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 PYTHON):

Solution:
import math
def crivo(N):
    A = [True] * (N+1)
    A[0] = A[1] = False
    for value, prime in enumerate(A):
        if prime:
            for i in range(value**2, N+1, value):
                A[i] = False
 
    return A
 


x = input()

m = map(int, raw_input().split())

maior = max(m)
primes = crivo(int(maior**(0.5)))

for i in m:
	r = int(math.sqrt(i))
	if(i ==  pow(r,2)and primes[r]):
		print "YES"
	else:
		print"NO"