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 verifica_primo(x):
    if(x< 4):
        return False
    if(x == 4):
        return True
    if (x%2==0):
        return False
    raiz = math.sqrt(x)
    if float(raiz).is_integer():
        if tabela[int(raiz)] == True:
            return True
    return False


def pre_calculo():
    tabela = [True]*1000000
    tabela[0] = False 
    tabela[1] = False
    for i in range(2,1000000):
        if (tabela[i] == True):
            for j in range(i*i, 1000000, i):
                tabela[j] = False
    return tabela                    


tabela = pre_calculo()
n = int(input())
vetor = list(map(int,input().split()))

for i in vetor:
    if verifica_primo(i) == True:
        print("YES")
    else:
        print("NO")