Problem: We know that prime numbers are positive integers that have exactly two distinct positive divisors. Similarly, we'll call a positive integer t Т-prime, if t has exactly three distinct positive divisors.

You are given an array of n positive integers. For each of them determine whether it is Т-prime or not.

Input

The first line contains a single positive integer, n (1 ≤ n ≤ 105), showing how many numbers are in the array. The next line contains n space-separated integers xi (1 ≤ xi ≤ 1012).

Please, do not use the %lld specifier to read or write 64-bit integers in С++. It is advised to use the cin, cout streams or the %I64d specifier.

Output

Print n lines: the i-th line should contain "YES" (without the quotes), if number xi is Т-prime, and "NO" (without the quotes), if it isn't.

Examples

Input

3
4 5 6


Output

YES
NO
NO

Note

The given test has three numbers. The first number 4 has exactly three divisors — 1, 2 and 4, thus the answer for this number is "YES". The second number 5 has two divisors (1 and 5), and the third number 6 has four divisors (1, 2, 3, 6), hence the answer for them is "NO".

Solution (in PYTHON3):

Solution:

import sys
from math import sqrt

def write_to_stdout(res):
    answer = '\n'.join(res)
    sys.stdout.write('%s\n' % (answer))

def read_input():
    l = input().rstrip().split()
    values = input().rstrip().split()
    return [int(i) for i in values]

def get_primes_set():
    N = 1000000
    mask = [1]*N
    for i in range(2, N):
        if mask[i]:
            for j in range(i*i, N, i):
                mask[j] = 0
    res = []
    for k in range(2, len(mask)):
        if mask[k]:
            res.append(k)
    return set(res)
    
    
def is_t_prime(n, primes):
    n_sqrt = sqrt(n)
    if n_sqrt != int(n_sqrt) or n == 1:
        return False
    if n_sqrt in primes:
        return True
    return False

def get_answer(values, primes):
    ans = []
    for val in values:
        if is_t_prime(val, primes):
            ans.append('YES')
        else:
            ans.append('NO')
    return ans
     
def main():
    values = read_input()
    #values = [4, 25, 9, 49, 121, 169, 0, 1, 2, 3]

    primes = get_primes_set()
    answer = get_answer(values, primes)
    write_to_stdout(answer)


    
    
if __name__ == '__main__':
    main()