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

def sqr_sieve():
  n = 10**6
  i = 2
  d = dict.fromkeys([i for i in range(1, n+1)], 0)
  d[1] = 1
  while i*i <= n:
    if d[i] == 0:
      j = i*i
      while j <= n:
        d[j] = 1
        j += i
    i += 1
  return d


n = int(input())
xs = list(map(int, input().split()))
d = sqr_sieve()
for x in xs:
  try:
    print('NO') if d[math.sqrt(x)] else print('YES')
  except KeyError:
    print('NO')