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:
import sys, math

# sys.stdin = open('in.txt')

# bool notPrime[MAXN+10]={true,true};
# int prime[MAXN+10]={0};
# int pn=0;
# void MakePrime()
# {
# for (int i=2;i<=MAXN;i++)
# {
# if (!notPrime[i]) prime[++pn]=i;
# for (int j=1;j<=pn && i*prime[j]<=MAXN;j++)
# {
# notPrime[i*prime[j]]=true;
# if (i%prime[j]==0) break;
# }
# }
# }

def MakePrime(n):
	notPrime = set(range(2))
	prime = []
	for i in xrange(2, n + 1):
		if i not in notPrime: prime.append(i)
		for p in prime:
			if i * p > n: break
			notPrime.add(i * p)
			if i % p == 0: break
	return notPrime

def ReadIn():
	input = [ int(x) for x in sys.stdin.read().split() ]
	n = input[0]
	a = input[1:]
	return a

def Solve(a, notPrime):
	for x in a:
		y = int(x ** .5)
		if y ** 2 != x or x == 1: print 'NO'
		elif y in notPrime: print 'NO'
		else: print 'YES'
			

notPrime = MakePrime(1000000)	
a = ReadIn()
Solve(a, notPrime)