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
import math
import itertools
from collections import defaultdict

n = int(sys.stdin.readline().rstrip())

nums = map(int, sys.stdin.readline().rstrip().split())

pr = [False for x in range(10**6 + 1)]
for i in range(2, 10**6):
	if pr[i] == False:
		for j in range(2*i, 10**6 + 1, i):
			pr[j] = True

for n in nums:
	if n==1:
		print("NO")
		continue
	cand = int(round(math.sqrt(n)))
	if cand**2 == n and pr[cand] == False:
		print("YES")
	else:
		print("NO")