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

def primes(n):
    lista = [False, False]

    for i in range(2, n+1):
        lista.append(True)
    
    sqrt = math.sqrt(n)
    p = 2
    while(p<=sqrt):
        if (lista[p]):
            for k in range(pow(p,2), n+1, p):
                lista[k] = False            

        p += 1
    return lista

primes = primes(1000000)

n = int(input())
numbers = [int(x) for x in input().split()]
 
for i in numbers:
    sqrt = math.sqrt(i)
    res = "NO"
    if (sqrt).is_integer():
        if primes[int(sqrt)]:
            res = "YES"
    print(res)