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:
import sys
import math
import collections
def get_ints(): return map(int, sys.stdin.readline().strip().split())
def get_list(): return list(map(int, sys.stdin.readline().strip().split()))
def get_string(): return sys.stdin.readline().strip()
for t in range(int(input())):
    n=int(input())
    p=0
    for i in range(2,math.ceil(math.sqrt(n))):
        count=0
        ans=[]
        if n%i==0:
            count+=1
            no=n//i
            ans.append(i)
            for j in range(2,math.ceil(math.sqrt(no))):
                if i==j:
                    continue
                if no%j==0:
                    val=no//j
                    if val!=i and val!=j:
                        ans.append(val)
                        ans.append(j)
                    if len(ans)==3:
                        print("YES")
                        print(*ans)
                        p+=1
                        count=3
                        break
        if count==3:
            break
    if p==0:
        print("NO")