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:
####################################################
# -*- coding: utf-8 -*-
import sys

w = sys.stdout.write
read = sys.stdin.readline
reads = sys.stdin.read

def r(f=None):
    if f:
        return map(f, read().split())
    else:
        return read().split()

def rs(t,f=None):
    result = []
    result_append = result.append
    for i in xrange(t):
        if f:
            result_append(tuple(map(f, read().split())))
        else:
            result_append(list(read().split()))
    return result


####################################################
import math
sqrt = math.sqrt
from collections import deque

[n] = r(int)
xs = r(int)

a = [False] * 1000001
a[1] = True
s = set()
s_add = s.add
for x in xrange(1, 1000001, 1):
    if not a[x]:
        s_add(x * x)
        for y in range(x * x, 1000001, x):
            a[y] = True

for x in xs:
    if x in s:
        w('YES\n')
    else:
        w('NO\n')