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 collections, math

local = False
if local:
    file = open("inputt.txt", "r")

def inp():
    if local:
        return file.readline().rstrip()
    else:
        return input().rstrip()

def ints():
    return [int(_) for _ in inp().split()]


t = int(inp())

for _ in range(t):
    n = int(inp())
    sqrtn = int(math.sqrt(n))

    found = False
    for a in range(2, sqrtn):
        if n % a == 0:
            rem = n//a
            for b in range(a+1, sqrtn):
                if rem % b == 0:
                    c = rem//b

                    if a != c and a != b and b != c:
                        print("YES")
                        print(str(a) + " " + str(b) + " " + str(c))
                        found = True
                        break
        
        if found:
            break
    
    if not found:
        print("NO")