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
from collections import defaultdict
from math import sqrt
input=sys.stdin.readline

for _ in range(int(input())):
    n=int(input())
    nn=n
    d=defaultdict(int)
    while n%2==0:
        d[2]+=1
        n//=2
    for i in range(3,int(sqrt(n))+1,2):
        while n%i==0:
            d[i]+=1
            n//=i
    if n>1:
        d[n]=1

    if len(d)==1 and sum(d.values())<6:
        print("NO")
        continue
    if len(d)==1:
        a=list(d.keys())[0]
        b=a*2
        c=nn//(a*b)
        print("YES")
        print(a,b,c)
        continue
    if len(d)==2 and sum(d.values())<4:
        print("NO")
        continue
    x=list(d.keys())
    a=x[0]
    b=x[1]
    c=nn//(a*b)
    print("YES")
    print(a,b,c)