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: Wrong Answer)

extern crate proconio;
use proconio::input;

fn main() {
  input! {
    n: usize,
    m: u32,
    q: u32
  }
  let mut abcd: Vec<(usize, usize, u32, u32)> = vec![];
  let mut aa: Vec<u32> = vec![0];
  
  for _ in 0..q {
    input! {
      a: usize,
      b: usize,
      c: u32,
      d: u32,
    }
    abcd.push((a,b,c,d));
  }
  
  println!("{}", resolve(&mut aa, &abcd, n, m));
}

fn resolve(
  aa: &mut Vec<u32>,
  abcd: &Vec<(usize, usize, u32, u32)>,
  n: usize,
  m: u32
) -> u32 {
  if aa.len() > n + 1 {
    score(aa, abcd)
  } else {
    let mut ans: u32 = 0;
    for k in aa[aa.len()-1]..(m+1) {
      aa.push(k);
      ans = ans.max(resolve(aa, abcd, n, m));
      aa.pop();
  	}
    ans
  }
}

fn score(aa: &Vec<u32>, abcd: &Vec<(usize, usize, u32, u32)>) -> u32 {
  let mut ans: u32 = 0;
  for (a,b,c,d) in abcd {
    if aa[*b] - aa[*a] == *c {
      ans += d;
    }
  }
  ans
}