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: Wrong Answer)

import java.io.BufferedReader;
			import java.io.FileReader;
			import java.io.IOException;
			import java.io.InputStreamReader;
			import java.io.PrintWriter;
			import java.math.BigInteger;
			import java.util.*;
			 
			 class Main{
					    void pre() throws Exception{}
					    int dp[][],a[][];
					    void solve(int TC) throws Exception{  
					 
					    	int n=ni();
					    	dp=new int[n][3];
					    	a=new int[n][3];
					   int cost=0;
					   for(int i=0;i<n;i++) 
					   {
						   for(int j=0;j<3;j++) {
							   	dp[i][j]=-1;
						   a[i][j]=ni();
					   		}
					   }
							   
					   getMax(n-1, 2 , n);
					   for(int i=0;i<n;i++) 
					   {
						   for(int j=0;j<3;j++) {
							   p(dp[i][j] + " ");
						   }
						   pn(" ");
					   }
					   pn(Math.max(dp[n-1][0], Math.max(dp[n-1][1], dp[n-1][2])));
					    }
					    int getMax(int i , int k , int n) {
					    		if(i<0)return 0;
					    		if(dp[i][k]!=-1)return dp[i][k];
					    		int max=Integer.MIN_VALUE;
					    		if(k==0) {
					    			max= Math.max(getMax(i-1 , 1, n),getMax(i-1,2,n)) + a[i][k];
					    		}
					    		else if(k==1) {
					    			max= Math.max(getMax(i-1 , 0, n),getMax(i-1,2,n)) + a[i][k];
					    		}
					    		else {
					    			max= Math.max(getMax(i-1 , 0, n),getMax(i-1,1,n)) + a[i][k];
					    		}
					    		dp[i][k]=max;
					    			
					    		return max;
					    	}	 
					    
					    
							
					     
					   
	
			
	
					     
					    static boolean multipleTC = false, memory = false;
					    FastReader in;PrintWriter out;
					    void run() throws Exception{
					        in = new FastReader();
					        out = new PrintWriter(System.out);
					        int T = (multipleTC)?ni():1;
					        pre();for(int t = 1; t<= T; t++)solve(t);
					        out.flush();
					        out.close();
					    }
					    public static void main(String[] args) throws Exception{
					        if(memory)new Thread(null, new Runnable() {public void run(){try{new Main().run();}catch(Exception e){e.printStackTrace();}}}, "1", 1 << 28).start();
					        else new Main().run();
					    }
					    void p(Object o){out.print(o);}
					    void pn(Object o){out.println(o);}
					    void nd(Object o){out.println(o);}
					    void pni(Object o){out.println(o);out.flush();}
					    String n()throws Exception{return in.next();}
					    String nln()throws Exception{return in.nextLine();}
					    int ni()throws Exception{return Integer.parseInt(in.next());}
					    long nl()throws Exception{return Long.parseLong(in.next());}
					    double nd()throws Exception{return Double.parseDouble(in.next());}
					    
					    class FastReader{
					        BufferedReader br;
					        StringTokenizer st;
					        public FastReader(){
					            br = new BufferedReader(new InputStreamReader(System.in));
					        }
					
					        public FastReader(String s) throws Exception{
					            br = new BufferedReader(new FileReader(s));
					        }
					
					        String next() throws Exception{
					            while (st == null || !st.hasMoreElements()){
					                try{
					                    st = new StringTokenizer(br.readLine());
					                }catch (IOException  e){
					                    throw new Exception(e.toString());
					                }
					            }
					            return st.nextToken();
					        }
					
					        String nextLine() throws Exception{
					            String str = "";
					            try{   
						                str = br.readLine();
						            }catch (IOException e){
					                throw new Exception(e.toString());
					            }  
					            return str;
					        }
					    }
			}