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;

fn read_line() -> String {
    let mut buf = String::new();
    io::stdin().read_line(&mut buf).expect("");
    buf.trim().to_string()
}

fn read_i32() -> i32 {
    read_line().parse().expect("")
}

fn read_vi32() -> Vec<i32> {
    read_line().split(' ').into_iter()
        .map(|w| w.parse().expect(""))
        .collect()
}

fn main() {
    let tmp = read_vi32();
    let n = tmp[0];
    let m = tmp[1];
    let q = tmp[2];

    let mut arr = vec![0; n as usize];

    let mut va = vec![];
    let mut vb = vec![];
    let mut vc = vec![];
    let mut vd = vec![];
    for i in 0..q {
        if let &[a, b, c, d] = &read_vi32()[..] {
            va.push(a-1);
            vb.push(b-1);
            vc.push(c);
            vd.push(d);
        }
    }

    let mut i = 0;
    let mut ans = 0;
    loop {
        if i == -1 {
            break;
        } else if i == n {
            let mut tmp = 0;
            for j in 0..va.len() {
                if arr[vb[j] as usize] - arr[va[j] as usize] == vc[j] {
                    tmp += vd[j];
                }
            }

            if ans < tmp {
                ans = tmp;
            }
            
            i -= 1;
        } else if arr[i as usize] == m {
            arr[i as usize] = 0;
            i -= 1;
        } else if i >= 1 && arr[i as usize] < arr[i as usize - 1] {
            arr[i as usize] = arr[i as usize - 1];
            i += 1;
        } else {
            arr[i as usize] += 1;
            i += 1;
        }
    }

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