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 math

prime = []
numberlist = []
for i in range(2, 1001):
	numberlist.append(i)
while numberlist[0] < 32:
	now = numberlist.pop(0)
	prime.append(now)
	newnumberlist = []
	while numberlist != []:
		next = numberlist.pop(0)
		if next%now != 0: newnumberlist.append(next)
	numberlist = newnumberlist
prime = prime + numberlist

N = int(input())
A = list(map(int, input().split()))
for i in range(0, N):
	itistprime = False
	x = int(math.sqrt(A[i]))
	if x*x == A[i]:
		for j in range(0, len(prime)):
			if x % prime[j] == 0:
				if x != prime[j]:
					break
			if j == len(prime) - 1:
				itistprime = True
	if itistprime and x != 1: print('YES')
	else: print('NO')