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:
t = int(input())


for qwe in range(t):
    
    # n1 = int(f.readline())
    n1 = int(input())
    
    flag = False
    
    for i1 in range(2, int(n1**0.5) + 1):
        if n1 % i1 == 0:
            a = i1
            n2 = n1 // i1
            
            for i2 in range(2, int(n2**0.5) + 1):
                if n2 % i2 == 0 and i2 != a:
                    b = i2
                    c = n2 // i2
                    
                    if c != a and c != b:
                        flag = True
                
                if flag:
                    break
            
        if flag:
            break
    
    if flag:
        print("YES")
        print(a, b, c)
    else:
        print("NO")