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 sqr(x):
    root = int(x**0.5)-1
    for _ in range(3):
        if(root * root == x):
            return root
        root += 1
    return -1


n = int(input())
a = list(map(int, input().split()))

num = 1_000_001
aux = [1] * num
aux[0] = 0
aux[1] = 0

for i in range(2, 1001):
    if aux[i] == 1:
        for j in range(i*i, num, i):
            aux[j] = 0

for e in a:
    root = sqr(e)
    if root != -1 and aux[root]:
        print('YES')
    else:
        print('NO')