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:
class Solution(object):
    def __init__(self):
        x_lim = 20
        self.largest_x = pow(2, x_lim)
        a = [1] * (self.largest_x + 1)
        end = self.largest_x + 1

        ans = set()
        for i in range(2, end):
            if a[i]:
                for j in range(pow(i, 2), end, i):
                    a[j] = 0
                ans.add(pow(i, 2))

        input()
        for x in map(int, input().split()):
            print('YES') if x in ans else print('NO')

    pass


def main():
    Solution()
    pass


if __name__ == '__main__':
    main()