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:
def eratosthenes(n):
    lis = [0 for i in range(n + 1)]
    lis2 = []
    for i in range(2, n + 1):
        if lis[i] == 0:
            lis2.append(i)
            for j in range(i * 2, n + 1):
                if j % i == 0:
                    lis[j] = 1
    return lis2
p=eratosthenes(1000)

import math
n=int(input())
li=[int(r) for r in input().split()]
for k in range(n):
    q=int(math.sqrt(li[k]))
    if q==1:
        print('NO')
    elif q**2!=li[k]:
        print('NO')
    else:
        for m in p:
            if q%m==0 and q not in p:
                print('NO')
                break
        else:
            print('YES')