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::str::FromStr;

fn read<T: FromStr>() -> T {
    let stdin = stdin();
    let stdin = stdin.lock();
    let token: String = stdin
        .bytes()
        .map(|c| c.expect("failed to read char") as char) 
        .skip_while(|c| c.is_whitespace())
        .take_while(|c| !c.is_whitespace())
        .collect();
    token.parse().ok().expect("failed to parse token")
}

fn next(nums: &mut [i32], m: i32) -> bool {
    let mut changed_i = 10000;
    let mut changed_to = 0;
    for i in (0..nums.len()).rev() {
        if nums[i] < m {
            nums[i] += 1;
            changed_i = i;
            changed_to = nums[i];
            break;
        }
    }
    if changed_i == 10000 {
        return false;
    } else {
        for i in changed_i..nums.len() {
            nums[i] = changed_to;
        }
    }
    return true;
}

fn score(nums: &[i32], crit: &[(usize, usize, i32, i32)]) -> i32 {
    let mut sum = 0;
    for &(a, b, c, d) in crit {
        //dbg!((a, b, c, d));
        if nums[b-1] - nums[a-1] == c {
            sum += d;
        }
    }
    sum
}

fn main() {
    let n: usize = read();
    let m: i32 = read();
    let q: i32 = read();

    let mut crit: Vec<(usize, usize, i32, i32)> = Vec::new();
    for _ in 0..q {
        crit.push((read(), read(), read(), read()));
    }

    let mut nums = vec![1; n];
    let mut max_score = 0;
    loop {
        max_score = std::cmp::max(max_score, score(&mut nums, &mut crit));

        if !next(&mut nums, m) {
            break;
        }
    }

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