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

public class Main {
	static int a[][] = new int[100005][4]; 
	static int dp[][] = new int[100005][4]; 
	static int  n ; 
	public static int fun(int ind , int flag) {
		if(ind == n ) return 0; 
		if(dp[ind][flag] != -1) return dp[ind][flag]; 
		int maxi = 0; 
		if(flag == 0) {
		   maxi = Math.max(maxi, a[ind][1] + fun(ind + 1, 1));
		   maxi = Math.max(maxi, a[ind][2] + fun(ind + 1 , 2)); 
		   maxi = Math.max(maxi, a[ind][3] + fun(ind + 1 , 3)); 
		}
		else if(flag == 1) {
			maxi = Math.max(maxi , a[ind][2] + fun(ind + 1, 2)); 
			maxi = Math.max(maxi, a[ind][3] + fun(ind + 1 , 3)); 
		}
		else if(flag == 2) {
			maxi = Math.max(maxi, a[ind][1] + fun(ind + 1 , 1)); 
			maxi = Math.max(maxi, a[ind][3] + fun(ind + 1, 3)); 
		}
		else {
			maxi = Math.max(maxi,a[ind][1] + fun(ind + 1, 1)); 
			maxi = Math.max(maxi, a[ind][2] + fun(ind + 1, 2)); 
		}
		return dp[ind][flag] = maxi; 
	}
	public static void solve(InputReader in) {
		 n = in.readInt();  
		for(int i = 0; i<n; i++) {
			for(int j = 1; j<=3; j++) {
				a[i][j] = in.readInt(); 
			}
		}
		for(int i = 0; i<n; i++) {
			for(int j = 0; j<4; j++) {
				dp[i][j] = -1; 
			}
		}
		System.out.println(fun(0,0)); 
	}
	public static void main(String[] args) {
		InputReader in = new InputReader(System.in); 
		int t = 1; 
		while(t-- > 0) {
			solve(in); 
		}
	}
}

class InputReader{
	private InputStream stream;
	private byte[] buf = new byte[1024];
	private int curChar;
	private int numChars;
	private SpaceCharFilter filter;

	 public InputReader(InputStream stream) {
		this.stream = stream;
	}

     public int read() {
		if (numChars == -1)
			throw new InputMismatchException();
		if (curChar >= numChars) {
			curChar = 0;
			try {
				numChars = stream.read(buf);
			} catch (IOException e) {
				throw new InputMismatchException();
			}
			if (numChars <= 0)
				return -1;
		}
		return buf[curChar++];
	}

     public int readInt() {
		int c = read();
		while (isSpaceChar(c))
			c = read();
		int sgn = 1;
		if (c == '-') {
			sgn = -1;
			c = read();
		}
		int res = 0;
		do {
			if (c < '0' || c > '9')
				throw new InputMismatchException();
			res *= 10;
			res += c - '0';
			c = read();
		} while (!isSpaceChar(c));
		return res * sgn;
	}

     public String readString() {
		int c = read();
		while (isSpaceChar(c))
			c = read();
		StringBuilder res = new StringBuilder();
		do {
			res.appendCodePoint(c);
			c = read();
		} while (!isSpaceChar(c));
		return res.toString();
	}

     public long readLong() {
		int c = read();
		while (isSpaceChar(c)) {
			c = read();
		}
		int sgn = 1;
		if (c == '-') {
			sgn = -1;
			c = read();
		}
		long res = 0;
		do {
			if (c < '0' || c > '9') {
				throw new InputMismatchException();
			}
			res *= 10;
			res += c - '0';
			c = read();
		} while (!isSpaceChar(c));
		return res * sgn;
	}
	
     public boolean isSpaceChar(int c) {
		if (filter != null)
			return filter.isSpaceChar(c);
		return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
	}
     
     public String next() {
		return readString();
	}
    
     public interface SpaceCharFilter {
		public boolean isSpaceChar(int ch);
	}
}