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, ceil

def sieve(n):

    prime = [True] * (n + 1)
    p = 2

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

    prime[0] = False
    prime[1] = False

    return prime

if __name__ == "__main__":
    n = int(input())
    xs = [int(i) for i in input().split(" ")]

    sieve_table = sieve(ceil(sqrt(10**12)))

    for x in xs:
        if sqrt(x).is_integer() and sieve_table[ceil(sqrt(x))]:
            print("YES")
        else:
            print("NO")