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: Runtime Error)

#![allow(dead_code, unused_imports, deprecated)]
use std::cmp::{max, min, Reverse};

use maplit::*;

use permutohedron::*;

use proconio::{input, fastout};
use proconio::marker::*;


const INF: usize = 1_000_000_007;
const MOD: usize = 2019;

#[fastout]
fn solve() {
  input! {
    n: usize, m: usize, q: usize,
    ps: [(usize, usize, usize, usize); q],
  };

  let mut seq = vec![1usize; n + m - 1];
  for i in 0..n {
    seq[i] = 0;
  }

  let mut h = Heap::new(&mut seq);
  let mut res = 0usize;
  while let Some(perm) = h.next_permutation() {
    let mut z_cnt = 0usize;
    let mut an = vec![];
    for j in 0..n + m - 1 {
      if perm[j] == 0 {
        z_cnt += 1;
      } else {
        an.push(z_cnt);
      }
    }

    let mut score = 0usize;
    for p in &ps {
      let (a, b, c, d) = p;
      if an[b - 1] - an[a - 1] == *c {
        score += d;
      }
    }
    
    res = max(res, score);
  }
  
  println!("{}", res);
}

fn main() {
  std::thread::Builder::new()
    .name("big stack size".into())
    .stack_size(32 * 1024 * 1024)
    .spawn(|| {
      solve();
    })
    .unwrap()
    .join()
    .unwrap();
}