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
t = int(input())
for _ in range(t):
    n = int(input())
    n_i = n
    if n<24:
        print("NO")
    else:
        a, b, c = 2, 2, 2
        sq = int(math.sqrt(n)) + 2
        for i in range(a,sq):
            if n%i==0:
                a = i
                n = n//a
                sq =  int(math.sqrt(n)) + 2
                break
        for i in range(a+1,sq):
            if n%i==0:
                b = i
                n = n//b
                break
        c = n
        if c==b or c==2 or b==2:
            print("NO")
        elif a==2 and n_i%2!=0:
            print("NO")
        else:
            print("YES")
            print(a, b, c)