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:
from math import sqrt
import datetime as dt
def test(s):
    
    lines = s.split("\n")
    
    n = map(int,lines[0].split())[0]
    
    li_num = map(int,lines[1].split())

    dt_start = dt.datetime.now()
    num = 1000010
    primes = [1] * num
    primes [0] = 0
    primes [1] = 0

    s_primes = set()
    for i in xrange(2, num):
        if primes[i]:
            s_primes.add(i * i)
            for j in xrange(2, num/i):
                primes[j*i] = 0

    for num in li_num:
        if num in s_primes:
            print 'YES'
        else:
            print 'NO'

s_all = ''
while True:
    try:
        s_all += (raw_input()) + '\n'
    except:
        break
test(s_all)