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 Lua (Lua 5.3.5) (judge verdict: Accepted)

local n,m,q=io.read("n","n","n")
local a,b,c,d={},{},{},{}
for i=1,q do
    a[i],b[i],c[i],d[i]=io.read("n","n","n","n")
end

local t={}
for i=1,10 do
    t[i]={}
end
for i=1,m do
    table.insert(t[1],{i})
end

for i=1,n-1 do
    for j,_ in pairs(t[i]) do
        local x=t[i][j]
        local p=x[#x]
        for k=p,m do
            local U={}
            for l=1,#x do
                U[l]=x[l]
            end
            table.insert(U,k)
            table.insert(t[i+1],U)
        end
    end
end

local answer=0
for _,T in pairs(t[n]) do
    local total=0
    for i=1,q do
        if T[b[i]]-T[a[i]]==c[i] then
            total=total+d[i]
        end
    end
    answer=math.max(answer,total)
end
print(answer)