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 isPrime(n) : 
    if (n <= 1) : 
        return False
    if (n <= 3) : 
        return True
    if (n % 2 == 0 or n % 3 == 0) : 
        return False
    i = 5
    while(i * i <= n) : 
        if (n % i == 0 or n % (i + 2) == 0) : 
            return False
        i = i + 6
  
    return True
t=int(input())
for i in range(t):
    n=int(input())
    x=isPrime(n)
    if x==True:
        print("NO")
    else:
        c=[]
        count=0
        vv=math.sqrt(n)
        vv=int(vv)
        i=2
        while i*i<n:
            if n%i==0:
                count+=1
                n=n//i
                c.append(i)
            if count==2:
                c.append(n)
                break
            i+=1
        if len(c)<3 or c[0]==c[1] or c[1]==c[2]:
            print("NO")
        else:
            print("YES")
            print(*c)