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 Java8 (OpenJDK 1.8.0) (judge verdict: Accepted)

import java.util.*;
import java.io.*;
//267630EY
public class Main
{
  static PrintWriter out=new PrintWriter(System.out);
  static int[] a;
  static int[] b;
  static int[] c;
  static int[][] dp;
 

  public static void main(String[] args) throws IOException
  {
    Scanner sc=new Scanner(System.in);
    int n=sc.nextInt();
    a=new int[n];
    b=new int[n];
    c=new int[n];
    dp=new int[n][4];
    for(int i=0;i<n;i++)
    {
      Arrays.fill(dp[i],-1);
    }
    for(int i=0;i<n;i++)
    {
      a[i]=sc.nextInt();
      b[i]=sc.nextInt();
      c[i]=sc.nextInt();
    }
    int ans=solve(0,0);
    out.println(ans);
    out.flush();
             
    
  }
  private static int solve(int n,int prev)
  {
    if(n==a.length) return 0;
    else if(dp[n][prev]!=-1) return dp[n][prev];
    {
      if(prev==0)
      {
        dp[n][prev]=Math.max(a[n]+solve(n+1,1),Math.max(b[n]+solve(n+1,2),c[n]+solve(n+1,3)));
      }
      else if(prev==1)
      {
        dp[n][prev]=Math.max(b[n]+solve(n+1,2),c[n]+solve(n+1,3));
      }
      else if(prev==2)
      {
        dp[n][prev]=Math.max(c[n]+solve(n+1,3),a[n]+solve(n+1,1));
      }
      else
      {
        dp[n][prev]=Math.max(a[n]+solve(n+1,1),b[n]+solve(n+1,2));
      }
      return dp[n][prev];
    }
  }
      
      
  
  static class Scanner
  {
    BufferedReader br;
    StringTokenizer tk=new StringTokenizer("");
    public Scanner(InputStream is) 
    {
      br=new BufferedReader(new InputStreamReader(is));
    }
    
    public boolean hasNext()
    {
      

      boolean result=false;
      
      try 
      {
        result = br.ready();
      } 
      catch (IOException e)
      {
        System.err.println(e);
      }
      return result;
    }
    
    public int nextInt() throws IOException
    {
      if(tk.hasMoreTokens())
        return Integer.parseInt(tk.nextToken());
      tk=new StringTokenizer(br.readLine());
      return nextInt();
    }
    public long nextLong() throws IOException
    {
      if(tk.hasMoreTokens())
        return Long.parseLong(tk.nextToken());
      tk=new StringTokenizer(br.readLine());
      return nextLong();
    }
    public String next() throws IOException
    {
      if(tk.hasMoreTokens())
        return (tk.nextToken());
      tk=new StringTokenizer(br.readLine());
      return next();
    }
    public String nextLine() throws IOException
    {
      tk=new StringTokenizer("");
      return br.readLine();
    }
    public double nextDouble() throws IOException
    {
      if(tk.hasMoreTokens())
        return Double.parseDouble(tk.nextToken());
      tk=new StringTokenizer(br.readLine());
      return nextDouble();
    }
    public char nextChar() throws IOException
    {
      if(tk.hasMoreTokens())
        return (tk.nextToken().charAt(0));
      tk=new StringTokenizer(br.readLine());
      return nextChar();
    }
    public int[] nextIntArray(int n) throws IOException
    {
      int a[]=new int[n];
      for(int i=0;i<n;i++)
        a[i]=nextInt();
      return a;
    }
    public long[] nextLongArray(int n) throws IOException
    {
      long a[]=new long[n];
      for(int i=0;i<n;i++)
        a[i]=nextLong();
      return a;
    }
    public int[] nextIntArrayOneBased(int n) throws IOException
    {
      int a[]=new int[n+1];
      for(int i=1;i<=n;i++)
        a[i]=nextInt();
      return a;
    }
    public long[] nextLongArrayOneBased(int n) throws IOException
    {
      long a[]=new long[n+1];
      for(int i=1;i<=n;i++)
        a[i]=nextLong();
      return a;
    }
  }
}