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:
import math

def primecheck(num):
    if(num == 1):
        return 0
    count = 0

    if(num % 2 == 0):
        num = num / 2
        count = count + 1

    i = 3
    while i <= int(math.sqrt(num)):
        if num % i == 0:
            num = num / i
            count = count + 1
        i = i + 2

    if((count > 1) or ((count == 1) and (num != 1))):
        return 0
    else:
        return 1               

count = int(input(''))
nums = [int(i) for i in input('').split(' ')]
for i in range(count):
    if ((int(pow((int)(math.sqrt(nums[i])), 2)) == nums[i]) and primecheck((int)(math.sqrt(nums[i])))):
        print("YES")
    else:
        print("NO")