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:
def is_prime(a):
    counter = 0
    for i in range(1, int(a ** 0.5) + 1):
        if a % i == 0:
            counter += 1
    return True if counter == 1 else False


n = int(input())
my_list = list(map(int, input().split()))
list_of_answers = []
for number in my_list:
    if number % 2 == 0 and number != 4 or number == 1:
        list_of_answers.append('NO')
    else:
        if (number ** 0.5).is_integer() and is_prime(int(number ** 0.5)):
            list_of_answers.append("YES")
        else:
            list_of_answers.append("NO")
for a in list_of_answers:
    print(a)