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:

def isPrime(number):
  count = 0
  raiz = pow(number, 1/2)
  raiz = int(raiz)
  for i in range(1, raiz + 1):
    if(number % i == 0):
      count += 1
      if((number / i) != i):
        count += 1
    if(count >= 3):
      return False
  return True

def tPrimes(number):
  raiz = pow(number, 1/2)
  resto = raiz % 1
  if(number == 1 or number == 2):
    print("NO")
  elif resto != 0:
    print("NO")
  else:
    raiz = int(raiz)
    if(isPrime(raiz)):
      print("YES")
    else:
      print("NO")

qtd = int(input())
numbers = input().split()

for i in range(qtd):
  tPrimes(int(numbers[i]))