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(x):
    l = [True] * (int(x)+1)
    l[0] = l[1] = False
    for p in range(2,int(x)):
        if l[p] == True:
            for _ in range(p*2, int(x),p):
                l[_] = False
    return l[1:]

tkpl = is_prime(1000000)

n = int(input())
l_new = input().split()

for m in l_new:
    if int(m) == 4:
        print('YES')
    elif int(m) < 4 or int(m) % 2 == 0:
        print('NO')
    else:
        m_sqrt = int(m) ** 0.5
        if m_sqrt % 1 == 0 and tkpl[int(m_sqrt)-1] == True:
            print('YES')
        else:
            print('NO')