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:
def generate_prime_array(n):
    arr = (n+1)*[1]
    m = 2
    for i in range(2,n+1):
        if arr[i] != 0:
            m = 2
            while i*m <= n:
                arr[i*m] = 0
                m = m+1
    return arr

from math import sqrt
def check_t_prime(numbers):
    prime_array = generate_prime_array(int(sqrt(max(numbers))))
    for i in numbers:
        if i == 1 or i == 0:
            print "NO"
        elif sqrt(i).is_integer() and prime_array[int(sqrt(i))] == 1:
            print "YES"
        else:
            print "NO"

length = int(raw_input())
numbers = map(int, raw_input().split())
check_t_prime(numbers)