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
def find(n):
    count=0
    flag=0
    ori=n
    for i in range(2,int(math.sqrt(n))+3):
        if(n%i==0):
            count+=1
            n=n//i
            liste.append(i)
        if(count>=2):
            r=ori//(liste[0]*liste[1])
            if(r!=liste[0] and r!=liste[1] and r!=1):
                liste.append(ori//(liste[0]*liste[1]))
                flag=1
                break
            else:
                count=1
                del liste[len(liste)-1]
    if(flag==1):
        return "YES"
    else:
        return "NO"
            
        
t=int(input())
for i in range(t):
    n=int(input())
    liste=[]
    y=find(n)
    if(y=="YES"):
        print(y)
        print(*liste)
    elif(y=="NO"):
        print(y)