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 sqr(x):
    root = int(x**0.5)-1
    if(root * root == x):
        return root
    root += 1
    if(root*root == x):
        return root
    root += 1
    if(root*root == x):
        return root
    return -1

prime = [1]*1000001
prime[0] = prime[1] = 0
for i in range(2, 1001): #raiz de 10^6, que é 10^3
    if(prime[i] == 1):
        for j in range(i*i, 1000001, i):
            prime[j] = 0

n = int(input())
numbers = map(int, input().split())
for i in numbers:
    root = int(sqr(i))
    if(root != -1 and prime[root]):
        print('YES')
    else:
        print('NO')