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 Tue Oct 27 16:07:43 2020

@author: hanks
"""

import math
n=int(input())
a=[int(x) for x in input().split()]
x=math.ceil(max(a)**0.5)
l=[True]*(x+1)
for i in range(2,x+1):
    if l[i-1]:
        j=i
        while j*i<=x:
            l[j*i-1]=False
            j+=1
for i in range(n):
    x=a[i]
    if x**0.5!=int(x**0.5):
        print('NO')
    elif x==1:
        print('NO')
    elif l[int(x**0.5)-1]:
        print('YES')
    else:
        print('NO')