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) : 
  
    # Corner cases 
    if (n <= 1) : 
        return False
    if (n <= 3) : 
        return True
  
    # This is checked so that we can skip  
    # middle five numbers in below loop 
    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
def print_factors(x):
    num=0
    fac=1
    li=[]
    tri=x
    for i in range(2, int(math.sqrt(x))+1):
        if tri % i == 0:
            num+=1
            fac = fac*i
            li.append(i)
            tri = tri/i
            if(num==2):
                break
    if(x%fac==0):
        if(int(x/fac)>i):
            li.append(int(x/fac))
    return li
           
isp= False
num = int(input())
 
for i in range(num):
    lis=[]
    a = int(input())
    if(a>=2):
        isp = isPrime(a)
        if(isp==True):
            print("NO")
        else:
            #print("YES")
            lis = print_factors(a)
            if(len(lis)==3):
                print("YES")
                for i in range(2):
                    print(lis[i],end=" ")
                print(lis[i+1])
            else:
                print("NO")
    else:
        print("NO")