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(unused_imports)]
use std::io::{stdout, Write, BufWriter};
#[allow(unused_imports)]
use std::cmp::{max, min, Ordering};
#[allow(unused_imports)]
use proconio::marker::{Isize1, Usize1, Bytes, Chars};

#[proconio::fastout]
fn main() {
    proconio::input!{
        n: usize,
        m: i32,
        q: usize,
        abcd: [(Usize1, Usize1, i32, i32); q],
    }
    let tmp: Vec<i32> = vec![];
    let mut seqs: Vec<Vec<i32>> = vec![];
    gen_seqs(1..=m, n, tmp, &mut seqs);
    let mut ans = 0;
    // eprintln!("{:?}", seqs);
    for seq in seqs {
        let point: i32 = abcd.iter().map(|(a, b, c, d)| {
            if seq[*b] - seq[*a] == *c { *d }
            else { 0 }}).sum();
        ans = max(ans, point);
    }
    println!("{}", ans);
}

// range: a..=b にたいして a <= a1 <= ... <= an <= b を満たす数列を列挙
// 呼び出し時には空のベクトル: Vec<i32> を渡す
use std::ops::RangeInclusive;
fn gen_seqs(range: RangeInclusive<i32>, n: usize, state: Vec<i32>, res: &mut Vec<Vec<i32>>) {
    if n == 0 {
        res.push(state);
        return;
    }
    let end = *range.end();
    for i in range {
        let mut state = state.clone();
        state.push(i);
        gen_seqs(i..=end, n - 1, state, res);
    }
}