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 math
for _ in range(int(input())):
    n=int(input())
    l=[]
    for i in range(2,int(math.sqrt(n))+1):
        if(n%i==0):
            t=n
            l.append(i)
            t=t//i
            for j in range(2,int(math.sqrt(t)+1)):
                if(t%j==0):
                    
                    
                    l.append(j)
                    l.append(t//j)
                    if(len(set(l))==3):
                        break
        if(len(set(l))==3):
            break
        else:
            l=[]
    if(len(l)==3):
        print("YES")
        print(l[0],l[1],l[2])
    else:
        print("NO")