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 primes_sieve2(limit):
    a = [True] * limit # Initialize the primality list
    a[0] = a[1] = False
    Lres = []
    i = 0
    for isprime in a:
        if isprime:
            Lres.append(i)
            for n in range(i*i, limit, i):     # Mark factors non-prime
                a[n] = False
        i += 1
    return Lres

def get_res(L):
    A = primes_sieve2(1000000)
    result = ''
    Lpt = [x**2 for x in A]
    Spt = set(Lpt)
    for elem in L:
        if elem in Spt:
            result += 'YES\n'
        else:
            result += 'NO\n'
    return result[:-1]

N = int(raw_input())

L = [int(s) for s in raw_input().split(" ")]
result = get_res(L)
print "{}".format(result)