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 Rust (1.42.0) (judge verdict: Accepted)

use itertools::Itertools;
use proconio::{derive_readable, fastout, input};

#[derive_readable]
#[derive(PartialEq, Debug, Clone)]
struct Pair {
  a: usize,
  b: usize,
  c: i32,
  d: u32,
}

#[allow(non_snake_case)]
#[fastout]
fn main() {
  input! {
    N: usize,
    M: i32,
    Q: usize,
    pairs: [Pair; Q],
  }

  let mut max_score = 0;
  // {A} := N 個で 1 以上 M 以下の数の組み合わせ
  for A in (1..=M).combinations_with_replacement(N) {
    // A[b] - A[a] が c なら d を得点する
    let pointables = pairs
      .iter()
      .filter(|&Pair { a, b, c, .. }| A[b - 1] - A[a - 1] == *c);
    let score = pointables.map(|&Pair { d, .. }| d).sum();
    max_score = max_score.max(score);
  }
  println!("{}", max_score);
}