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(unused_imports)]
#![allow(non_snake_case)]
use std::cmp::*;
use std::collections::*;
use std::io::Write;

#[allow(unused_macros)]
macro_rules! debug {
    ($($e:expr),*) => {
        #[cfg(debug_assertions)]
        $({
            let (e, mut err) = (stringify!($e), std::io::stderr());
            writeln!(err, "{} = {:?}", e, $e).unwrap()
        })*
    };
}

fn dfs(
    array: &mut Vec<usize>,
    n: usize,
    cur: usize,
    queries: &Vec<Vec<(usize, usize, i64)>>,
    m: usize,
) -> i64 {
    if cur == n {
        return 0;
    }
    let mut cands_point = HashMap::new();
    cands_point.insert(array[cur - 1], 0);
    for &(a, c, d) in queries[cur].iter() {
        let cand = array[a] + c;
        if cand <= m && cand >= array[cur - 1] {
            *cands_point.entry(cand).or_insert(0) += d;
        }
    }
    let mut ret = 0;
    for &cand in cands_point.keys() {
        array[cur] = cand;
        let temp = dfs(array, n, cur + 1, queries, m);
        ret = max(ret, temp + cands_point[&cand]);
    }

    ret
}

fn main() {
    let v = read_vec::<usize>();
    let (n, m, q) = (v[0], v[1], v[2]);
    let mut queries = vec![vec![]; n];
    for i in 0..q {
        let v = read_vec::<i64>();
        let (a, b, c, d) = (v[0] as usize - 1, v[1] as usize - 1, v[2] as usize, v[3]);
        queries[b].push((a, c, d));
    }
    let mut array = vec![1; n];
    let ans = dfs(&mut array, n, 1, &queries, m);
    println!("{}", ans);
}

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()
}