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 _ in range(int(input())) :
    n=int(input())
    s=[]
    try:
     for i in range(2,int(math.sqrt(n))+1):
        if n%i==0:
            g=(n//i)
            a=i+0
            break
     for i in range(a+1,int(math.sqrt(g))+1):
        if g%i==0:
            b=i
            break
    
     for i in range(2,int(math.sqrt(n))+1):
        if n%i==0:
            s.append(i)
    except:
     print("NO")
     continue
    if len(s)>=3:
        print("YES")
        print(a,b,n//(a*b))
    else:
        print("NO")