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:
from math import ceil, sqrt

INF = 1000001

def sieve():
    primes = [True for i in range(INF)]

    primes[1] = False

    p = 2
    while p * p <= INF:

        if primes[p]:

            for i in range(p*p, INF, p):
                if primes[i]:
                    primes[i] = False

        p += 1

    return primes


def main():
    n = int(input())
    x = [int(i) for i in input().split()]

    primes = sieve()

    for i in x:
        sqr = sqrt(i)
        res = ceil(sqr)

        print("YES" if (sqr == res) and primes[res] else "NO")


if __name__ == "__main__":
    main()