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 std::io::Read;
use std::cmp::max;

fn main() {
    let mut buf = String::new();
    std::io::stdin().read_to_string(&mut buf).unwrap();

    let answer = solve(&buf);

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

fn solve(input: &str) -> String {
    let mut iterator = input.split_whitespace();

    let n: usize = iterator.next().unwrap().parse().unwrap();
    let m: usize = iterator.next().unwrap().parse().unwrap();
    let q: usize = iterator.next().unwrap().parse().unwrap();

    let mut queries: Vec<Vec<usize>> = vec![vec![0; 4]; q];
    for i in 0..q {
        let a: usize = iterator.next().unwrap().parse().unwrap();
        let b: usize = iterator.next().unwrap().parse().unwrap();
        let c: usize = iterator.next().unwrap().parse().unwrap();
        let d: usize = iterator.next().unwrap().parse().unwrap();
        queries[i][0] = a;
        queries[i][1] = b;
        queries[i][2] = c;
        queries[i][3] = d;
    }

    let mut ans: usize = 0;

    let mut arrays: Vec<Vec<usize>> = Vec::new();
    let mut buf: Vec<usize> = vec![0; n];
    dfs(0, n, 1, m, &mut buf, &mut arrays);

    for array in arrays.iter() {
        let mut point: usize = 0;
        for query in queries.iter() {
            if array[query[1] - 1] - array[query[0] - 1] == query[2] {
                point += query[3];
            }
        }
        ans = max(ans, point);
    }

    return ans.to_string()
}

fn dfs(i: usize, n: usize, start: usize, end: usize, buf: &mut Vec<usize>, result: &mut Vec<Vec<usize>>) {
    if i == n {
        result.push(buf.clone());
        return;
    } else {
        for j in start..=end {
            buf[i] = j;
            dfs(i + 1, n, j, end, buf, result);
        }
    }
}