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:
def main():
  from sys import stdin, stdout
  tprime = [True] * (1000007)
  tprime[0] = False
  tprime[1] = False

  for i in range(2,len(tprime)):
    if tprime[i]:
      for j in range(i*2, 1000007, i):
        tprime[j] = False

  numeros = stdin.readline()
  valor = stdin.readline().split()

  for i in valor:
    if int(i) ** 0.5 == int((int(i) ** 0.5)) and tprime[int(int(i) ** 0.5)]:	
      stdout.write("YES\n")
    else:
      stdout.write("NO\n")

if __name__ == "__main__":
  main()