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:
from collections import deque
from math import sqrt
def factors(n):
  d=deque()
  for x in range(2,int(sqrt(n)+1)):
    if n%x==0 :
      d.append(x)
      if n//x!=x :
        d.append(n//x)
  return d,set(d)
t=int(input())
while(t):
  n=int(input())
  f,m=factors(n)
  flag=a=b=c=0
  for x in range(len(f)):
    fa,ma=factors(f[x])
    for y in range(len(fa)):
      if f[x]//fa[y]!=fa[y] and fa[y]!=n//f[x] and f[x]//fa[y]!=n//f[x]:
       # print(y,x,f[x],fa[y])
        flag=1
        a,b,c=fa[y],n//f[x],f[x]//fa[y]
        break
    if flag :
      break
  if flag:
    print("YES")
    print(a,b,c)
  else:
    print("NO")
  t-=1