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
def ld(a, last):
    found  = False
    for div in range(last,int(math.sqrt(a))+1):
        if a % div == 0:
            found = True
            return div
    if not found:
        return False
def do(int):
    x = ld(int,2)
    if x:
        y = ld(int//x, x+1)
        if y:
            z = int//(x*y)
            if x != y and x != z and y != z:
                print("Yes")
                print(x,y,z)
            else:
                print("No")
        else: print("No")
    else:
        print("No")
    
t = int(input())
a = []
for inp in range(0,t):
    inp = int(input())
    a.append(inp)

for element in a:
    do(element)