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;
use std::cmp;
use std::collections::BinaryHeap;
use std::collections::HashMap;
use std::collections::HashSet;
use std::f64::consts::PI;

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

fn calc(a: &Vec<usize>, qs: &Vec<(usize,usize,usize,usize)>) -> usize {
    let mut res = 0;
    for &q in qs.iter() {
        if a[q.1] -  a[q.0] == q.2 {
            res += q.3;
        }
    }

    res
}

fn next(a: &mut Vec<usize>, m: usize) -> bool {
    for i in (0..a.len()).rev() {
        if a[i] < m {
            a[i] += 1;
            for j in i+1..a.len() {
                a[j] = a[i];
            }

            return true;
        }
    }
    false
}


fn main() {
    let line: Vec<usize> = read_line().split_whitespace().map(|s| s.parse().unwrap()).collect();
    let n = line[0];
    let m = line[1];
    let q = line[2];
    let mut qs = Vec::new();
    for i in 0..q {
        let line: Vec<usize> = read_line().split_whitespace().map(|s| s.parse().unwrap()).collect();
        let a = line[0]-1;
        let b = line[1]-1;
        let c = line[2];
        let d = line[3];

        qs.push((a,b,c,d));
    }

    let mut a = vec![1; n];
    let mut ans = 0;
    loop {

        ans = cmp::max(ans, calc(&a, &qs));
        if !next(&mut a, m) {
            break;
        }
    }

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