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:
'''input
3
4 5 6



'''
 
from collections import defaultdict as df
from bisect import bisect_left as bl 
from itertools import combinations as c
import sys
from math import *
from random import randint as R
import heapq as hp
#import time


def si(n):
	pr=[1]*n
	pr[0]=0
	pr[1]=0

	for i in range(4,n,2):
		pr[i]=0

	for i in range(3,int(n**0.5)+1,2):
		if pr[i]==1:
			for j in range(i*i,n,2*i):
				pr[j]=0

	return pr
		
pr=si(1000001)

n=input()
A=[int(x) for x in raw_input().split()]
from math import sqrt
for i in A:
	sq=int(sqrt(i))
	ans="NO"
	if sq*sq==i:
		if pr[sq]==1:
			ans="YES"
	print ans