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
import sys
std = sys.stdin
if __name__ == "__main__":
   n = int(std.readline())
   data = [int(x) for x in std.readline().rstrip('\n').split()]
   m =  math.floor(max(data) ** 0.5)
   # precalculation shit
   T = [True] * (m+1)
   T[0] = False
   T[1] = False
   for i in range(2, math.ceil(m**0.5)+1):
      for j in range(i*i,m+1, i):
         T[j] = False
   #main shit..
   for x in data:
      l = math.floor(x ** 0.5)
      if T[l]:
         if l * l == x:
            sys.stdout.write("YES\n")
         else:
            sys.stdout.write("NO\n")
      else:
         sys.stdout.write("NO\n")