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:
#!/usr/bin/env python3
import os
from io import BytesIO

input = BytesIO(os.read(0, os.fstat(0).st_size)).readline


def check(x):
    if x == 1:
        return False
    if (x == 4) or (x == 9):
        return True

    n = int(x**0.5)
    if (n * n != x) or (n & 1 == 0) or (n % 3 == 0):
        return False

    cnt, sqrt_n = 5, int(n**0.5)
    while cnt <= sqrt_n:
        if n % cnt == 0:
            return False
        cnt += 2 if cnt % 3 == 2 else 4

    return True


def main():
    input()
    os.write(1, '\n'.join('YES' if check(xi) else 'NO' for xi in map(int, input().split())).encode())


if __name__ == '__main__':
    main()