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)

#![allow(dead_code)]
#![allow(unused_imports)]
#![allow(non_camel_case_types)]
#![allow(non_snake_case)]
use ascii::{AsciiChar, AsciiStr, AsciiString};
use indexmap::IndexMap;
use itertools::*;
use libm::*;
use num::*;
use ordered_float::OrderedFloat;
use permutohedron::LexicalPermutation;
use proconio::marker::{Bytes, Chars};
use proconio::{fastout, input};
use std::cmp::{max, min, Ordering};
use std::collections::{BTreeMap, BTreeSet, BinaryHeap, HashMap, HashSet, VecDeque};
use std::mem::swap;

type query = (usize, usize, usize, usize);

fn calc(q: &Vec<query>, A: &Vec<usize>) -> usize {
    let mut res = 0;
    for (a, b, c, d) in q.iter() {
        if A[*b] - A[*a] == *c {
            res += *d
        }
    }
    res
}

fn dfs((q, n, m): (&Vec<query>, usize, usize), A: &mut Vec<usize>, res: &mut usize) {
    if A.len() > n {
        let p = calc(q, A);
        *res = max(*res, p);
        return
    }
    let e = A.last().unwrap();
    for i in *e..=m {
        A.push(i);
        dfs((q, n, m), A, res);
        A.pop();
    }

}

fn main() {
    input!(n:usize, m:usize, q:usize, v:[(usize, usize, usize, usize); q]);
    let mut A = vec![1];
    let mut ans = 0;
    dfs((&v, n, m), &mut A, &mut ans);
    println!("{}", ans);
}