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:
import sys
def sieve(n):
	ary = [True]*(n+1)
	ary[0] = ary[1] = False
	for i in range(4, n+1, 2):
		ary[i] = False
	for i in range(3, int(n**0.5)+1, 2):
		for j in range(i*i, n+1, i):
			ary[j] = False
	return ary

def f(n):
	if n==1:
		return "NO"
	m = int(n**0.5)
	if primes[m] and m*m == n:
		return "YES"
	return "NO"

primes = sieve(10**6+1)
n = sys.stdin.readline()
ary = map(int, sys.stdin.readline().split())
for i in ary:
	print (f(i))