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 math
n=int(input())
s=list(map(int,input().split()))
a=10**6


def sieve(n):
    isprime=[True]*(n+1)
    isprime[1]=False
    for i in range(2,int(n**0.5)+1):
        if isprime[i]==True:
            for j in range(2*i,n+1,i):
                isprime[j]=False
    return isprime


primes=sieve(a)
for i in s:
    if i==1:
        print('NO')
        continue
    t=math.sqrt(i)
    if int(t)!=t:
        print('NO')
    else:
        if primes[int(t)]:
            print('YES')
        else:
            print('NO')