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 math import sqrt as S 
def div(x):
    d=[]
    if x==1:
        return [1]
    if x==2:
        return [1,2]
    cnt=[1,n]
    for i in range(2,int(S(x))+1):
        if x %i==0:
            cnt.append(i) 
    return cnt 
def check(arr):
    if 1 in arr or 0 in arr:
        return 0 
    return len(set(arr))==3 

import sys 
input=sys.stdin.readline 
t=int(input())
ans=[]
for i in range(t): 
    n=int(input()) 
    f=0 
    cnt=div(n)
    for x in cnt : 
        y=n//x
        if f: break 
        for z in div(y):
            if check([x,z,y//z]):
                ans=[x,z,y//z]
                f=1 
                break 
    if f:
        print('YES')
        print(*ans)
    else:
        print('NO')