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: Wrong Answer)

use proconio::{input, marker::Usize1};
use std::cmp;

fn main() {
    input! {
        n: usize,
        m: usize,
        q: usize,
        abcds: [(Usize1, Usize1, usize, u64); q],
    }

    let mut dp = vec![vec![0; m]; n];
    for i in 0..n - 1 {
        for j in 0..m {
            dp[i + 1][j] = cmp::max(dp[i + 1][j], dp[i][j]);
            for k in j + 1..m {
                let abcds = abcds
                    .iter()
                    .copied()
                    .filter(|&(a, _, c, _)| a == i && j + c <= k)
                    .collect::<Vec<_>>();
                if !abcds.is_empty() && abcds.iter().any(|(_, _, c, _)| j + c == k) {
                    dp[i + 1][k] = cmp::max(
                        dp[i + 1][k],
                        dp[i][j] + abcds.into_iter().map(|(_, _, _, d)| d).sum::<u64>(),
                    );
                }
            }
        }
    }
    println!("{}", dp[n - 1].iter().max().unwrap());
}