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
res=[1,1,1]
def del1(a,k,d):
    sqrtlam=lambda x : math.sqrt(x)
    for i in range(d,math.ceil(sqrtlam(a))):   
        if a%i==0:
            if(k)==1:
                if(int(a/i)!=res[0]):
                    res[1]=int(i)
                    res[2]=int(a/i)
                    return 1
            else:
                res[0]=i
              
                if(del1(a/i,k+1,i+1)):
                    return 1
                
    return 0
                
n=int(input())
for i in range(n):
    res=[1,1,1]
    b=int(input())
    if(del1(b,0,2)==0 ):
        print("NO")
    else:
        print("YES")
        print (*res)