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
def oula(r):
	prime=[0 for i in range(r+1)]
	common=[]
	for i in range(2,r+1):
		if prime[i]==0:
			common.append(i)
		for j in common:
			if i*j>r:
				break
			prime[i*j]=1
			if i%j==0:
				break
	return common
common=oula(1000)
def prime(s):
	if s<2:
		return False
	for i in common:
		if i>=s:
			return True
		if s%i==0:
			return False
	return True
n=int(input())
l1=[int(x) for x in input().split()]
for i in range(n):
	sqr=math.sqrt(l1[i])
	if int(sqr)==sqr:
		if prime(int(sqr))==True:
			print('YES')
		else:
			print('NO')
	else:
		print('NO')