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 fact(n):
    if n%2==0 and not n==2:
        return True
    for i in range(3,1000,2):
        if n%i==0 and not n==i:
            return True
    return False

def can_sqrt(a):
    p=1;q=1000000
    while q-p>1:
        v=(p+q)//2
        v2=v*v
        if v2==a:
            return v
        elif v2>a:
            q=v
        else:
            p=v
    return False
    
n=int(input())
x=map(int,input().split())
for i in x:
    sq=can_sqrt(i)
    if sq:
        if not fact(sq):
            print('YES')
            continue
    print('NO')