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

n = int(input())
x = list(map(int, input().split()))

primos = [1] * 1000001
primos[0], primos[1] = 0, 0
for i in range(2, 1001):
  if primos[i] == 1:
    for j in range(i * i, 1000001, i):
      if j >= 1000001:
        break
      primos[j] = 0

for i in range(len(x)):
  raiz = math.sqrt(x[i])
  if (int(raiz * 1000000)) % 1000000 == 0:
    if x[i] == 0 or x[i] == 1:
      print("NO") 
    elif primos[int(raiz * 1000000) // 1000000]:
      print("YES")
    else:
      print("NO")
  else:
    print("NO")