Problem:
Score : 100 points

Problem Statement

Taro's summer vacation starts tomorrow, and he has decided to make plans for it now.

The vacation consists of N days.
For each i (1 \leq i \leq N), Taro will choose one of the following activities and do it on the i-th day:

A: Swim in the sea. Gain a_i points of happiness.

B: Catch bugs in the mountains. Gain b_i points of happiness.

C: Do homework at home. Gain c_i points of happiness.

As Taro gets bored easily, he cannot do the same activities for two or more consecutive days.

Find the maximum possible total points of happiness that Taro gains.

Constraints

All values in input are integers.

1 \leq N \leq 10^5

1 \leq a_i, b_i, c_i \leq 10^4

Input

Input is given from Standard Input in the following format:

N
a_1 b_1 c_1
a_2 b_2 c_2
:
a_N b_N c_N

Output

Print the maximum possible total points of happiness that Taro gains.

Sample Input 1

3
10 40 70
20 50 80
30 60 90

Sample Output 1

210

If Taro does activities in the order C, B, C, he will gain 70 + 50 + 90 = 210 points of happiness.

Sample Input 2

1
100 10 1

Sample Output 2

100

Sample Input 3

7
6 7 8
8 8 3
2 5 2
7 8 6
4 6 8
2 3 4
7 5 1

Sample Output 3

46

Taro should do activities in the order C, A, B, A, C, B, A.

Solution in C# (.NET Core 3.1.201) (judge verdict: Wrong Answer)

using System;
using System.Collections;
using System.Collections.Generic;

using System.Linq;
public class dp_c {

    static DateTime START_TIME;
#if !MYTEST
    public static void Main() {
        START_TIME = DateTime.Now;
        System.Console.WriteLine(Answer());
    }
    public static void debugOut(string str) { }
    public static string ReadLine(){
        return System.Console.ReadLine();
    }
#endif
    public static string Answer() {
        var p = ReadLine().Trim().Split(' ');
        //              1234567890
        // int.MaxValue=2147483647
        var N = int.Parse(p[0]);
        var happy = new int[N, 3];
        var dp = new int[N];
        var acts = new int[N];
        var result = "";
        for (var i = 0; i < N; i++) {
            p = ReadLine().Trim().Split(' ');
            for (var j = 0; j < p.Length; j++) {
                happy[i, j] = int.Parse(p[j]);
            }
            dp[i] = 0;
        }
        var lastActivity = -1;
        dp[0] = 0;
        for (var i = 0; i < N; i++) {
            if (i > 0) {
                lastActivity = acts[i - 1]; //前日の動作
            }
            for (var j = 0; j < happy.GetLength(1); j++) {
                if (j != lastActivity) {
                    var pre = dp[i];
                    dp[i] = Math.Max(dp[i], happy[i, j]);
                    if (dp[i] != pre) {
                        acts[i] = j;
                    }
                }
            }
        }
        result = dp.Sum().ToString();
        return result;
    }

    #region LOCAL
#if MYTEST
    static System.IO.StreamReader FS = null;
    public static void Main() {
        START_TIME = DateTime.Now;
        if (System.IO.File.Exists("dp_c.txt")) {
            FS = new System.IO.StreamReader("dp_c.txt");
        }
        try {
            while (true) {
                START_TIME = DateTime.Now;
                var testcase = seekNextCase();
                if (!string.IsNullOrEmpty(testcase)) {
                    debugOut($"TEST > {testcase}\n");
                }
                var ans = Answer();
                System.Console.WriteLine(ans);  // debug
                debugOut($"{(DateTime.Now - START_TIME).TotalMilliseconds} msec.\n");
                if (FS != null && !FS.EndOfStream) {
                    var expect = ReadLine();
                    var res = "";
                    if (ans == expect) {
                        res = "OK";
                        Console.ForegroundColor = ConsoleColor.Green;
                    } else {
                        res = "NG";
                        Console.ForegroundColor = ConsoleColor.Red;
                    }
                    debugOut($"{testcase} {res} expect={expect} actual={ans}\n");
                    System.Console.ResetColor();
                }
            }
        } finally {
            System.Console.ResetColor();
            if (FS != null) FS.Close();
        }
    }
    public static void debugOut(string str) {
        System.Console.Error.Write(str);
    }
    public static string ReadLine() {
        if (FS != null && !FS.EndOfStream) {
            var line = FS.ReadLine();
            // debugOut(line + "\n");
            if (FS.EndOfStream) {
                FS.Close();
                FS = null;
            }
            return line;
        }
        debugOut("\nuser input>\n");
        return System.Console.ReadLine();
    }
    public static string seekNextCase() {
        while (FS != null) {
            var line = ReadLine();
            if (line.StartsWith("---")) {
                return line;
            }
        }
        return null;
    }
#endif
    #endregion
}