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::derive_readable;
use proconio::input;

#[derive_readable]
#[derive(Debug, Clone, Copy)]
struct Query {
    a: usize,
    b: usize,
    c: usize,
    d: i32,
}

fn main() {
    input! {
        n: usize,
        m: usize,
        q: usize,
        qu: [Query; q]
    };
    let mut qb = vec![Vec::new(); 11];
    for q in qu.iter() {
        qb[q.b].push(q);
    }
    let mut ans = 0;
    let mut queue = std::collections::VecDeque::new();
    queue.push_back((0_usize, 0_i32, vec![1_usize]));

    while !queue.is_empty() {
        let (i, s, seq) = queue.pop_front().unwrap();
        ans = std::cmp::max(ans, s);
        if i == n {
            continue;
        }
        for j in seq[i] ..= m {
            let mut seq = seq.clone();
            seq.push(j);
            let s = qb[i + 1].iter().fold(s, |s, q| {
                if seq[q.b] - seq[q.a] == q.c {
                    s + q.d
                } else {
                    s
                }
            });
            let state = (i + 1, s, seq);
            queue.push_back(state);
        }
    }
    println!("{:?}", ans);
}