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 math
import sys

MX = 10 ** 6
isprime = [1] * (MX + 5)
prime = []


def sieve():
    isprime[0] = isprime[1] = 0
    prime.append(2)
    i = 4
    while i <= MX:
        isprime[i] = 0
        i += 2
    i = 3
    while i * i <= MX:
        j = i * i
        while j <= MX:
            isprime[j] = 0
            j += 2 * i
        i += 2
    i = 3
    while i <= MX:
        if isprime[i] == 1:
            prime.append(i)
        i += 2


def main():
    sieve()
    n = int(input())
    s = set()
    for val in prime:
        s.add(val * val)
    a = list(map(int, input().split()))
    for val in a:
        if val in s:
            print("YES")
        else:
            print("NO")


if __name__ == '__main__':
    main()