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 PYTHON):

Solution:
import math

max_num = int(1e6) + 1

sieve = [True]*max_num
sieve[:2] = [False, False] # mark 0 and 1 as composite
for i in range(2, max_num):
    if not sieve[i]: # already marked composite
        continue

    for j in range(i*2, max_num, i):
        sieve[j] = False

if __name__ == '__main__':
    n = int(raw_input())
    nums = [int(num) for num in raw_input().split()]

    for num in nums:
        a = math.sqrt(num)
        print 'YES' if int(a) == a and sieve[int(a)] else 'NO'