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 Haskell (GHC 8.8.3) (judge verdict: Accepted)

{-# OPTIONS_GHC -O2 #-}
{-# LANGUAGE TypeApplications #-}
{-# LANGUAGE Strict #-}
{-# LANGUAGE StrictData #-}
import qualified Data.Vector.Unboxed as VU
import qualified Data.Vector.Unboxed.Mutable as VUM
import Data.Array.Unboxed
import Data.Array.ST
import qualified Data.ByteString.Char8 as BS
import Control.Monad
import Data.List
import Data.Char

main :: IO ()
main = do
    (n,m,q) <- (\vec -> (vec VU.! 0, vec VU.! 1, vec VU.! 2)) . VU.unfoldrN 3 (BS.readInt . BS.dropWhile isSpace) <$> BS.getLine
    vec <- VU.replicateM q $ (\vec -> (vec VU.! 0, vec VU.! 1, vec VU.! 2, vec VU.! 3)) . VU.unfoldrN 4 (BS.readInt . BS.dropWhile isSpace) <$> BS.getLine
    let all :: [[Int]]
        all = [ [x1,x2,x3,x4,x5,x6,x7,x8,x9,x10] | x1 <- [1..m], x2 <- [x1..m], x3 <- [x2..m], x4 <- [x3..m], x5 <- [x4..m], x6 <- [x5..m], x7 <- [x6..m], x8 <- [x7..m], x9 <- [x8..m], x10 <- [x9..m]]
    let solve :: [Int] -> [(Int,Int,Int,Int)] -> Int
        solve _ []      = 0
        solve xs ((a,b,c,d):ys) = if (xs !! (b-1)) - (xs !! (a-1)) == c then d+(solve xs ys) else solve xs ys
    print $ maximum [ solve xs (VU.toList vec) | xs <- map (take n) all]