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:
import sys
import math
def main():
    pass
def binary(n):
    return (bin(n).replace("0b", ""))
def decimal(s):
    return (int(s, 2))
def pow2(n):
    p = 0
    while n > 1:
        n //= 2
        p += 1
    return (p)
def isPrime(n):
    if (n == 1):
        return (False)
    else:
        root = int(n ** 0.5)
        root += 1
        for i in range(2, root):
            if (n % i == 0):
                return (False)
        return (True)
def sinp():return sys.stdin.readline().strip()
def iinp():return int(input())
def ninp():return map(int,sys.stdin.readline().strip().split())
def linp():return list(map(int,sys.stdin.readline().strip().split()))
def p(a): print(a)

n=int(input())
N=1000000
a=[1]*N
a[0]=a[1]=0
s=set()
for i,j in enumerate(a):
    if(j):
        s.add(i*i)
        for k in range(2*i,N,i):
            a[k]=0
for x in map(int,(input().split())):
    if x in s:
        print("YES")
    else:
        print("NO")