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:
from sys import stdin
import math


def get_user_input():
    return list(map(int, stdin.readline().rstrip().split()))


all_num = [0]*10000001
all_num[1] = 1
all_num[2] = 0

for i in range(2, 1001, 1):
    if all_num[i]:
        continue
    for j in range(2*i, 1000001, i):
        all_num[j] = 1


n = int(input())
input_list = get_user_input()
for i in range(0, len(input_list)):
    sqr = int(math.sqrt(input_list[i]))

    if sqr*sqr == input_list[i] and not(all_num[sqr]):
        print("YES")
    else:
        print("NO")