Problem: You are given one integer number n. Find three distinct integers a, b, c such that 2 ≤ a, b, c and a ⋅ b ⋅ c = n or say that it is impossible to do it.

If there are several answers, you can print any.

You have to answer t independent test cases.

Input

The first line of the input contains one integer t (1 ≤ t ≤ 100) — the number of test cases.

The next n lines describe test cases. The i-th test case is given on a new line as one integer n (2 ≤ n ≤ 10^9).

Output

For each test case, print the answer on it. Print "NO" if it is impossible to represent n as a ⋅ b ⋅ c for some distinct integers a, b, c such that 2 ≤ a, b, c.

Otherwise, print "YES" and any possible such representation.

Example

Input


5
64
32
97
2
12345


Output


YES
2 4 8 
NO
NO
NO
YES
3 5 823 

Solution (in PYTHON3):

Solution:
def isPrime(n):
    if n == 2 or n == 3: return True
    if n % 2 == 0 or n < 2: return False
    for i in range(3, int(n ** 0.5) + 1, 2):
        if n % i == 0:
            return False    
    return True

t = int(input())
for _ in range(t):
  f = 0
  n = int(input())
  if isPrime(n):
    print("NO")
    continue
  for i in range(2, int(n ** 0.5) + 1):
    if n % i == 0:
      if not isPrime(n // i):
        m = n // i
        for j in range(2, int(m ** 0.5) + 1):
          if m % j == 0 and i != j != (m // j) != i:
            print("YES")
            print(i, j, m // j)
            f = 1
            break
    if f:
      break
  if not f:
    print("NO")