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 primeFactors(n): 
    output=[]
    while n % 2 == 0: 
        output.append(2)
        n = n / 2 
    for i in range(3,int(math.sqrt(n))+1,2):  
        while n%i==0: 
            output.append(i) 
            n = n / i 
    if n > 2: 
        output.append(int(n))
    return output
t=int(input())
for g in range(0,t):
    n=int(input())
    a=primeFactors(n)
    a.sort()
    output=1
    i=1
    x=y=z=0
    x=a[0]
    if(len(a)==1):
        output=0
    if(output==1):
        if(a[1]!=a[0]):
            y=a[1]
            z=int(n/(x*y))
        else:
            if(len(a)>2):
                y=a[1]*a[2]
                z=int(n/(x*y))
            else:
                output=0
    if(output==1 and z!=1 and x!=y and y!=z and x!=z):
        print("YES")
        print(x,y,z)
    else:
        print("NO")