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
input=sys.stdin.readline
t=int(input())
import math 
from functools import reduce

def factors(n):    
    return set(reduce(list.__add__, 
                ([i, n//i] for i in range(1, int(n**0.5) + 1) if n % i == 0)))
for i in range(t):
    n=int(input())
    ffactor=(factors(n))
    #print(ffactor)
    ffactor2=list(set(ffactor))
    ffactor2.sort()
    ok=False
    #print(ffactor2)
    for i in range(len(ffactor2)):
        for j in range(i+1,len(ffactor2)):
            for k in range(j+1,len(ffactor2)):
                if ffactor2[i]>=2 and ffactor2[j]>=2 and ffactor2[k]>=2:
                    if ffactor2[i]*ffactor2[j]*ffactor2[k]==n:
                        ok=True
                        f=ffactor2[i]
                        s=ffactor2[j]
                        t=ffactor2[k]
                        break
            if ok==True:
                break
        if ok==True:
            break
    if ok==True:
        print("YES")
        print(int(f),int(s),int(t))
    else:
        print("NO")