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:
"""
Just get primes from 1 - 10**6
"""

from math import sqrt

N = 10**6 + 5
sqr = sqrt(N)

is_prime = [True]*(10**6+5)
is_prime[0] = is_prime[1] = False

cur = 2

while(cur <= sqr):
	for i in range(cur*2,N,cur):
		is_prime[i] = False
	for i in range(cur+1,N):
		if is_prime[i] == True:
			cur = i
			break


#we have all prime nums till now


n = int(input())
list1 = list(map(int, input().split()))
for i in range(n):

	this_num = list1[i]
	this_sqr = sqrt(this_num)
	#print(this_num,this_sqr,is_prime[int(this_sqr)])
	if (int(this_sqr)==this_sqr) and (is_prime[int(this_sqr)]):
		print("YES")
	else:
		print("NO")