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
for i in range(int(input())) :
    n = int(input())
    a,b = 0,0
    for i in range(2, math.floor(math.sqrt(n))+1) :
        if n%i == 0 :
            a = i
            break
    if a != 0 :
        for j in range(a+1, math.floor(math.sqrt(n//a))+1) :
            if (n//i)%j == 0 :
                b = j
                break
        if b != 0 and a != b and b != n//(a*b) :
            print('YES')
            print(a, b, n//(a*b))
        else :
            print('NO')
    else :
        print('NO')