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:
# @author Matheus Alves dos Santos

import math

def get_primes(upper_limit):
    

    primes = [True] * (upper_limit + 1)
    size = int(math.ceil(math.sqrt(len(primes))))
    primes[0], primes[1] = False, False

    for i in range(2, size):
        if (primes[i]):
            for j in range(2 * i, len(primes), i):
                primes[j] = False
    
    return primes

primes = get_primes(1000000)
n_values = int(input())
values = map(int, input().split())

for v in values:
    sqrt_v = math.sqrt(v)
    answer = primes[int(sqrt_v)] if (sqrt_v % 1 == 0) else False    

    print("YES") if answer else print("NO")