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 sys import stdin, stdout
import sys
INF=1e9
import bisect
def get_int(): return int(stdin.readline().strip())
def get_ints(): return map(int,stdin.readline().strip().split()) 
def get_array(): return list(map(int,stdin.readline().strip().split()))
def get_string(): return stdin.readline().strip()
def op(c): return stdout.write(c)
#from collections import defaultdict 
import math
for _ in range(int(stdin.readline())):
    n=get_int()
    a,b,c=0,0,0
    f=0
    for i in range(2,int(math.sqrt(n))+1):
        if n%i==0:
            a=i
            n=n//i
            for j in range(i+1,int(math.sqrt(n))+1):
                if n%j==0:
                    b=j
                    n=n//j
                    f=1
                    break
            if f==1:
                break
    if f==1 and n not in [a,b]  :
        print("YES")
        print(a,b,n)
        continue
    print("NO")