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,sys
t = int(input())
answer = []
while t!=0:
    t-=1
    n = int(input())
    num = n
    if num in answer:
        print('NO')
        continue
    even = True if num%2==0 else False
    if even == True:
        arr = [1]
        counter = 1
    else:
        arr = [2]
        counter = 2
    while len(arr)!=3:
        i = arr[-1]+1
        if i>n:
            break
        while n%i!=0 and i<int(pow(n,0.5)):
            i+=1
        arr.append(i)
        n=n//i
    if n!=1 and len(arr)==3 and (n not in arr) and arr[1]*arr[2]*n == num:
        print('YES')
        arr.append(n)
        arr = map(str,arr[1:])
        print(' '.join(arr))
    else:
        if num not in answer:
            answer.append(num)
        print('NO')