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 eratosthenes(n):
    sieve = list(range(n + 1))
    sieve[1] = 0 
    for i in sieve:
        if i > 1:
            for j in range(i + i, len(sieve), i):
                sieve[j] = 0
    return sieve


n = int(input())
my_list = list(map(int, input().split()))
set_of_answers = set()
for i in eratosthenes(1000000):
    if i != 0:
        set_of_answers.add(i ** 2)
for a in my_list:
    print("YES") if a in set_of_answers else print("NO")