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 t_primo(num, tabela_primos):
    raiz = int(math.sqrt(num))
    if raiz * raiz == num and tabela_primos[raiz] == True:
        return "YES"
    return "NO"

def encontra_primos():
    maximo = 1000001 
    tabela_primos = [True] * maximo
    tabela_primos[1] = False

    for i in range(2, maximo):
        if tabela_primos[i] == True:
            j = i * i
            if j > maximo:
                break
            while j < maximo:
                tabela_primos[j] = False
                j += i
    return tabela_primos

tabela_primos = encontra_primos()
input()
numeros = input().split()

for valor in numeros:
    print(t_primo(int(valor), tabela_primos))