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 collections import defaultdict
import math
def prime(n):
    ans=[]
    al=defaultdict(int)
    while(n%2==0):
        al[2]=al[2]+1
        ans.append(2)    
        n=n//2
    for i in range(3,int(math.sqrt(n))+1,2):
        while(n%i==0):
            al[i]+=1
            ans.append(i)
            n=n//i
    if(n>2):
        al[n]=1
        ans.append(n)
    ans=list(set(ans))    
    return ans,al;
t=int(input())
for i in range(t):
        
    n=int(input())
    ans,al=prime(n)
    if(len(ans)>=3):
        print('YES')
        a=ans[0]**al[ans[0]]
        b=ans[1]**al[ans[1]]
        c=n//(a*b)
        print(a,b,c)    
    elif(len(ans)==2):
        if(al[ans[0]]+al[ans[1]]>=4):
            a=ans[0]
            b=ans[1]
            c=n//(a*b)
            print('YES')
            print(a,b,c)
        else:
            print('NO')
    else:
        if(al[ans[0]]>5):
            print('YES')
            a=ans[0]*ans[0]
            b=ans[0]
            c=n//(a*b)
            print(a,b,c)
        else:
            print('NO')