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 
import math
def div(n):
    y=n
    c=0
    ans=[]
    for i in range(2,int(math.sqrt(n))+1):
        if y%i==0:
            c+=1
            y=y//i
            ans.append(i)
            if c>=2:
                break
    print("YES" if c>=2 and y not in ans else "NO") 
    if c>=2 and y not in ans:
        print(*(ans+[y]))           

for _ in range(int(input())):
    n = int(input())
    div(n)