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 *
for i in range(int(input())):
    n=int(input())
    j=2
    count=0
    num=[]
    while j**2<=n:
        if n%j==0:
            if len(num)==1:
                if n%(j*num[0])!=0:
                    j+=1
                    continue
            num.append(j)
            
            count+=1
        if count==2:
            break
        j+=1
    #print(num)
    if count<2:
        print("NO")
        continue
    if count==2:
        val=n//(num[0]*num[1])
        if val in num:
            print("NO")
            continue
        if val*num[0]*num[1]!=n:
            print("NO")
            continue
        print("YES")
        print(num[0], num[1], val)