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 dell(num):
    global ans
    for i in range(2, 2 + int(math.sqrt(num))):
        if num % i == 0:
            ans.append(i)
            return dell(num // i)
    if num >= 2:
        ans.append(num)


t = int(input())
for _ in range(t):
    num = int(input())
    ans = []
    dell(num)
    ans = sorted(ans)
  #  print(ans)
    if len(ans) < 3:
        print('NO')
        continue

    ch1 = ans[0]
    ch2 = ans[1]
    ind = 2
    if ch2 == ch1:
        ch2 *= ans[2]
        ind = 3

    ch3 = 1
    for j in range(ind, len(ans)):
        ch3 *= ans[j]

    if min(ch3, ch1, ch2) >= 2 and ch1 != ch2 and ch1 != ch3 and ch2 != ch3:
        print('YES')
        print(ch1, ch2, ch3)
    else:
        print('NO')