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 proconio::input;

#[allow(unused_imports)]
use proconio::marker::{Bytes, Chars, Usize1};
#[allow(unused_imports)]
use std::cmp::*;
#[allow(unused_imports)]
use std::collections::*;
#[allow(unused_imports)]
use std::ops::*;

#[derive(Clone, Debug, Default)]
struct Struct;

fn dfs(a: &mut Vec<usize>, i: usize, n:usize, m: usize, bq: &Vec<Vec<(usize, usize, i32, usize)>>, score:usize) -> usize {
    let mut val_to_score = vec![0; m + 1];
    for v in &bq[i] {
        let good_val = a[v.0] + v.2 as usize;
        if good_val <= m {
            val_to_score[good_val] += v.3;
        }
    }
    let mut max_score = 0;
    for val in a[i-1]..=m {
        if val == a[i-1] || val_to_score[val] != 0 {
            a[i] = val;
            if i == n-1 {
                max_score = max(max_score, score + val_to_score[val]);
            } else {
                max_score = max(max_score,dfs(a, i+1, n, m, bq, score + val_to_score[val]));
            }
        }
    }
    max_score
}

//#[proconio::fastout]
fn main() {
    input! {
        n: usize,
        m: usize,
        q: usize,
        v: [(Usize1,Usize1,i32,usize);q],
    }

    let mut bq = vec![Vec::new(); n];
    for i in 0..q {
        let b = v[i].1;
        bq[b].push(v[i]);
    }

    let mut a = vec![1; n];
    let ans = dfs(&mut a, 1, n, m, &bq, 0);

    println!("{}", ans);
}