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:
class Eratostenes:
  def __init__(self, until):
    self.Primes = []
    Is_prime = [True for i in range(until + 10)]

    for i in range(2,until):

      if Is_prime[i]:

        self.Primes.append(i)

        for e in range(2*i,until,i):
          Is_prime[e] = False

def busqueda_binaria(x, array):

  Izq, Der = 0, len(array)-1

  while Izq <= Der:

    middle = (Izq + Der) // 2

    if array[middle] == x:
      return middle

    elif x > array[middle]:
      Izq = middle + 1

    else:
      Der = middle - 1

  return -1



if __name__ == "__main__":
  primes = Eratostenes(1000000)

  primes_array = [prime * prime for prime in primes.Primes]
  size = int(input())
  queries = [int(i) for i in  input().split()]

  for i in range(size):
    index = busqueda_binaria(queries[i], primes_array)

    print("YES" if index != -1 else "NO")