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 Java7 (OpenJDK 1.7.0) (judge verdict: Runtime Error)

/*
595 ms	104520 KB
*/
import java.util.*;

public class Main {
    public static void main(String args[]) {
 		Scanner scan = new Scanner(System.in);
      	int v = scan.nextInt();
      	int e = scan.nextInt();
      	Graph graph = new Graph(v);
      
      	for(int edge = 0; edge < e; edge++){
          int a = scan.nextInt();
          int b = scan.nextInt();
         graph.addEdge(a, b);
        }
      	scan.close();
      	System.out.println(graph.longestPath(v));
	}
  
  public static class Graph{
 	public int size; 
    public ArrayList<Integer> edge[]; 
  
    public Graph(int vertices)  
    { 
        this.size = vertices; 
        edge = new ArrayList[vertices+1]; 
        for (int i = 0; i <= vertices; i++)  
            edge[i] = new ArrayList<>(); 
    } 
    public void addEdge(int a,int b) 
    { 
        edge[a].add(b); 
    } 
   public void visit(int node, ArrayList<Integer> adj[], int dp[], 
                                    boolean visited[]) 
    { 
        // Mark as visited 
        visited[node] = true; 
  
        // Traverse for all its children 
        for (int i = 0; i < adj[node].size(); i++)  
        { 
  
            // If not visited 
            if (!visited[adj[node].get(i)]) 
                visit(adj[node].get(i), adj, dp, visited); 
  
            // Store the max of the paths 
            dp[node] = Math.max(dp[node], 1 + dp[adj[node].get(i)]); 
        } 
    } 
    public int longestPath(int n) 
    { 
        ArrayList<Integer> adj[] = edge; 
        int[] dp = new int[n+1]; 
        boolean[] visited = new boolean[n + 1]; 
      
        for (int i = 1; i <= n; i++)  
         if (!visited[i]) visit(i, adj, dp, visited); 
         
  
        int answer = 0; 
  
        for (int i = 1; i <= n; i++)  answer = Math.max(answer, dp[i]); 
        return answer; 
    } 
  }
}