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:
t = int(input())
import math 
for i in range(t):
    n = int(input())
    res = []
    c = 0
    a = 0
    q = int(math.sqrt(n)) + 2
    
    for j in range(2,q):
        if n % j == 0:
            n = n // j
            res.append(j)
            a = j + 1
            c += 1
            break
    if c == 1:
        q = int(math.sqrt(n)) + 2
        for j in range(a,q):
            if n % j == 0:
                n = n // j
                res.append(j)
                c += 1
                break
        
    if c < 2 or res[0] == n or res[1] == n:
        print('No')
    else:
        print('Yes')
        print(res[0],res[1],n)