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 defaultdict, deque
from itertools import permutations
from sys import stdin,stdout
from bisect import bisect_left, bisect_right
from copy import deepcopy
#from random import randint

int_input=lambda : int(stdin.readline())
string_input=lambda : stdin.readline()
multi_int_input =lambda : map(int, stdin.readline().split())
multi_input = lambda : stdin.readline().split()
list_input=lambda : list(map(int,stdin.readline().split()))
string_list_input=lambda: list(string_input())
MOD = pow(10,9)+7
import math

test = int_input()
def solve(n):
    for i in range(2, int(math.sqrt(n))+1):
        if(n%i==0):
            a=i
            tmp=n//i
            for j in range(i+1, int(math.sqrt(tmp))+1):
                if(tmp%j==0 and (tmp//j!=a and tmp//j!=j)):
                    print("YES")
                    print(a,j,tmp//j)
                    return

    print("NO")
    return

for _ in range(test):

    n = int_input()

    solve(n)