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 Kotlin (1.3.71) (judge verdict: Wrong Answer)

var a: Array<Int> = arrayOf()
var b: Array<Int> = arrayOf()
var c: Array<Int> = arrayOf()
var d: Array<Int> = arrayOf()

fun main() {
    val l = readLine()!!.split(' ').map { it.toInt() }
    a = Array(l[2]) { 0 }
    b = Array(l[2]) { 0 }
    c = Array(l[2]) { 0 }
    d = Array(l[2]) { 0 }
    for (i in 0 until l[2]) {
        val line = readLine()!!.split(' ').map { it.toInt() }
        a[i] = line[0]-1
        b[i] = line[1]-1
        c[i] = line[2]
        d[i] = line[3]
    }
    var arr = Array(l[0]) { 1 }
    var max = 0
    for (s in l[0]-1 downTo 0) {
        for (t in 1..l[1]) {
            arr[s] = t
            max = Math.max(max, eval(arr))
        }
    }
    println(max)
}

fun eval(arr: Array<Int>): Int {
    var res = 0
    for (x in 0 until a.size) {
        if (arr[b[x]]-arr[a[x]] == c[x]) {
            res += d[x]
        }
    }
    return res
}