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)

#![allow(non_snake_case)]
// 解説を見た。
use proconio::input;
// use std::collections::HashMap;

fn calc(_N: i64, _M: i64, _Q: i64, abcds: &[(i64, i64, i64, i64)], As: &[i64]) -> i64 {
    return abcds
        .iter()
        .map(|(a, b, c, d)| if As[*b as usize - 1] -
            As[*a as usize - 1] == *c
        {
            *d
        } else {
            0
        })
        .sum();
}

fn main() {
    input! {
        N: i64,
        M: i64,
        Q: i64,
        abcds: [(i64, i64, i64, i64); Q],
    }

    // Mが少ないから、全探索いけるのでは?
    // 単調非減少 10^10くらい? 間に合わじ
    // → 全探索で間に合うらしいです。まじ?

    // 数学の問題だね、重複ありの組み合わせは「しきり」を使って考える
    // 1 ||||| 2 3 4 5 6 7 8 9 ... (M-1)
    // (M + N - 1)_C_N
    // 最大で19C10 → 10万くらい これなら間に合うわー

    // うっ、どうやって書くんだ?
    // しきりを挟むindexをPsで表現する
    let mut stack: Vec<Vec<i64>> = Vec::new();
    stack.push(Vec::new());

    let mut ans = 0i64;

    // スタックからpopして、N個に満たなかったら単調非減少を維持しつつ新しい値をpushする
    while !stack.is_empty() {
        let top = stack.pop().unwrap();

        let len = top.len();
        if len == N as usize {
            // 解決フェーズ
            let As: Vec<i64> = top.iter()
                .enumerate()
                .map(|(ind, &val)| val - ind as i64 + 1)
                .collect();
            let score = calc(N, M, Q, &abcds, &As);

            if score > ans {
                ans = score;
            }
        } else {
            // 追加フェーズ
            let tail: Option<&i64> = if len == 0 { None } else { top.get(len - 1) };
            for i in (*tail.unwrap_or(&-1) + 1)..(N + M - 1) {
                // 新しい配列を生成する点に注意
                let mut new = top.clone();
                new.push(i);
                stack.push(new);
            }
        }

    }

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