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

n = int(input())
l = [int(x) for x in input().split()]


def sieve_of_eratosthenes(n):
    primes = [True] * (n + 1)
    p = 2
    while p <= n:
        if primes[p]:
            for i in range(p * 2, n + 1, p):
                primes[i] = False
        p += 1
    return primes

list_1 = sieve_of_eratosthenes(int(math.sqrt(max(l))) + 1)
for i in range(n):
    m = int(math.sqrt(l[i]))
    if l[i] == 1 or l[i] == 2:
        print('NO')
        continue
    if m * m == l[i] and list_1[m] == True:
        print('YES')
    else:
        print('NO')