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:

from math import sqrt

limits = 1000000
prime_flag_list = [True] * limits

prime_flag_list[0] = prime_flag_list[1] = False

for i in range(2, int(sqrt(limits))):
    if prime_flag_list[i] == True:
        for j in range(i*i, limits, i):
            prime_flag_list[j] = False


def is_t_prime(n):
    if n == 4:
        return True
    if n < 4 or n%2==0:
        return False

    if sqrt(n) == int(sqrt(n)):
        return prime_flag_list[int(sqrt(n))]

    return False

input()
numbers = list(map(int, input().split()))

for i in numbers:
    print('YES' if is_t_prime(i) else 'NO')