Problem:
Score : 300 points

Problem Statement

Given are positive integers N, M, Q, and Q quadruples of integers ( a_i , b_i , c_i , d_i ).

Consider a sequence A satisfying the following conditions:

A is a sequence of N positive integers.

1 \leq A_1 \leq A_2 \le \cdots \leq A_N \leq M.

Let us define a score of this sequence as follows:

The score is the sum of d_i over all indices i such that A_{b_i} - A_{a_i} = c_i. (If there is no such i, the score is 0.)

Find the maximum possible score of A.

Constraints

All values in input are integers.

2 ≤ N ≤ 10

1 \leq M \leq 10

1 \leq Q \leq 50

1 \leq a_i < b_i \leq N ( i = 1, 2, ..., Q )

0 \leq c_i \leq M - 1 ( i = 1, 2, ..., Q )

(a_i, b_i, c_i) \neq (a_j, b_j, c_j) (where i \neq j)

1 \leq d_i \leq 10^5 ( i = 1, 2, ..., Q )

Input

Input is given from Standard Input in the following format:

N M Q
a_1 b_1 c_1 d_1
:
a_Q b_Q c_Q d_Q

Output

Print the maximum possible score of A.

Sample Input 1

3 4 3
1 3 3 100
1 2 2 10
2 3 2 10

Sample Output 1

110

When A = \{1, 3, 4\}, its score is 110. Under these conditions, no sequence has a score greater than 110, so the answer is 110.

Sample Input 2

4 6 10
2 4 1 86568
1 4 0 90629
2 3 0 90310
3 4 1 29211
3 4 3 78537
3 4 2 8580
1 2 1 96263
1 4 2 2156
1 2 0 94325
1 4 3 94328

Sample Output 2

357500

Sample Input 3

10 10 1
1 10 9 1

Sample Output 3

1

Solution in OCaml (4.10.0) (judge verdict: Time Limit Exceeded)

open Batteries
(* 重複順列 *)
let rec dup_perm n lst =
  if n = 0 then [[]]
  else flatmap (fun x -> List.map (fun y -> x :: y)
                                  (dup_perm (n - 1) lst))
               lst
and flatten = function
  [] -> []
| x::xs -> x @ (flatten xs)
and flatmap func ls = flatten (List.map func ls)


let n, m, q = Scanf.sscanf (read_line()) "%d %d %d" (fun n m q ->
  n, m, q
)
let abcd = List.init q @@ fun a ->Scanf.sscanf (read_line()) "%d %d %d %d" (fun a b c d ->
  (a,b,c,d)
)

let a_list = dup_perm n @@ List.init m @@ fun b -> b+1


let rec check target lst ans =
  match lst with
  | [] -> ans
  | first :: rest ->
    let a,b,c,d = first in
    if target.(b-1) - target.(a-1) = c then check target rest (d+ans) else check target rest ans


let rec loop lst ans =
  match lst with
  | [] -> ans
  | first :: rest -> (
    let target = List.sort compare first |> Array.of_list in
    let r = check target abcd 0 in if r > ans then loop rest r else loop rest ans
  )

let _ = Printf.printf "%d\n" @@ loop a_list 0