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 JavaScript (Node.js 12.16.1) (judge verdict: Accepted)

const input = require("fs").readFileSync("/dev/stdin", "utf8")
const lines = input.split('\n')
const [N, M, Q] = lines[0].split(' ').map(Number)
const q = Array(Q)
for (let i = 0; i < Q; i++) {
    q[i] = lines[i + 1].split(' ').map(Number)
}

const f = (A) => {
    let sum = 0
    for (let i = 0; i < Q; i++) {
        const a = A[q[i][0] - 1]
        const b = A[q[i][1] - 1]
        if (b - a === q[i][2]) {
            sum += q[i][3]
        }
    }
    return sum
}

const ss = []
const s = []
let v = 0
while (v !== undefined) {
    if (s.length === N) {
        ss.push([...s])
        s.pop()
        v++
    } else if (v >= M) {
        v = s.pop()
    } else {
        s.push(v + 1)
    }
}

let A = null
let ans = 0
while (A = ss.pop()) {
   ans = Math.max(ans, f(A)) 
}

console.log(ans)