Python 3 solution for this coding contest problem.
A prime number is a natural number which has exactly two distinct natural number divisors: 1 and itself. For example, the first four prime numbers are: 2, 3, 5 and 7.
Write a program which reads a list of N integers and prints the number of prime numbers in the list.
Constraints
1 ≤ N ≤ 10000
2 ≤ an element of the list ≤ 108
Input
The first line contains an integer N, the number of elements in the list.
N numbers are given in the following lines.
Output
Print the number of prime numbers in the given list.
Examples
Input
5
2
3
4
5
6
Output
3
Input
11
7
8
9
10
11
12
13
14
15
16
17
Output
4 | instruction | 0 | 73,272 | 22 | 146,544 |
"Correct Solution:
```
n=int(input())
cnt=0
for i in range(n):
a=int(input())
ans=True
for j in range(2,int(a**0.5)+1):
if a%j==0:
ans=False
break
if ans:
cnt+=1
print(cnt)
``` | output | 1 | 73,272 | 22 | 146,545 |
Provide a correct Python 3 solution for this coding contest problem.
A prime number is a natural number which has exactly two distinct natural number divisors: 1 and itself. For example, the first four prime numbers are: 2, 3, 5 and 7.
Write a program which reads a list of N integers and prints the number of prime numbers in the list.
Constraints
1 ≤ N ≤ 10000
2 ≤ an element of the list ≤ 108
Input
The first line contains an integer N, the number of elements in the list.
N numbers are given in the following lines.
Output
Print the number of prime numbers in the given list.
Examples
Input
5
2
3
4
5
6
Output
3
Input
11
7
8
9
10
11
12
13
14
15
16
17
Output
4 | instruction | 0 | 73,273 | 22 | 146,546 |
"Correct Solution:
```
def is_prime(n):
for i in range(2, int(n ** 0.5) + 1):
if n % i == 0: return False
return True
count = 0
for i in range(int(input())):
if is_prime(int(input())) : count += 1
print(count)
``` | output | 1 | 73,273 | 22 | 146,547 |
Provide a correct Python 3 solution for this coding contest problem.
A prime number is a natural number which has exactly two distinct natural number divisors: 1 and itself. For example, the first four prime numbers are: 2, 3, 5 and 7.
Write a program which reads a list of N integers and prints the number of prime numbers in the list.
Constraints
1 ≤ N ≤ 10000
2 ≤ an element of the list ≤ 108
Input
The first line contains an integer N, the number of elements in the list.
N numbers are given in the following lines.
Output
Print the number of prime numbers in the given list.
Examples
Input
5
2
3
4
5
6
Output
3
Input
11
7
8
9
10
11
12
13
14
15
16
17
Output
4 | instruction | 0 | 73,274 | 22 | 146,548 |
"Correct Solution:
```
import math
def isPrime(n):
for i in range(2, int(math.sqrt(n))+1):
if n % i == 0:
return False
return True
N = int(input())
nums = [int(input()) for i in range(N)]
print(sum([isPrime(n) for n in nums]))
``` | output | 1 | 73,274 | 22 | 146,549 |
Provide a correct Python 3 solution for this coding contest problem.
A prime number is a natural number which has exactly two distinct natural number divisors: 1 and itself. For example, the first four prime numbers are: 2, 3, 5 and 7.
Write a program which reads a list of N integers and prints the number of prime numbers in the list.
Constraints
1 ≤ N ≤ 10000
2 ≤ an element of the list ≤ 108
Input
The first line contains an integer N, the number of elements in the list.
N numbers are given in the following lines.
Output
Print the number of prime numbers in the given list.
Examples
Input
5
2
3
4
5
6
Output
3
Input
11
7
8
9
10
11
12
13
14
15
16
17
Output
4 | instruction | 0 | 73,275 | 22 | 146,550 |
"Correct Solution:
```
import math
def is_prime(a):
for i in range(2,int(math.sqrt(a))+1):
if a%i==0:
return False
return True
n = int(input())
cnt = 0
for i in range(n):
x = int(input())
if is_prime(x):
cnt+=1
print(cnt)
``` | output | 1 | 73,275 | 22 | 146,551 |
Provide a correct Python 3 solution for this coding contest problem.
A prime number is a natural number which has exactly two distinct natural number divisors: 1 and itself. For example, the first four prime numbers are: 2, 3, 5 and 7.
Write a program which reads a list of N integers and prints the number of prime numbers in the list.
Constraints
1 ≤ N ≤ 10000
2 ≤ an element of the list ≤ 108
Input
The first line contains an integer N, the number of elements in the list.
N numbers are given in the following lines.
Output
Print the number of prime numbers in the given list.
Examples
Input
5
2
3
4
5
6
Output
3
Input
11
7
8
9
10
11
12
13
14
15
16
17
Output
4 | instruction | 0 | 73,276 | 22 | 146,552 |
"Correct Solution:
```
import math
primenum =int(input())
ans = 0
for p in range(primenum):
targ = int(input())
for t in range(2,math.floor(math.sqrt(targ)) + 1):
if targ % t == 0:
break
else:
ans += 1
print(ans)
``` | output | 1 | 73,276 | 22 | 146,553 |
Provide a correct Python 3 solution for this coding contest problem.
A prime number is a natural number which has exactly two distinct natural number divisors: 1 and itself. For example, the first four prime numbers are: 2, 3, 5 and 7.
Write a program which reads a list of N integers and prints the number of prime numbers in the list.
Constraints
1 ≤ N ≤ 10000
2 ≤ an element of the list ≤ 108
Input
The first line contains an integer N, the number of elements in the list.
N numbers are given in the following lines.
Output
Print the number of prime numbers in the given list.
Examples
Input
5
2
3
4
5
6
Output
3
Input
11
7
8
9
10
11
12
13
14
15
16
17
Output
4 | instruction | 0 | 73,277 | 22 | 146,554 |
"Correct Solution:
```
import math
x = 0
a = int(input())
for _ in range(a):
n = int(input())
if n == 1:
x = x + 1
continue
for i in range(2,int(math.sqrt(n))+1):
if n % i == 0:
x = x + 1
break
print(a-x)
``` | output | 1 | 73,277 | 22 | 146,555 |
Provide a correct Python 3 solution for this coding contest problem.
A prime number is a natural number which has exactly two distinct natural number divisors: 1 and itself. For example, the first four prime numbers are: 2, 3, 5 and 7.
Write a program which reads a list of N integers and prints the number of prime numbers in the list.
Constraints
1 ≤ N ≤ 10000
2 ≤ an element of the list ≤ 108
Input
The first line contains an integer N, the number of elements in the list.
N numbers are given in the following lines.
Output
Print the number of prime numbers in the given list.
Examples
Input
5
2
3
4
5
6
Output
3
Input
11
7
8
9
10
11
12
13
14
15
16
17
Output
4 | instruction | 0 | 73,278 | 22 | 146,556 |
"Correct Solution:
```
import math
def S(N) :
for i in range(2, int(math.sqrt(N))+1) :
if N % i == 0 :
return 'F'
return 'T'
n = int(input())
ans = 0
for j in range(n) :
a = int(input())
if S(a) == 'T' :
ans += 1
print(ans)
``` | output | 1 | 73,278 | 22 | 146,557 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
A prime number is a natural number which has exactly two distinct natural number divisors: 1 and itself. For example, the first four prime numbers are: 2, 3, 5 and 7.
Write a program which reads a list of N integers and prints the number of prime numbers in the list.
Constraints
1 ≤ N ≤ 10000
2 ≤ an element of the list ≤ 108
Input
The first line contains an integer N, the number of elements in the list.
N numbers are given in the following lines.
Output
Print the number of prime numbers in the given list.
Examples
Input
5
2
3
4
5
6
Output
3
Input
11
7
8
9
10
11
12
13
14
15
16
17
Output
4
Submitted Solution:
```
from sys import stdin
n = int(input())
xs = [int(input()) for _ in range(n)]
ans = 0
for x in xs:
flg = True
for y in range(2, int(x**0.5+1)):
if x % y == 0:
flg = False
break
if flg:
ans += 1
print(ans)
``` | instruction | 0 | 73,279 | 22 | 146,558 |
Yes | output | 1 | 73,279 | 22 | 146,559 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
A prime number is a natural number which has exactly two distinct natural number divisors: 1 and itself. For example, the first four prime numbers are: 2, 3, 5 and 7.
Write a program which reads a list of N integers and prints the number of prime numbers in the list.
Constraints
1 ≤ N ≤ 10000
2 ≤ an element of the list ≤ 108
Input
The first line contains an integer N, the number of elements in the list.
N numbers are given in the following lines.
Output
Print the number of prime numbers in the given list.
Examples
Input
5
2
3
4
5
6
Output
3
Input
11
7
8
9
10
11
12
13
14
15
16
17
Output
4
Submitted Solution:
```
def is_prime(num):
for i in range(2, int(num ** 0.5) + 1):
if num % i == 0:
return False
return True
n = int(input())
nums = [int(input()) for _ in range(n)]
print(sum(map(is_prime, nums)))
``` | instruction | 0 | 73,280 | 22 | 146,560 |
Yes | output | 1 | 73,280 | 22 | 146,561 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
A prime number is a natural number which has exactly two distinct natural number divisors: 1 and itself. For example, the first four prime numbers are: 2, 3, 5 and 7.
Write a program which reads a list of N integers and prints the number of prime numbers in the list.
Constraints
1 ≤ N ≤ 10000
2 ≤ an element of the list ≤ 108
Input
The first line contains an integer N, the number of elements in the list.
N numbers are given in the following lines.
Output
Print the number of prime numbers in the given list.
Examples
Input
5
2
3
4
5
6
Output
3
Input
11
7
8
9
10
11
12
13
14
15
16
17
Output
4
Submitted Solution:
```
from math import sqrt
s = int(input())
ct = 0
for i in range(s):
ok = 1
x = int(input())
for z in range(2, int(sqrt(x))+1):
if x % z == 0:
ok = 0
break
ct += ok
print(ct)
``` | instruction | 0 | 73,281 | 22 | 146,562 |
Yes | output | 1 | 73,281 | 22 | 146,563 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
A prime number is a natural number which has exactly two distinct natural number divisors: 1 and itself. For example, the first four prime numbers are: 2, 3, 5 and 7.
Write a program which reads a list of N integers and prints the number of prime numbers in the list.
Constraints
1 ≤ N ≤ 10000
2 ≤ an element of the list ≤ 108
Input
The first line contains an integer N, the number of elements in the list.
N numbers are given in the following lines.
Output
Print the number of prime numbers in the given list.
Examples
Input
5
2
3
4
5
6
Output
3
Input
11
7
8
9
10
11
12
13
14
15
16
17
Output
4
Submitted Solution:
```
from math import sqrt
n = int(input())
ans = 0
for i in range(n):
x = int(input())
ok = 1
for z in range(2, int(sqrt(x))+1):
if x % z == 0:
ok = 0
break;
ans += ok
print(ans)
``` | instruction | 0 | 73,282 | 22 | 146,564 |
Yes | output | 1 | 73,282 | 22 | 146,565 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
A prime number is a natural number which has exactly two distinct natural number divisors: 1 and itself. For example, the first four prime numbers are: 2, 3, 5 and 7.
Write a program which reads a list of N integers and prints the number of prime numbers in the list.
Constraints
1 ≤ N ≤ 10000
2 ≤ an element of the list ≤ 108
Input
The first line contains an integer N, the number of elements in the list.
N numbers are given in the following lines.
Output
Print the number of prime numbers in the given list.
Examples
Input
5
2
3
4
5
6
Output
3
Input
11
7
8
9
10
11
12
13
14
15
16
17
Output
4
Submitted Solution:
```
n = int(input())
def Is_prime(n):
if n % 2 == 0:
return False
i = 3
while i < int(n ** (0.5))+ 1:
if n % i == 0:
return False
return True
count = 0
for j in range(0,n):
if Is_prime(n):
count += 1
``` | instruction | 0 | 73,283 | 22 | 146,566 |
No | output | 1 | 73,283 | 22 | 146,567 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
A prime number is a natural number which has exactly two distinct natural number divisors: 1 and itself. For example, the first four prime numbers are: 2, 3, 5 and 7.
Write a program which reads a list of N integers and prints the number of prime numbers in the list.
Constraints
1 ≤ N ≤ 10000
2 ≤ an element of the list ≤ 108
Input
The first line contains an integer N, the number of elements in the list.
N numbers are given in the following lines.
Output
Print the number of prime numbers in the given list.
Examples
Input
5
2
3
4
5
6
Output
3
Input
11
7
8
9
10
11
12
13
14
15
16
17
Output
4
Submitted Solution:
```
for i in range(0, N):
j = A[i] - 2
if j == 0 or j == 1:
counter += 1
else:
while j > 1:
if A[i] % j == 0:
break
else:
j -= 1
else:
counter += 1
``` | instruction | 0 | 73,284 | 22 | 146,568 |
No | output | 1 | 73,284 | 22 | 146,569 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
A prime number is a natural number which has exactly two distinct natural number divisors: 1 and itself. For example, the first four prime numbers are: 2, 3, 5 and 7.
Write a program which reads a list of N integers and prints the number of prime numbers in the list.
Constraints
1 ≤ N ≤ 10000
2 ≤ an element of the list ≤ 108
Input
The first line contains an integer N, the number of elements in the list.
N numbers are given in the following lines.
Output
Print the number of prime numbers in the given list.
Examples
Input
5
2
3
4
5
6
Output
3
Input
11
7
8
9
10
11
12
13
14
15
16
17
Output
4
Submitted Solution:
```
from math import ceil, sqrt
def f(n):
if n == 2:
return 1
if n % 2 == 0:
return 0
for i in range(3, ceil(sqrt(n)), 2):
if pred(n, i):
return 0
else:
return 1
def g(n):
d = {}
for _ in range(n):
i = int(input())
if not (i in d):
d[i] = f(i)
yield d[i]
n = int(input())
print(sum(g(n)))
``` | instruction | 0 | 73,285 | 22 | 146,570 |
No | output | 1 | 73,285 | 22 | 146,571 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
A prime number is a natural number which has exactly two distinct natural number divisors: 1 and itself. For example, the first four prime numbers are: 2, 3, 5 and 7.
Write a program which reads a list of N integers and prints the number of prime numbers in the list.
Constraints
1 ≤ N ≤ 10000
2 ≤ an element of the list ≤ 108
Input
The first line contains an integer N, the number of elements in the list.
N numbers are given in the following lines.
Output
Print the number of prime numbers in the given list.
Examples
Input
5
2
3
4
5
6
Output
3
Input
11
7
8
9
10
11
12
13
14
15
16
17
Output
4
Submitted Solution:
```
c = 0
def is_prime(n):
b = list(range(2, int(n**1/2)+1))
for i in b:
if not(n % i):
return False
return True
for _ in range(int(input())):
if is_prime(int(input())):
c += 1
print(c)
``` | instruction | 0 | 73,286 | 22 | 146,572 |
No | output | 1 | 73,286 | 22 | 146,573 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You're given an integer n. For every integer i from 2 to n, assign a positive integer a_i such that the following conditions hold:
* For any pair of integers (i,j), if i and j are coprime, a_i ≠ a_j.
* The maximal value of all a_i should be minimized (that is, as small as possible).
A pair of integers is called [coprime](https://en.wikipedia.org/wiki/Coprime_integers) if their [greatest common divisor](https://en.wikipedia.org/wiki/Greatest_common_divisor) is 1.
Input
The only line contains the integer n (2 ≤ n ≤ 10^5).
Output
Print n-1 integers, a_2, a_3, …, a_n (1 ≤ a_i ≤ n).
If there are multiple solutions, print any of them.
Examples
Input
4
Output
1 2 1
Input
3
Output
2 1
Note
In the first example, notice that 3 and 4 are coprime, so a_3 ≠ a_4. Also, notice that a=[1,2,3] satisfies the first condition, but it's not a correct answer because its maximal value is 3. | instruction | 0 | 73,390 | 22 | 146,780 |
Tags: constructive algorithms, number theory
Correct Solution:
```
#imgur.com/Pkt7iIf.png
#n, m = map(int, input().split())
#n = int(input())
#d = list(map(int, input().split()))
def sieve(n):
res = []
prime = [True for i in range(n+1)]
p = 2
while (p * p <= n):
if (prime[p] == True):
for i in range(p * 2, n+1, p):
prime[i] = False
p += 1
for p in range(2, n):
if prime[p]: res.append(p)
return res
n = int(input())
primes = sieve(n+1)
primes.reverse()
r = [0]*(n+1)
color = 1
while len(primes) > 0:
a = primes.pop()
t = a
while a < n+1:
if r[a] == 0:
r[a] = color
a += t
color +=1
[print(i, end = ' ') for i in r[2:]]
``` | output | 1 | 73,390 | 22 | 146,781 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You're given an integer n. For every integer i from 2 to n, assign a positive integer a_i such that the following conditions hold:
* For any pair of integers (i,j), if i and j are coprime, a_i ≠ a_j.
* The maximal value of all a_i should be minimized (that is, as small as possible).
A pair of integers is called [coprime](https://en.wikipedia.org/wiki/Coprime_integers) if their [greatest common divisor](https://en.wikipedia.org/wiki/Greatest_common_divisor) is 1.
Input
The only line contains the integer n (2 ≤ n ≤ 10^5).
Output
Print n-1 integers, a_2, a_3, …, a_n (1 ≤ a_i ≤ n).
If there are multiple solutions, print any of them.
Examples
Input
4
Output
1 2 1
Input
3
Output
2 1
Note
In the first example, notice that 3 and 4 are coprime, so a_3 ≠ a_4. Also, notice that a=[1,2,3] satisfies the first condition, but it's not a correct answer because its maximal value is 3. | instruction | 0 | 73,391 | 22 | 146,782 |
Tags: constructive algorithms, number theory
Correct Solution:
```
#!/usr/bin/env python
import os
import operator
import sys
import bisect
import _operator
from _collections import defaultdict
from io import BytesIO, IOBase
def inar():
return [int(k) for k in input().split()]
def power(x, p,m):
res = 1
while p:
if p & 1:
res = (res * x) % m
x = (x * x) % m
p >>= 1
return res
def main():
#mod=1000000007
# for _ in range(int(input())):
# #n=int(input())
# st=input()
# dic=defaultdict(int)
# n=len(st)
# for i in range(len(st)):
# dic[st[i]]+=1
# ans=n-max(dic.values())
# for i in range(0,10):
# for j in range(0,10):
# ok = True
# count = 0
# for k in range(n):
# if ok:
# if st[k]==str(i):
# count+=1
# ok=False
# else:
# if st[k]==str(j):
# count+=1
# ok=True
# if count%2!=0:
# count-=1
# #print(count)
# ans=min(ans,n-count)
# print(ans)
# n=int(input())
# arr=inar()
# sm1=0
# sm2=0
# for i in range(n):
# sm1+=arr[i]
# for i in range(n,2*n):
# sm2+=arr[i]
# if sm1!=sm2:
# print(*arr)
# else:
# counter=0
# for i in range(n):
# if arr[i]!=arr[2*n-i-1]:
# temp=arr[i]
# arr[i]=arr[2*n-i-1]
# arr[2*n-i-1]=temp
# counter=1
# break
# if counter:
# print(*arr)
# else:
# print(-1)
# n=int(input())
# arr=inar()
# odd=0
# even=0
# for i in range(n):
# if arr[i]%2==0:
# even+=1
# else:
# odd+=1
# if odd>0 and even>0:
# arr.sort()
# print(*arr)
# else:
# print(*arr)
#
n = int(input())
primes=[1]*(n+1)
ans=[0]*(n+1)
for i in range(2,int(n**0.5)+1):
if primes[i]==1:
for j in range(i*i,n+1,i):
if primes[j]==1:
primes[j]=0
k=1
for i in range(2,int(n**0.5)+1):
if ans[i]==0:
ans[i]=k
k+=1
for j in range(i*i,n+1,i):
if ans[j]==0:
ans[j]=ans[i]
for i in range(2,n+1):
if ans[i]==0:
ans[i]=k
k+=1
print(*ans[2:n+1])
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()
``` | output | 1 | 73,391 | 22 | 146,783 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You're given an integer n. For every integer i from 2 to n, assign a positive integer a_i such that the following conditions hold:
* For any pair of integers (i,j), if i and j are coprime, a_i ≠ a_j.
* The maximal value of all a_i should be minimized (that is, as small as possible).
A pair of integers is called [coprime](https://en.wikipedia.org/wiki/Coprime_integers) if their [greatest common divisor](https://en.wikipedia.org/wiki/Greatest_common_divisor) is 1.
Input
The only line contains the integer n (2 ≤ n ≤ 10^5).
Output
Print n-1 integers, a_2, a_3, …, a_n (1 ≤ a_i ≤ n).
If there are multiple solutions, print any of them.
Examples
Input
4
Output
1 2 1
Input
3
Output
2 1
Note
In the first example, notice that 3 and 4 are coprime, so a_3 ≠ a_4. Also, notice that a=[1,2,3] satisfies the first condition, but it's not a correct answer because its maximal value is 3. | instruction | 0 | 73,392 | 22 | 146,784 |
Tags: constructive algorithms, number theory
Correct Solution:
```
n=int(input())
def pr(x):
for i in range(2, x):
if x % i == 0:
return False
else:
return True
z=1
l=[0]*(n-1)
# q=list(filter(lambda x: (pr(x)==True) , range(2,n+1)))
# print(q)
for i in range(2,n+1):#list(filter(lambda x: (pr(x)) , range(2,n+1))):
if(l[i-2]>0):
continue
else:
f=1
while(i*f<=n):
if(l[i*f-2]==0):
l[i*f-2]=z
f+=1
z+=1
print(*l)
``` | output | 1 | 73,392 | 22 | 146,785 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You're given an integer n. For every integer i from 2 to n, assign a positive integer a_i such that the following conditions hold:
* For any pair of integers (i,j), if i and j are coprime, a_i ≠ a_j.
* The maximal value of all a_i should be minimized (that is, as small as possible).
A pair of integers is called [coprime](https://en.wikipedia.org/wiki/Coprime_integers) if their [greatest common divisor](https://en.wikipedia.org/wiki/Greatest_common_divisor) is 1.
Input
The only line contains the integer n (2 ≤ n ≤ 10^5).
Output
Print n-1 integers, a_2, a_3, …, a_n (1 ≤ a_i ≤ n).
If there are multiple solutions, print any of them.
Examples
Input
4
Output
1 2 1
Input
3
Output
2 1
Note
In the first example, notice that 3 and 4 are coprime, so a_3 ≠ a_4. Also, notice that a=[1,2,3] satisfies the first condition, but it's not a correct answer because its maximal value is 3. | instruction | 0 | 73,393 | 22 | 146,786 |
Tags: constructive algorithms, number theory
Correct Solution:
```
n=int(input())
s=[-1]*n
ind=1
cu=1
while ind<n:
if s[ind]==-1:
s[ind::ind+1]=len(s[ind::ind+1])*[cu]
cu+=1
ind+=1
for i in s[1:]:
print(i,end=" ")
print()
``` | output | 1 | 73,393 | 22 | 146,787 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You're given an integer n. For every integer i from 2 to n, assign a positive integer a_i such that the following conditions hold:
* For any pair of integers (i,j), if i and j are coprime, a_i ≠ a_j.
* The maximal value of all a_i should be minimized (that is, as small as possible).
A pair of integers is called [coprime](https://en.wikipedia.org/wiki/Coprime_integers) if their [greatest common divisor](https://en.wikipedia.org/wiki/Greatest_common_divisor) is 1.
Input
The only line contains the integer n (2 ≤ n ≤ 10^5).
Output
Print n-1 integers, a_2, a_3, …, a_n (1 ≤ a_i ≤ n).
If there are multiple solutions, print any of them.
Examples
Input
4
Output
1 2 1
Input
3
Output
2 1
Note
In the first example, notice that 3 and 4 are coprime, so a_3 ≠ a_4. Also, notice that a=[1,2,3] satisfies the first condition, but it's not a correct answer because its maximal value is 3. | instruction | 0 | 73,394 | 22 | 146,788 |
Tags: constructive algorithms, number theory
Correct Solution:
```
from math import *
n=int(input())
ar=[0,0]
k=1
for i in range(1,n+1):
ar.append(0)
for i in range(2,n+1,1):
if ar[i]==0:
for j in range(i,n+1,i):
ar[j]=k
k=k+1
for i in range(2,n+1):
print(ar[i],end=" ")
``` | output | 1 | 73,394 | 22 | 146,789 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You're given an integer n. For every integer i from 2 to n, assign a positive integer a_i such that the following conditions hold:
* For any pair of integers (i,j), if i and j are coprime, a_i ≠ a_j.
* The maximal value of all a_i should be minimized (that is, as small as possible).
A pair of integers is called [coprime](https://en.wikipedia.org/wiki/Coprime_integers) if their [greatest common divisor](https://en.wikipedia.org/wiki/Greatest_common_divisor) is 1.
Input
The only line contains the integer n (2 ≤ n ≤ 10^5).
Output
Print n-1 integers, a_2, a_3, …, a_n (1 ≤ a_i ≤ n).
If there are multiple solutions, print any of them.
Examples
Input
4
Output
1 2 1
Input
3
Output
2 1
Note
In the first example, notice that 3 and 4 are coprime, so a_3 ≠ a_4. Also, notice that a=[1,2,3] satisfies the first condition, but it's not a correct answer because its maximal value is 3. | instruction | 0 | 73,395 | 22 | 146,790 |
Tags: constructive algorithms, number theory
Correct Solution:
```
n = int(input())
cont = 1
lista = [0]*(n-1)
for i in range(2, n+1):
mudou = False
for j in range(i, n+1, i):
if lista[j-2] == 0:
lista[j-2] = cont
mudou = True
if mudou:
cont += 1
for e in lista:
print(e, end=" ")
``` | output | 1 | 73,395 | 22 | 146,791 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You're given an integer n. For every integer i from 2 to n, assign a positive integer a_i such that the following conditions hold:
* For any pair of integers (i,j), if i and j are coprime, a_i ≠ a_j.
* The maximal value of all a_i should be minimized (that is, as small as possible).
A pair of integers is called [coprime](https://en.wikipedia.org/wiki/Coprime_integers) if their [greatest common divisor](https://en.wikipedia.org/wiki/Greatest_common_divisor) is 1.
Input
The only line contains the integer n (2 ≤ n ≤ 10^5).
Output
Print n-1 integers, a_2, a_3, …, a_n (1 ≤ a_i ≤ n).
If there are multiple solutions, print any of them.
Examples
Input
4
Output
1 2 1
Input
3
Output
2 1
Note
In the first example, notice that 3 and 4 are coprime, so a_3 ≠ a_4. Also, notice that a=[1,2,3] satisfies the first condition, but it's not a correct answer because its maximal value is 3. | instruction | 0 | 73,396 | 22 | 146,792 |
Tags: constructive algorithms, number theory
Correct Solution:
```
prime = [-1 for i in range(100005)]
p = 2
avail = 1
while (p * p <= 100005):
if (prime[p] == -1):
for i in range(p, 100005, p):
if prime[i] == -1:
prime[i] = avail
avail += 1
p += 1
#print(avail)
for i in range(2, 100005):
if prime[i] == -1:
#print(i, "id unmakred")
prime[i] = avail
avail += 1
n = int(input())
print(*prime[2 : n + 1])
``` | output | 1 | 73,396 | 22 | 146,793 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You're given an integer n. For every integer i from 2 to n, assign a positive integer a_i such that the following conditions hold:
* For any pair of integers (i,j), if i and j are coprime, a_i ≠ a_j.
* The maximal value of all a_i should be minimized (that is, as small as possible).
A pair of integers is called [coprime](https://en.wikipedia.org/wiki/Coprime_integers) if their [greatest common divisor](https://en.wikipedia.org/wiki/Greatest_common_divisor) is 1.
Input
The only line contains the integer n (2 ≤ n ≤ 10^5).
Output
Print n-1 integers, a_2, a_3, …, a_n (1 ≤ a_i ≤ n).
If there are multiple solutions, print any of them.
Examples
Input
4
Output
1 2 1
Input
3
Output
2 1
Note
In the first example, notice that 3 and 4 are coprime, so a_3 ≠ a_4. Also, notice that a=[1,2,3] satisfies the first condition, but it's not a correct answer because its maximal value is 3. | instruction | 0 | 73,397 | 22 | 146,794 |
Tags: constructive algorithms, number theory
Correct Solution:
```
import math
def main():
n = int(input())
d = [0, 0, 1, 2]
m = 2
for i in range(4, n + 1):
f = False
for j in range(2, int(math.sqrt(i)) + 1):
if i % j == 0:
d.append(d[j])
f = True
break
if f is False:
m += 1
d.append(m)
for di in d[2: n + 1]:
print(di, end=" ")
if __name__ == "__main__":
main()
``` | output | 1 | 73,397 | 22 | 146,795 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You're given an integer n. For every integer i from 2 to n, assign a positive integer a_i such that the following conditions hold:
* For any pair of integers (i,j), if i and j are coprime, a_i ≠ a_j.
* The maximal value of all a_i should be minimized (that is, as small as possible).
A pair of integers is called [coprime](https://en.wikipedia.org/wiki/Coprime_integers) if their [greatest common divisor](https://en.wikipedia.org/wiki/Greatest_common_divisor) is 1.
Input
The only line contains the integer n (2 ≤ n ≤ 10^5).
Output
Print n-1 integers, a_2, a_3, …, a_n (1 ≤ a_i ≤ n).
If there are multiple solutions, print any of them.
Examples
Input
4
Output
1 2 1
Input
3
Output
2 1
Note
In the first example, notice that 3 and 4 are coprime, so a_3 ≠ a_4. Also, notice that a=[1,2,3] satisfies the first condition, but it's not a correct answer because its maximal value is 3.
Submitted Solution:
```
from sys import stdin,stdout
from itertools import combinations
from collections import defaultdict,OrderedDict
import math
import heapq
def listIn():
return list((map(int,stdin.readline().strip().split())))
def stringListIn():
return([x for x in stdin.readline().split()])
def intIn():
return (int(stdin.readline()))
def stringIn():
return (stdin.readline().strip())
def primes(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 isPrime(n) :
if (n <= 1) :
return False
if (n <= 3) :
return True
if (n % 2 == 0 or n % 3 == 0) :
return False
i = 5
while(i * i <= n) :
if (n % i == 0 or n % (i + 2) == 0) :
return False
i = i + 6
return True
def leastPrimeFactor(n) :
least_prime = [0] * (n + 1)
least_prime[1] = 1
for i in range(2, n + 1) :
if (least_prime[i] == 0) :
least_prime[i] = i
for j in range(2 * i, n + 1, i) :
if (least_prime[j] == 0) :
least_prime[j] = i
return least_prime
if __name__=="__main__":
n=intIn()
A=leastPrimeFactor(n)
prime_n=sorted(set(A[2:]))
#print(prime_n)
di={}
c=1
for ele in prime_n:
di[ele]=c
c+=1
#print(di)
ans=[0]*(n+1)
for i in range(2,n+1):
ans[i]=di[A[i]]
print(*ans[2:])
``` | instruction | 0 | 73,398 | 22 | 146,796 |
Yes | output | 1 | 73,398 | 22 | 146,797 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You're given an integer n. For every integer i from 2 to n, assign a positive integer a_i such that the following conditions hold:
* For any pair of integers (i,j), if i and j are coprime, a_i ≠ a_j.
* The maximal value of all a_i should be minimized (that is, as small as possible).
A pair of integers is called [coprime](https://en.wikipedia.org/wiki/Coprime_integers) if their [greatest common divisor](https://en.wikipedia.org/wiki/Greatest_common_divisor) is 1.
Input
The only line contains the integer n (2 ≤ n ≤ 10^5).
Output
Print n-1 integers, a_2, a_3, …, a_n (1 ≤ a_i ≤ n).
If there are multiple solutions, print any of them.
Examples
Input
4
Output
1 2 1
Input
3
Output
2 1
Note
In the first example, notice that 3 and 4 are coprime, so a_3 ≠ a_4. Also, notice that a=[1,2,3] satisfies the first condition, but it's not a correct answer because its maximal value is 3.
Submitted Solution:
```
n=(int)(input())
l=[0]*(n+1)
m=1
for i in range(2,n+1):
if l[i]==0:
for j in range(i,n+1,i):
l[j]=m
m+=1
print(*l[2::])
``` | instruction | 0 | 73,399 | 22 | 146,798 |
Yes | output | 1 | 73,399 | 22 | 146,799 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You're given an integer n. For every integer i from 2 to n, assign a positive integer a_i such that the following conditions hold:
* For any pair of integers (i,j), if i and j are coprime, a_i ≠ a_j.
* The maximal value of all a_i should be minimized (that is, as small as possible).
A pair of integers is called [coprime](https://en.wikipedia.org/wiki/Coprime_integers) if their [greatest common divisor](https://en.wikipedia.org/wiki/Greatest_common_divisor) is 1.
Input
The only line contains the integer n (2 ≤ n ≤ 10^5).
Output
Print n-1 integers, a_2, a_3, …, a_n (1 ≤ a_i ≤ n).
If there are multiple solutions, print any of them.
Examples
Input
4
Output
1 2 1
Input
3
Output
2 1
Note
In the first example, notice that 3 and 4 are coprime, so a_3 ≠ a_4. Also, notice that a=[1,2,3] satisfies the first condition, but it's not a correct answer because its maximal value is 3.
Submitted Solution:
```
N = int(input())
M = [0]*100010
c = 0
for i in range(2,N+1):
if M[i] == 0:
c+=1
M[i] = c
for j in range(i,N+1,i):
M[j] = c
for i in range(2,N+1):
print(M[i], end=" ")
print()
``` | instruction | 0 | 73,400 | 22 | 146,800 |
Yes | output | 1 | 73,400 | 22 | 146,801 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You're given an integer n. For every integer i from 2 to n, assign a positive integer a_i such that the following conditions hold:
* For any pair of integers (i,j), if i and j are coprime, a_i ≠ a_j.
* The maximal value of all a_i should be minimized (that is, as small as possible).
A pair of integers is called [coprime](https://en.wikipedia.org/wiki/Coprime_integers) if their [greatest common divisor](https://en.wikipedia.org/wiki/Greatest_common_divisor) is 1.
Input
The only line contains the integer n (2 ≤ n ≤ 10^5).
Output
Print n-1 integers, a_2, a_3, …, a_n (1 ≤ a_i ≤ n).
If there are multiple solutions, print any of them.
Examples
Input
4
Output
1 2 1
Input
3
Output
2 1
Note
In the first example, notice that 3 and 4 are coprime, so a_3 ≠ a_4. Also, notice that a=[1,2,3] satisfies the first condition, but it's not a correct answer because its maximal value is 3.
Submitted Solution:
```
def mindel(n):
if n % 2 == 0:
return 2
d = 3
while d * d <= n and n % d != 0:
d += 2
return d
if __name__ == "__main__":
n = int(input())
data = [1]*(n-1)
isPrime = [1]*(n-1)
i = 2
while i**2 <= n:
if isPrime[i-2]:
j = i**2
while j <= n:
isPrime[j-2] = 0
j += i
i += 1
curc = 1
for i in range(2, n+1):
if isPrime[i-2]:
data[i-2] = curc
curc += 1
else:
data[i-2] = data[mindel(i)-2]
for i in data:
print(i, end=' ')
``` | instruction | 0 | 73,401 | 22 | 146,802 |
Yes | output | 1 | 73,401 | 22 | 146,803 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You're given an integer n. For every integer i from 2 to n, assign a positive integer a_i such that the following conditions hold:
* For any pair of integers (i,j), if i and j are coprime, a_i ≠ a_j.
* The maximal value of all a_i should be minimized (that is, as small as possible).
A pair of integers is called [coprime](https://en.wikipedia.org/wiki/Coprime_integers) if their [greatest common divisor](https://en.wikipedia.org/wiki/Greatest_common_divisor) is 1.
Input
The only line contains the integer n (2 ≤ n ≤ 10^5).
Output
Print n-1 integers, a_2, a_3, …, a_n (1 ≤ a_i ≤ n).
If there are multiple solutions, print any of them.
Examples
Input
4
Output
1 2 1
Input
3
Output
2 1
Note
In the first example, notice that 3 and 4 are coprime, so a_3 ≠ a_4. Also, notice that a=[1,2,3] satisfies the first condition, but it's not a correct answer because its maximal value is 3.
Submitted Solution:
```
from math import *
from collections import Counter,defaultdict,deque
from sys import stdin, stdout
input = stdin.readline
I=lambda:int(input())
M =lambda:map(int,input().split())
LI=lambda:list(map(int,input().split()))
for _ in range(1):
n=I()
for i in range(n-1):
if i%2==0:print(1,end=" ")
else:print(2,end=" ")
``` | instruction | 0 | 73,402 | 22 | 146,804 |
No | output | 1 | 73,402 | 22 | 146,805 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You're given an integer n. For every integer i from 2 to n, assign a positive integer a_i such that the following conditions hold:
* For any pair of integers (i,j), if i and j are coprime, a_i ≠ a_j.
* The maximal value of all a_i should be minimized (that is, as small as possible).
A pair of integers is called [coprime](https://en.wikipedia.org/wiki/Coprime_integers) if their [greatest common divisor](https://en.wikipedia.org/wiki/Greatest_common_divisor) is 1.
Input
The only line contains the integer n (2 ≤ n ≤ 10^5).
Output
Print n-1 integers, a_2, a_3, …, a_n (1 ≤ a_i ≤ n).
If there are multiple solutions, print any of them.
Examples
Input
4
Output
1 2 1
Input
3
Output
2 1
Note
In the first example, notice that 3 and 4 are coprime, so a_3 ≠ a_4. Also, notice that a=[1,2,3] satisfies the first condition, but it's not a correct answer because its maximal value is 3.
Submitted Solution:
```
from math import ceil
def is_prime(num):
sq = ceil(num ** (1/2))
for i in range(2,sq+1):
if num % i == 0:
return False
return True
n = int(input())
counter = 1
for i in range(2, n+1):
if is_prime(i):
counter += 1
print(counter, end=' ')
elif i % 2 == 0:
print(1, end=' ')
else:
print(2, end=' ')
``` | instruction | 0 | 73,403 | 22 | 146,806 |
No | output | 1 | 73,403 | 22 | 146,807 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You're given an integer n. For every integer i from 2 to n, assign a positive integer a_i such that the following conditions hold:
* For any pair of integers (i,j), if i and j are coprime, a_i ≠ a_j.
* The maximal value of all a_i should be minimized (that is, as small as possible).
A pair of integers is called [coprime](https://en.wikipedia.org/wiki/Coprime_integers) if their [greatest common divisor](https://en.wikipedia.org/wiki/Greatest_common_divisor) is 1.
Input
The only line contains the integer n (2 ≤ n ≤ 10^5).
Output
Print n-1 integers, a_2, a_3, …, a_n (1 ≤ a_i ≤ n).
If there are multiple solutions, print any of them.
Examples
Input
4
Output
1 2 1
Input
3
Output
2 1
Note
In the first example, notice that 3 and 4 are coprime, so a_3 ≠ a_4. Also, notice that a=[1,2,3] satisfies the first condition, but it's not a correct answer because its maximal value is 3.
Submitted Solution:
```
def generate(n):
'''prime=[True for i in range(n+1)]
p=2
while(p*p<=n):
if(prime[p]==True):
for j in range(p*p,n+1,p):
prime[j]=False
p=p+1
i1=1
for k in range(2,n+1):
if(prime[k]==True):
print(i1,end=' ')
i1=i1+1
else:
print(1,end=' ')'''
j=2
for i in range(2,n+1):
if(i%2==1):
print(j,end=' ')
j=j+1
else:
print(1,end=' ')
print()
t=int(input())
generate(t)
``` | instruction | 0 | 73,404 | 22 | 146,808 |
No | output | 1 | 73,404 | 22 | 146,809 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You're given an integer n. For every integer i from 2 to n, assign a positive integer a_i such that the following conditions hold:
* For any pair of integers (i,j), if i and j are coprime, a_i ≠ a_j.
* The maximal value of all a_i should be minimized (that is, as small as possible).
A pair of integers is called [coprime](https://en.wikipedia.org/wiki/Coprime_integers) if their [greatest common divisor](https://en.wikipedia.org/wiki/Greatest_common_divisor) is 1.
Input
The only line contains the integer n (2 ≤ n ≤ 10^5).
Output
Print n-1 integers, a_2, a_3, …, a_n (1 ≤ a_i ≤ n).
If there are multiple solutions, print any of them.
Examples
Input
4
Output
1 2 1
Input
3
Output
2 1
Note
In the first example, notice that 3 and 4 are coprime, so a_3 ≠ a_4. Also, notice that a=[1,2,3] satisfies the first condition, but it's not a correct answer because its maximal value is 3.
Submitted Solution:
```
n=int(input())
ll=[]
for i in range(n-1):
ll.append(1)
print(*ll)
``` | instruction | 0 | 73,405 | 22 | 146,810 |
No | output | 1 | 73,405 | 22 | 146,811 |
Provide a correct Python 3 solution for this coding contest problem.
Given are positive integers A and B.
Let us choose some number of positive common divisors of A and B.
Here, any two of the chosen divisors must be coprime.
At most, how many divisors can we choose?
Definition of common divisor
An integer d is said to be a common divisor of integers x and y when d divides both x and y.
Definition of being coprime
Integers x and y are said to be coprime when x and y have no positive common divisors other than 1.
Definition of dividing
An integer x is said to divide another integer y when there exists an integer \alpha such that y = \alpha x.
Constraints
* All values in input are integers.
* 1 \leq A, B \leq 10^{12}
Input
Input is given from Standard Input in the following format:
A B
Output
Print the maximum number of divisors that can be chosen to satisfy the condition.
Examples
Input
12 18
Output
3
Input
420 660
Output
4
Input
1 2019
Output
1 | instruction | 0 | 73,976 | 22 | 147,952 |
"Correct Solution:
```
def GCD(a, b):
while b:
a, b = b, a % b
return a
a, b = map(int, input().split())
n = GCD(a,b)
i = 2
table = []
while i * i <= n:
while n % i == 0:
n = n // i
table.append(i)
i += 1
if n > 1:
table.append(n)
print(len(set(table))+1)
``` | output | 1 | 73,976 | 22 | 147,953 |
Provide a correct Python 3 solution for this coding contest problem.
Given are positive integers A and B.
Let us choose some number of positive common divisors of A and B.
Here, any two of the chosen divisors must be coprime.
At most, how many divisors can we choose?
Definition of common divisor
An integer d is said to be a common divisor of integers x and y when d divides both x and y.
Definition of being coprime
Integers x and y are said to be coprime when x and y have no positive common divisors other than 1.
Definition of dividing
An integer x is said to divide another integer y when there exists an integer \alpha such that y = \alpha x.
Constraints
* All values in input are integers.
* 1 \leq A, B \leq 10^{12}
Input
Input is given from Standard Input in the following format:
A B
Output
Print the maximum number of divisors that can be chosen to satisfy the condition.
Examples
Input
12 18
Output
3
Input
420 660
Output
4
Input
1 2019
Output
1 | instruction | 0 | 73,977 | 22 | 147,954 |
"Correct Solution:
```
a,b=map(int,input().split())
from fractions import *
g=gcd(a,b)
c=i=1
while g>1 and i*i<=g:
i+=1
if g%i==0:
c+=1
while g%i==0:
g//=i
print(c+(g>1))
``` | output | 1 | 73,977 | 22 | 147,955 |
Provide a correct Python 3 solution for this coding contest problem.
Given are positive integers A and B.
Let us choose some number of positive common divisors of A and B.
Here, any two of the chosen divisors must be coprime.
At most, how many divisors can we choose?
Definition of common divisor
An integer d is said to be a common divisor of integers x and y when d divides both x and y.
Definition of being coprime
Integers x and y are said to be coprime when x and y have no positive common divisors other than 1.
Definition of dividing
An integer x is said to divide another integer y when there exists an integer \alpha such that y = \alpha x.
Constraints
* All values in input are integers.
* 1 \leq A, B \leq 10^{12}
Input
Input is given from Standard Input in the following format:
A B
Output
Print the maximum number of divisors that can be chosen to satisfy the condition.
Examples
Input
12 18
Output
3
Input
420 660
Output
4
Input
1 2019
Output
1 | instruction | 0 | 73,978 | 22 | 147,956 |
"Correct Solution:
```
import fractions
A, B = map(int, input().split())
GCD = fractions.gcd(A, B)
k = 1
cnt = 1
while GCD > 1:
k += 1
if k ** 2 > GCD:
cnt += 1
break
if GCD % k:
continue
cnt += 1
while GCD % k == 0:
GCD //= k
print(cnt)
``` | output | 1 | 73,978 | 22 | 147,957 |
Provide a correct Python 3 solution for this coding contest problem.
Given are positive integers A and B.
Let us choose some number of positive common divisors of A and B.
Here, any two of the chosen divisors must be coprime.
At most, how many divisors can we choose?
Definition of common divisor
An integer d is said to be a common divisor of integers x and y when d divides both x and y.
Definition of being coprime
Integers x and y are said to be coprime when x and y have no positive common divisors other than 1.
Definition of dividing
An integer x is said to divide another integer y when there exists an integer \alpha such that y = \alpha x.
Constraints
* All values in input are integers.
* 1 \leq A, B \leq 10^{12}
Input
Input is given from Standard Input in the following format:
A B
Output
Print the maximum number of divisors that can be chosen to satisfy the condition.
Examples
Input
12 18
Output
3
Input
420 660
Output
4
Input
1 2019
Output
1 | instruction | 0 | 73,979 | 22 | 147,958 |
"Correct Solution:
```
import fractions
A,B=map(int,input().split())
A,B=min(A,B),max(A,B)
g=fractions.gcd(A,B)
ans=1
for i in range(2,int(g**0.5+1)):
if g%i==0:
ans+=1
while g%i==0:
g/=i
if g==1:
break
if g!=1:
ans+=1
print(ans)
``` | output | 1 | 73,979 | 22 | 147,959 |
Provide a correct Python 3 solution for this coding contest problem.
Given are positive integers A and B.
Let us choose some number of positive common divisors of A and B.
Here, any two of the chosen divisors must be coprime.
At most, how many divisors can we choose?
Definition of common divisor
An integer d is said to be a common divisor of integers x and y when d divides both x and y.
Definition of being coprime
Integers x and y are said to be coprime when x and y have no positive common divisors other than 1.
Definition of dividing
An integer x is said to divide another integer y when there exists an integer \alpha such that y = \alpha x.
Constraints
* All values in input are integers.
* 1 \leq A, B \leq 10^{12}
Input
Input is given from Standard Input in the following format:
A B
Output
Print the maximum number of divisors that can be chosen to satisfy the condition.
Examples
Input
12 18
Output
3
Input
420 660
Output
4
Input
1 2019
Output
1 | instruction | 0 | 73,980 | 22 | 147,960 |
"Correct Solution:
```
import fractions
a, b= (int(i) for i in input().split())
m=fractions.gcd(a,b)
pf={}
for i in range(2,int(m**0.5)+1):
while m%i==0:
pf[i]=pf.get(i,0)+1
m//=i
if m > 1:
pf[m]=1
print(len(pf)+1)
``` | output | 1 | 73,980 | 22 | 147,961 |
Provide a correct Python 3 solution for this coding contest problem.
Given are positive integers A and B.
Let us choose some number of positive common divisors of A and B.
Here, any two of the chosen divisors must be coprime.
At most, how many divisors can we choose?
Definition of common divisor
An integer d is said to be a common divisor of integers x and y when d divides both x and y.
Definition of being coprime
Integers x and y are said to be coprime when x and y have no positive common divisors other than 1.
Definition of dividing
An integer x is said to divide another integer y when there exists an integer \alpha such that y = \alpha x.
Constraints
* All values in input are integers.
* 1 \leq A, B \leq 10^{12}
Input
Input is given from Standard Input in the following format:
A B
Output
Print the maximum number of divisors that can be chosen to satisfy the condition.
Examples
Input
12 18
Output
3
Input
420 660
Output
4
Input
1 2019
Output
1 | instruction | 0 | 73,981 | 22 | 147,962 |
"Correct Solution:
```
import fractions
a, b = map(int, input().split())
x = fractions.gcd(a, b)
t = x
i = 2
ans = 1;
while i * i <= t:
if x % i == 0:
while x % i == 0:
x /= i
ans += 1
i += 1
if x != 1:
ans += 1
print(ans)
``` | output | 1 | 73,981 | 22 | 147,963 |
Provide a correct Python 3 solution for this coding contest problem.
Given are positive integers A and B.
Let us choose some number of positive common divisors of A and B.
Here, any two of the chosen divisors must be coprime.
At most, how many divisors can we choose?
Definition of common divisor
An integer d is said to be a common divisor of integers x and y when d divides both x and y.
Definition of being coprime
Integers x and y are said to be coprime when x and y have no positive common divisors other than 1.
Definition of dividing
An integer x is said to divide another integer y when there exists an integer \alpha such that y = \alpha x.
Constraints
* All values in input are integers.
* 1 \leq A, B \leq 10^{12}
Input
Input is given from Standard Input in the following format:
A B
Output
Print the maximum number of divisors that can be chosen to satisfy the condition.
Examples
Input
12 18
Output
3
Input
420 660
Output
4
Input
1 2019
Output
1 | instruction | 0 | 73,982 | 22 | 147,964 |
"Correct Solution:
```
from math import *
g = gcd(*map(int,input().split()))
D = {}
n = 2
while n*n<=g:
if g%n:
n+=1
else:
g//=n
D[n]=D.get(n,0)+1
if 1<g:
D[g]=D.get(g,0)+1
print(len(D)+1)
``` | output | 1 | 73,982 | 22 | 147,965 |
Provide a correct Python 3 solution for this coding contest problem.
Given are positive integers A and B.
Let us choose some number of positive common divisors of A and B.
Here, any two of the chosen divisors must be coprime.
At most, how many divisors can we choose?
Definition of common divisor
An integer d is said to be a common divisor of integers x and y when d divides both x and y.
Definition of being coprime
Integers x and y are said to be coprime when x and y have no positive common divisors other than 1.
Definition of dividing
An integer x is said to divide another integer y when there exists an integer \alpha such that y = \alpha x.
Constraints
* All values in input are integers.
* 1 \leq A, B \leq 10^{12}
Input
Input is given from Standard Input in the following format:
A B
Output
Print the maximum number of divisors that can be chosen to satisfy the condition.
Examples
Input
12 18
Output
3
Input
420 660
Output
4
Input
1 2019
Output
1 | instruction | 0 | 73,983 | 22 | 147,966 |
"Correct Solution:
```
a,b = (int(i) for i in input().split())
def gcd(a,b):
if a%b: return gcd(b,a%b)
else: return b
g = gcd(a,b)
num,ans = g,1
for i in range(2,int(g**0.5)+1):
if num%i==0:
ans+=1
while num%i==0: num//=i
if num!=1: ans+=1
print(ans)
``` | output | 1 | 73,983 | 22 | 147,967 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Given are positive integers A and B.
Let us choose some number of positive common divisors of A and B.
Here, any two of the chosen divisors must be coprime.
At most, how many divisors can we choose?
Definition of common divisor
An integer d is said to be a common divisor of integers x and y when d divides both x and y.
Definition of being coprime
Integers x and y are said to be coprime when x and y have no positive common divisors other than 1.
Definition of dividing
An integer x is said to divide another integer y when there exists an integer \alpha such that y = \alpha x.
Constraints
* All values in input are integers.
* 1 \leq A, B \leq 10^{12}
Input
Input is given from Standard Input in the following format:
A B
Output
Print the maximum number of divisors that can be chosen to satisfy the condition.
Examples
Input
12 18
Output
3
Input
420 660
Output
4
Input
1 2019
Output
1
Submitted Solution:
```
from fractions import gcd
A, B = map(int, input().split())
C = gcd(A, B)
ans = 1
i = 2
for i in range(2, int(-(-C**0.5//1))+1):
if C % i == 0:
ans += 1
while C % i == 0:
C //= i
i += 1
if C != 1:
ans += 1
print(ans)
``` | instruction | 0 | 73,984 | 22 | 147,968 |
Yes | output | 1 | 73,984 | 22 | 147,969 |
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