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 sys import stdin
input=lambda:stdin.readline().strip()
from collections import defaultdict
def fun(n,dict1):
    if n%2==0 and (n//2)!=2 and dict1[2]==0:
        #print(dict1[2])
        return [2,n//2]
    elif n%3==0 and (n//3)!=3 and dict1[n//3]==0 and dict1[3]==0:
        return [3,n//3]
    else:
        i=2
        while i*i<n:
            if n%i==0 and (n//i)!=i and dict1[n//i]==0 and dict1[i]==0:
                #print(dict1[i],'i',i)
                return [i,n//i]
            i+=1
    return -1
for _ in range(int(input())):
    n=int(input())
    if n<8:
        print('NO')
    else:
        dict1=defaultdict(int)
        a=fun(n,dict1)
        if a==(-1):
            print('NO')
        else:
            a,b=a
            dict1[a]+=1
            #print(dict1)
            c=fun(b,dict1)
            if c==(-1):
                print('NO')
            else:
                print('YES')
                print(a,c[0],c[1])