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:
def dividened(number,dict1):
    for i in range(2,int((number)**(1/2))+1):
        if number%i==0 and dict1.get(i)==None:
            dict1[i] = 1
            return number//i,i,dict1
    
        
    return 1,number,dict1
        
        

for _ in range(int(input())):
    number = int(input())
    d = []
    case=  True
    dict1 = {}
    for i in range(2):
        number,op,dict1=  dividened(number,dict1)
        
        if number==1 :
            print("NO")
            case = False
            break
        else:
            d.append(op)
            
    if dict1.get(number)==None:
        d.append(number)
    else:
        case = False
        print("NO")
               
            
    if case:
        print("YES")
        print(*d)