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 python
from math import sqrt

def get_prime_list(n):
    n = int(n)
    prime_list = []
    prime_mark = [False, False] + [True for _ in range(n - 1)]
    for base in range(2, n + 1):
        if prime_mark[base]: 
            prime_list.append(base)
        for prime in prime_list:
            composite = prime * base
            if composite > n:
                break
            prime_mark[composite] = False 
    return prime_mark
    #return prime_list
input()
numbers = input().split()
primes = get_prime_list(10**6)
ans = []
for x in numbers:
    x = int(x)
    sq = int(sqrt(x))
    if x == sq ** 2 and primes[sq]:
        ans.append("YES")
    else:
        ans.append("NO")
print('\n'.join(ans))