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
EPS = 1e-6
n = int(raw_input())
a = list(map(int,raw_input().split()))
to = int(1e6) + 3
p = [True] * to
p[0] = p[1] = False
for i in range(2, to):
    if p[i]:
        for j in range(i*i, to, i):
            p[j] = False
for i in range(n):
    if a[i] == 1:
        print('NO')
        continue
    x = math.sqrt(a[i])
    if abs(x - int(x)) < EPS:
        if p[int(x)]:
            print('YES')
        else:
            print('NO')
    else:
        print('NO')