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 Java (OpenJDK 11.0.6) (judge verdict: Accepted)

import java.io.*;
import java.util.*;

public class Main {

    public static void main(String[] args) throws Exception {
        pw = new PrintWriter(System.out);
        sc = new MScanner(System.in);
        int n = sc.nextInt();
        int[] a = new int[n + 1], b = new int[n + 1], c = new int[n + 1];
        for(int i = 1; i <= n; ++i){
            a[i] = sc.nextInt();
            b[i] = sc.nextInt();
            c[i] = sc.nextInt();
        }
        int[][] dp = new int[n + 1][3];
        for(int day = 1; day <= n; ++day){
            dp[day][0] = a[day] + Math.max(dp[day - 1][1], dp[day - 1][2]);
            dp[day][1] = b[day] + Math.max(dp[day - 1][0], dp[day - 1][2]);
            dp[day][2] = c[day] + Math.max(dp[day - 1][1], dp[day - 1][0]);
        }
        pw.println(Math.max(Math.max(dp[n][0], dp[n][1]), dp[n][2]));
        pw.flush();
    }
    static PrintWriter pw;
    static MScanner  sc;
    static class MScanner {
        StringTokenizer st;
        BufferedReader br;
        public MScanner(InputStream system) {
            br = new BufferedReader(new InputStreamReader(system));
        }

        public MScanner(String file) throws Exception {
            br = new BufferedReader(new FileReader(file));
        }

        public String next() throws IOException {
            while (st == null || !st.hasMoreTokens())
                st = new StringTokenizer(br.readLine());
            return st.nextToken();
        }
        public int[] intArr(int n) throws IOException {
            int[]in=new int[n];for(int i=0;i<n;i++)in[i]=nextInt();
            return in;
        }
        public long[] longArr(int n) throws IOException {
            long[]in=new long[n];for(int i=0;i<n;i++)in[i]=nextLong();
            return in;
        }
        public int[] intSortedArr(int n) throws IOException {
            int[]in=new int[n];for(int i=0;i<n;i++)in[i]=nextInt();
            shuffle(in);
            Arrays.sort(in);
            return in;
        }
        public long[] longSortedArr(int n) throws IOException {
            long[]in=new long[n];for(int i=0;i<n;i++)in[i]=nextLong();
            shuffle(in);
            Arrays.sort(in);
            return in;
        }
        public Integer[] IntegerArr(int n) throws IOException {
            Integer[]in=new Integer[n];for(int i=0;i<n;i++)in[i]=nextInt();
            return in;
        }
        public Long[] LongArr(int n) throws IOException {
            Long[]in=new Long[n];for(int i=0;i<n;i++)in[i]=nextLong();
            return in;
        }
        public String nextLine() throws IOException {
            return br.readLine();
        }

        public int nextInt() throws IOException {
            return Integer.parseInt(next());
        }

        public double nextDouble() throws IOException {
            return Double.parseDouble(next());
        }

        public char nextChar() throws IOException {
            return next().charAt(0);
        }

        public long nextLong() throws IOException {
            return Long.parseLong(next());
        }

        public boolean ready() throws IOException {
            return br.ready();
        }

        public void waitForInput() throws InterruptedException {
            Thread.sleep(3000);
        }
    }
    static void shuffle(int[]in) {
        for(int i=0;i<in.length;i++) {
            int idx=(int)(Math.random()*in.length);
            int tmp=in[i];
            in[i]=in[idx];
            in[idx]=tmp;
        }
    }
    static void shuffle(long[]in) {
        for(int i=0;i<in.length;i++) {
            int idx=(int)(Math.random()*in.length);
            long tmp=in[i];
            in[i]=in[idx];
            in[idx]=tmp;
        }
    }
}