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)

macro_rules! parse_line {
    [$( $x:tt : $t:ty ),+] => {
        //declare variables
        $( let $x: $t; )+
        {
            use std::str::FromStr;
            // read
            let mut buf = String::new();
            std::io::stdin().read_line(&mut buf).unwrap();
            #[allow(deprecated)]
            let mut splits = buf.trim_right().split_whitespace();
            // assign each variable
            $(
                $x = splits.next().and_then(|s| <$t>::from_str(s).ok()).unwrap();
            )+
            // all strs should be used for assignment
            assert!(splits.next().is_none());
        }
    };
}

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

fn main() {
    parse_line![n: usize, m: usize, q: usize];

    let queries = {
        let mut temp = vec![];
        for _ in 0..q {
            parse_line![a: usize, b: usize, c: usize, d: usize];
            temp.push(Query {
                a: a,
                b: b,
                c: c,
                d: d,
            });
        }
        temp
    };

    let mut max_score = 0;
    let mut nums = vec![1; n];

    loop {
        let score = queries
            .iter()
            .filter(|&&Query { a, b, c, .. }| nums[b - 1] - nums[a - 1] == c)
            .map(|&Query { d, .. }| d)
            .sum::<usize>();

        max_score = std::cmp::max(max_score, score);

        if next_nums(&mut nums, m).is_none() {
            break;
        }
    }

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

fn next_nums(nums: &mut [usize], m: usize) -> Option<()> {
    let len = nums.len();
    // この位の値をカウントアップ
    nums[len - 1] += 1;
    if nums[len - 1] > m {
        // これ以上位上げができなければ終了
        if len - 1 == 0 {
            None
        } else {
            // 次の位をカウントアップ
            next_nums(&mut nums[..len - 1], m)?;
            // この数列は単調非減少だから
            // この位の値が次の位の値と同じになるようにする
            nums[len - 1] = nums[len - 2];
            Some(())
        }
    } else {
        Some(())
    }
}