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 atexit
import io
import sys
import bisect

_I_B = sys.stdin.read().splitlines()
input = iter(_I_B).__next__
_O_B = io.StringIO()
sys.stdout = _O_B

@atexit.register
def write():
    sys.__stdout__.write(_O_B.getvalue())


def main():
    n = int(10**6)
    t = list(range(3, n + 1, 2))
    isPrime, i, v = [2], 0, 3
    ls = len(t)
    while v < n:
        if t[i]:
            isPrime.append(t[i])
            j = i + v
            while j < ls:
                t[j] = 0
                j += v
        i += 1
        v = 2 * i + 3
    input()
    for i in map(int,input().split()):
        root=i**0.5
        idx=bisect.bisect_right(isPrime,root)
        # print(idx,len(isPrime))
        if ((idx!=0) and isPrime[idx-1]==root) or (idx==0 and isPrime[idx]==root):
            print('YES')
        else:
            print('NO')

if __name__=='__main__':
    main()