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 primes(n):
    sieve = set(range(3, n + 1, 2))
    if n >= 2:
        sieve.add(2)
    for i in range(3, int(n ** 0.5) + 1, 2):
        if i in sieve:
            sieve -= set(range(2 * i, n + 1, i))
    return sieve

n = input()
a = [int(el ** 0.5) if int(el ** 0.5) ** 2 == el else 1 for el in map(int, input().split())]
primes_a = primes(max(a))
res = []
for el in a:
    res.append("YES" if el in primes_a else "NO")
print("\n".join(res))