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 PYTHON):

Solution:
limite = 1000000

def calcular_banderas():
    principal = [True] * limite
    principal[0] = principal[1] = False
    for i in range(2, limite):
        if principal[i] == True:
            for j in range(i*i, limite, i):
                principal[j] = False
    return principal

def esTPrimo(n):
    if n == 4:
        return True
    if n < 4 or n%2==0:
        return False
    sqrt_n = n**0.5
    if sqrt_n==int(sqrt_n):
        if banderas[int(sqrt_n)] == True:
            return True
    return False



banderas = calcular_banderas()

n = int(input())
xi = list(map(int, raw_input().split(" ")))

for i in xi:
    if esTPrimo(i) == True:
        print("YES")
    else:
        print("NO")