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 std::vec::Vec;

fn read<T: std::str::FromStr>() -> T {
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).ok();
    s.trim().parse().ok().unwrap()
}

fn read_vec<T: std::str::FromStr>() -> Vec<T> {
    read::<String>().split_whitespace().map(|e| e.parse().ok().unwrap()).collect()
}

fn read_touple3<T: std::str::FromStr + Copy>() -> (T, T, T) {
  let v: Vec<T> = read_vec();
  assert_eq!(v.len(), 3);
  (v[0], v[1], v[2])
}

fn read_touple4<T: std::str::FromStr + Copy>() -> (T, T, T, T) {
  let v: Vec<T> = read_vec();
  assert_eq!(v.len(), 4);
  (v[0], v[1], v[2], v[3])
}

fn main() {
   use std::cmp::max;
    let (n, m, q) = read_touple3::<usize>();
    let mut Q = vec![];
    for _ in 0..q {
      let (a, b, c, d) = read_touple4::<usize>();
      Q.push((a- 1, b  - 1, c, d));
    }


    let mut vs = vec![];
    make_vec(m, n, 0, 1, vec![], &mut vs);
    let mut ans = 0;
    for v in &vs {
      let mut hoge = 0;
      for &(a, b, c, d) in &Q {
        if v[b] - v[a] == c {
          hoge += d;
        }
      }

      ans = max(ans, hoge);
    }

    println!("{}", ans);

}

fn make_vec(m: usize, n: usize, pos: usize, now: usize, v: Vec<usize>, data: &mut Vec<Vec<usize>>) {
    if pos == n {
      data.push(v);
      return
    }

    for i in now..=m {
      let mut t = v.clone();
      t.push(i);
      make_vec(m, n, pos+1, i, t, data);
    }
}