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 eratosfen(n):
    num = [True]*10**6
    num[0], num[1] = False, False
    for j in range(2,1000000):
        if num[j] == True:
            for k in range(2*j,1000000,j):
                num[k] = False
    a = [j*j for j in range(1000000) if num[j] == True]
    return a

def binary(b,x):
    l, r = 0, long-1
    while l <= r:
        m = (l+r)//2
        if a[m] == x:
            return True
        elif a[m] < x:
            l = m+1
        else:
            r = m - 1
    return False

n = int(input())
a = eratosfen(n)
long = len(a)
for i in map(int, input().split()):
    print('YES' if binary(a,i) else 'NO')