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:
from math import sqrt
def sieve(n):
    arr = [True]*(n+1)
    arr[0] = False
    arr[1] = False
    i = 2
    while i*i <= n:
        if arr[i] == True:
            for j in range(2*i,n+1,i):
                if arr[j] == True:
                    arr[j] = False
        i+=1
    return arr

def isPrime(n):
    if n == 1:
        return False
    if n == 2:
        return True
    if n%2 == 0:
        return False
    i = 2
    while i*i <= n:
        if n%i == 0:
            return False
        i+=1
    return True

def isSquare(n):
    if int(sqrt(n))*int(sqrt(n)) == n:
        return True
    return False

n = int(input().strip())
x = list(map(int,input().strip().split()))[:n]
arr = sieve(10**6)
#print(arr[988027])
for i in x:
    if isSquare(i):
        #print(int(sqrt(i)))
        if arr[int(sqrt(i))] == True:
            print("YES")
        else:
            print("NO")
    else:
        print("NO")