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


def sieve():
    n = 10**6
    prime = [True for _ in range(n+1)]
    # print(prime)
    prime[0] = False
    prime[0] = False
    for i in range(2, int(math.sqrt(n))+1):
        if prime[i] == True:
            for j in range(i*i, n+1, i):
                prime[j] = False
    return prime


def solve(val):

        if val == 1:
            return False
        elif val < 4 and n % 2 == 0:
            return False
        elif val == 4:
            return True
        else:
            sq = math.sqrt(val)
            if sq == int(sq):
                if prime[int(sq)] == True:
                    return True
            return False


prime = sieve()
n = int(input())
arr = map(int, input().split(' '))
for i in arr:
    if solve(i) == True:
        print('YES')
    else:
        print('NO')