Problem:
Score : 500 points

Problem Statement

There are K items placed on a grid of squares with R rows and C columns. Let (i, j) denote the square at the i-th row (1 \leq i \leq R) and the j-th column (1 \leq j \leq C). The i-th item is at (r_i, c_i) and has the value v_i.

Takahashi will begin at (1, 1), the start, and get to (R, C), the goal. When he is at (i, j), he can move to (i + 1, j) or (i, j + 1) (but cannot move to a non-existent square).

He can pick up items on the squares he visits, including the start and the goal, but at most three for each row. It is allowed to ignore the item on a square he visits.

Find the maximum possible sum of the values of items he picks up.

Constraints

1 \leq R, C \leq 3000

1 \leq K \leq \min(2 \times 10^5, R \times C)

1 \leq r_i \leq R

1 \leq c_i \leq C

(r_i, c_i) \neq (r_j, c_j) (i \neq j)

1 \leq v_i \leq 10^9

All values in input are integers.

Input

Input is given from Standard Input in the following format:

R C K
r_1 c_1 v_1
r_2 c_2 v_2
:
r_K c_K v_K

Output

Print the maximum possible sum of the values of items Takahashi picks up.

Sample Input 1

2 2 3
1 1 3
2 1 4
1 2 5

Sample Output 1

8

He has two ways to get to the goal:

Visit (1, 1), (1, 2), and (2, 2), in this order. In this case, the total value of the items he can pick up is 3 + 5 = 8.

Visit (1, 1), (2, 1), and (2, 2), in this order. In this case, the total value of the items he can pick up is 3 + 4 = 7.

Thus, the maximum possible sum of the values of items he picks up is 8.

Sample Input 2

2 5 5
1 1 3
2 4 20
1 2 1
1 3 4
1 4 2

Sample Output 2

29

We have four items in the 1-st row. The optimal choices are as follows:

Visit (1, 1) (1, 2), (1, 3), (1, 4), (2, 4), and (2, 5), in this order, and pick up all items except the one on (1, 2). Then, the total value of the items he picks up will be 3 + 4 + 2 + 20 = 29.

Sample Input 3

4 5 10
2 5 12
1 5 12
2 3 15
1 2 20
1 1 28
2 4 26
3 2 27
4 5 21
3 5 10
1 3 10

Sample Output 3

142

Solution in Java (OpenJDK 11.0.6) (judge verdict: Wrong Answer)

import java.io.DataInputStream;
import java.io.FileInputStream;
import java.io.IOException;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.HashMap;
import java.util.Map;

public class Main {
    static class Reader {
        final private int BUFFER_SIZE = 1 << 16;
        private DataInputStream din;
        private byte[] buffer;
        private int bufferPointer, bytesRead;

        public Reader() {
            din = new DataInputStream(System.in);
            buffer = new byte[BUFFER_SIZE];
            bufferPointer = bytesRead = 0;
        }

        public Reader(String file_name) throws IOException {
            din = new DataInputStream(new FileInputStream(file_name));
            buffer = new byte[BUFFER_SIZE];
            bufferPointer = bytesRead = 0;
        }

        public String readLine() throws IOException {
            byte[] buf = new byte[1_000_000]; // line length
            int cnt = 0, c;
            while ((c = read()) != -1) {
                if (c == '\n')
                    break;
                buf[cnt++] = (byte) c;
            }
            return new String(buf, 0, cnt);
        }

        public int nextInt() throws IOException {
            int ret = 0;
            byte c = read();
            while (c <= ' ')
                c = read();
            boolean neg = (c == '-');
            if (neg)
                c = read();
            do {
                ret = ret * 10 + c - '0';
            } while ((c = read()) >= '0' && c <= '9');

            if (neg)
                return -ret;
            return ret;
        }

        public long nextLong() throws IOException {
            long ret = 0;
            byte c = read();
            while (c <= ' ')
                c = read();
            boolean neg = (c == '-');
            if (neg)
                c = read();
            do {
                ret = ret * 10 + c - '0';
            }
            while ((c = read()) >= '0' && c <= '9');
            if (neg)
                return -ret;
            return ret;
        }

        public double nextDouble() throws IOException {
            double ret = 0, div = 1;
            byte c = read();
            while (c <= ' ')
                c = read();
            boolean neg = (c == '-');
            if (neg)
                c = read();

            do {
                ret = ret * 10 + c - '0';
            }
            while ((c = read()) >= '0' && c <= '9');

            if (c == '.') {
                while ((c = read()) >= '0' && c <= '9') {
                    ret += (c - '0') / (div *= 10);
                }
            }

            if (neg)
                return -ret;
            return ret;
        }

        private void fillBuffer() throws IOException {
            bytesRead = din.read(buffer, bufferPointer = 0, BUFFER_SIZE);
            if (bytesRead == -1)
                buffer[0] = -1;
        }

        private byte read() throws IOException {
            if (bufferPointer == bytesRead)
                fillBuffer();
            return buffer[bufferPointer++];
        }

        public void close() throws IOException {
            if (din == null)
                return;
            din.close();
        }
    }

    void solve(Reader sc, PrintWriter pw) throws IOException {
        int R = sc.nextInt();
        int C = sc.nextInt();
        int K = sc.nextInt();
        R++;
        C++;
        Map<Integer, Integer> values = new HashMap<>();
        for (int i = 0; i < K; i++) {
            int r = sc.nextInt();
            int c = sc.nextInt();
            int v = sc.nextInt();
            values.put(r * C + c, v);
        }

        long[][][] dp = new long[4][R][C];
//        long INF = Long.MAX_VALUE / 10;
//        for (long[][] arrs : dp) {
//            for (long[] arr : arrs) {
//                Arrays.fill(arr, INF);
//            }
//        }
//        dp[0][0][0] = 0;

        long result = 0;
        for (int row = 0; row < R; row++) {
            for (int col = 0; col < C; col++) {
                for (int rowCnt = 0; rowCnt <= 3; rowCnt++) {
//                    if (dp[rowCnt][row][col] == INF) {
//                        continue;
//                    }
                    //no pickup
                    // go right
                    if (col + 1 < C) {
                        dp[rowCnt][row][col + 1] = Math.max(dp[rowCnt][row][col + 1], dp[rowCnt][row][col]);
                    }
                    if (row + 1 < R) {
                        dp[0][row + 1][col] = Math.max(dp[0][row + 1][col], dp[rowCnt][row][col]);
                    }

                    // pickup
                    int key = row * C + col;
                    if (values.containsKey(key)) {
                        int value = values.get(key);
                        // go right
                        if (rowCnt < 3) {
                            if (col + 1 < C) {
                                dp[rowCnt + 1][row][col + 1] = Math.max(dp[rowCnt + 1][row][col + 1], dp[rowCnt][row][col] + value);
                            }

                            if (row + 1 < R) {
                                dp[0][row + 1][col] = Math.max(dp[0][row + 1][col], dp[rowCnt][row][col] + value);
                            }
                        }
                    }
                }
            }
        }

        for (int i = 0; i <= 3; i++) {
            result = Math.max(result, dp[i][R-1][C - 1] + i < 3 ? values.getOrDefault(R * C - 1, 0) : 0);
        }
        pw.println(result);
    }

    public static void main(String[] args) throws IOException {
        Reader sc = new Reader();
//        PrintWriter pw = new PrintWriter(System.out);
        PrintWriter pw = new PrintWriter(System.out, true);
        new Main().solve(sc, pw);
        pw.flush();
        pw.close();
        sc.close();
    }
}