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:
# -*- coding: utf-8 -*-
"""
Created on Mon Oct 26 20:43:57 2020

@author: Genius Huang He
"""
from math import sqrt

def prime(a):
    d = dict()
    for i in range(1,a+1):
        d[i] = True
    d[1] = False
    for i in range(2,int((a+1)**0.5)+1):
        if d[i]:
            for j in range(2,a//i+1):
                if d[i*j]:
                    d[i*j] = False
    return d

m = int(input())
k = prime(1000000)
#print(k)
print("\n".join([["NO","YES"][((sqrt(i)) % 1 == 0) and k[sqrt(i)]] for i in [int(x) for x in input().split()]]))