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 get_prime(n):
    if n == 2:
        return [2]
    else:
        prime_sqrt_n = get_prime(int((n-1)**0.5) + 1)
        is_prime = [1] * (n-1)
        for p in prime_sqrt_n:
            q = p
            while q < n // p + 1:
                is_prime[p * q - 2] = 0
                q += 1
        return [i for i, j in enumerate(is_prime, start = 2) if j ==1]

prime_min = get_prime(10 ** 3)
input()
t_list = [*map(int, input().split())]
for squared_t in t_list:
    if squared_t == 1:
        print('NO')
        continue
    t = int(squared_t ** 0.5)
    if t ** 2 != squared_t:
        print('NO')
        continue
    sqrt_t = int(t ** 0.5)
    j = 0
    prime = True
    while prime_min[j] <= sqrt_t:
        if t % prime_min[j] ==0:
            print('NO')
            prime = False
            break
        if j < len(prime_min) - 1:
        	  j += 1
        else:
        	  break
    if prime:
        print('YES')