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 math import *
for _ in range(int(input())):
    n = int(input())
    e = []
    a = False
    for i in range(2, int(sqrt(n)) + 1):
        m = n / i
        if m.is_integer() == True:
            for j in range(2, int(sqrt(m)) + 1):
                if m % j == 0:
                    if (n / (i * j)).is_integer() == True and i != j and j != (n / (i * j)) and (n / (i * j)) != i:
                        e.append([i, j,int( n / (i * j))])
                        a=True
                        break
    if a == False:
        print("NO")
    else:
        print("YES")
        print(*e[0])