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 PYTHON):

Solution:
# questao: http://codeforces.com/problemset/problem/230/B
# coding: utf-8
import math

def remove_multiplos(primos, inicio):
    valor = inicio+1
    for i in xrange(inicio+valor, len(primos), valor):
        primos[i] = False


primos = [True] * 10**6
primos[0] = False

for i in xrange(1, len(primos)):
    if primos[i] == True:
        remove_multiplos(primos, i)

rep = int(raw_input())

numeros = map(int, raw_input().split())

for numero in numeros:
    sqrt = math.sqrt(numero)
    if round(sqrt) == sqrt and sqrt != 1:
        if primos[int(sqrt-1)]:
            print "YES"
        else:
            print "NO"
    else:
        print "NO"