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:

# -*- coding: utf-8 -*-
# @Date    : 2020-01-23 16:32:49
# @Author  : raj lath (oorja.halt@gmail.com)
# @Link    : link
# @Version : 1.0.0

import sys
sys.setrecursionlimit(10**5+1)

inf     =  int(10 ** 20)
max_val =  inf
min_val = -inf

RW  = lambda : sys.stdin.readline().strip()
RI  = lambda : int(RW())
RMI = lambda : [int(x) for x in sys.stdin.readline().strip().split()]
RWI = lambda : [x for x in sys.stdin.readline().strip().split()]


for _ in range(RI()):
    inp = RI()
    answer = []
    i = 2
    while len(answer) < 2  and  i * i < inp:
        if inp % i == 0:
            answer.append(i)
            inp //= i
        i += 1
    if len(answer) == 2 and inp not in answer:
        print("YES")
        print(*answer, inp)
    else:
        print("NO")