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

def primo(num):
    # Corner cases
    if (num <= 1):
        return False
    if (num <= 3):
        return True
    if (num % 2 == 0 or num % 3 == 0):
        return False
    k = int(sqrt(num))+1
    for i in range(5,k,6):
        if (num % i == 0 or num % (i + 2) == 0):
            return False
    return True

def three_dividors(number):

    raiz = int(sqrt(number))
    if (raiz * raiz != number):
        return False
    if (primo(raiz)):
        return True
    else:
        return False


times = int(input())
entrada = input().split(' ')

for i in range(len(entrada)):
    if three_dividors(int(entrada[i])):
        print("YES")
    else:
        print("NO")