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 input::{Input, ReadMode};
type ABCD = (usize, usize, usize, usize);

fn main() {
    let mut input = Input::new(ReadMode::Line);

    let n: usize = input.parse();
    let m: usize = input.parse();
    let q: usize = input.parse();
    let v = (0..q)
        .map(|_| (input.parse(), input.parse(), input.parse(), input.parse()))
        .collect::<Vec<ABCD>>();

    let mut ans = 0;
    dfs(n, m, &v, vec![1], &mut ans);
    println!("{}", ans);
}

fn dfs(n: usize, m: usize, v: &Vec<ABCD>, mut a: Vec<usize>, ans: &mut usize) {
    if a.len() == n + 1 {
        let mut tmp = 0;
        for e in v {
            if a[e.1] - a[e.0] == e.2 {
                tmp += e.3;
            }
        }
        *ans = *ans.max(&mut tmp);
        return;
    }
    let l = a.len();
    a.push(a[l - 1]);
    while a[l] <= m {
        dfs(n, m, v, a.clone(), ans);
        a[l] += 1;
    }
}

#[allow(dead_code)]
pub mod input {
    use std::io::{BufRead, Read};

    pub enum ReadMode {
        Full,
        Line,
    }

    pub struct Input<'a> {
        lock: std::io::StdinLock<'static>,
        iter: Option<std::str::SplitAsciiWhitespace<'a>>,
        mode: ReadMode,
    }

    impl<'a> Input<'a> {
        fn naive_read(&mut self) -> Option<std::str::SplitAsciiWhitespace<'a>> {
            let mut s = Box::leak(Box::new(String::new()));
            let res = match self.mode {
                ReadMode::Full => self.lock.read_to_string(&mut s),
                ReadMode::Line => self.lock.read_line(&mut s),
            };
            res.ok().expect("failed to read");
            Some(s.split_ascii_whitespace())
        }
        pub fn new(mode: ReadMode) -> Self {
            let lock = Box::leak(Box::new(std::io::stdin())).lock();
            let iter = None;
            Self { lock, iter, mode }
        }
        pub fn read_line(&mut self) -> String {
            let mut s = String::new();
            self.lock.read_line(&mut s).ok().expect("failed to read");
            s
        }
        pub fn parse<T: std::str::FromStr>(&mut self) -> T {
            match &mut self.iter {
                Some(iter) => {
                    let x = match iter.next() {
                        Some(x) => x,
                        None => {
                            self.iter = self.naive_read();
                            self.iter.as_mut().unwrap().next().expect("reached EOF")
                        }
                    };
                    x.parse().ok().expect("failed to parse")
                }
                None => {
                    self.iter = self.naive_read();
                    self.parse()
                }
            }
        }
    }
}