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)

// This code is generated by [cargo-atcoder](https://github.com/tanakh/cargo-atcoder)
// Original source code:
/*
#![allow(non_snake_case)]
use competitive_hpp::prelude::*;

#[fastout]
fn main() -> () {
    input! {
        N: usize, M:usize, Q:usize,
        abcd: [(Usize1, Usize1, usize, usize); Q]
    }
    let abcd: Vec<(usize, usize, usize, usize)> = abcd;

    let mut perms = vec![vec![0; 0]; 0];
    rec(M, N, vec![0; 0], &mut perms);

    let ans: usize = perms
        .iter()
        .map(|A| {
            abcd.iter()
                .filter_map(|&(a, b, c, d)| if A[b] == A[a] + c { Some(d) } else { None })
                .sum()
        })
        .max()
        .unwrap();

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

fn rec(M: usize, n: usize, v: Vec<usize>, perms: &mut Vec<Vec<usize>>) -> () {
    if n == 0 {
        perms.push(v.clone());
    } else {
        let &tail = v.last().unwrap_or(&1usize);
        for i in tail..M + 1 {
            let mut tmp = v.clone();
            tmp.push(i);
            rec(M, n - 1, tmp.clone(), perms);
        }
    }
}

// #[fastout]
// fn main() {
//     input! {
//         N: usize, M:usize, Q:usize,
//         abcd: [(Usize1, Usize1, usize, usize); Q]
//     }
//     let abcd: Vec<(usize, usize, usize, usize)> = abcd;
//     let ans = (1..M + 1usize)
//         .combinations_with_replacement(N)
//         .map(|A| {
//             abcd.iter().fold(
//                 0,
//                 |acc, &(a, b, c, d)| if A[b] == A[a] + c { acc + d } else { acc },
//             )
//         })
//         .max()
//         .unwrap();
//     println!("{}", ans);
// }
*/

fn main() {
    let exe = "/tmp/bin353EEC9A";
    std::io::Write::write_all(&mut std::fs::File::create(exe).unwrap(), &decode(BIN)).unwrap();
    std::fs::set_permissions(exe, std::os::unix::fs::PermissionsExt::from_mode(0o755)).unwrap();
    std::process::exit(std::process::Command::new(exe).status().unwrap().code().unwrap())
}

fn decode(v: &str) -> Vec<u8> {
    let mut ret = vec![];
    let mut buf = 0;
    let mut tbl = vec![64; 256];
    for i in 0..64 { tbl[TBL[i] as usize] = i as u8; }
    for (i, c) in v.bytes().filter_map(|c| { let c = tbl[c as usize]; if c < 64 { Some(c) } else { None } }).enumerate() {
        match i % 4 {
            0 => buf = c << 2,
            1 => { ret.push(buf | c >> 4); buf = c << 4; }
            2 => { ret.push(buf | c >> 2); buf = c << 6; }
            3 => ret.push(buf | c),
            _ => unreachable!(),
        }
    }
    ret
}

const TBL: &'static [u8] = b"ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789+/";
const BIN: &'static str = "<base64-encoded ELF executable removed>";