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.math.BigDecimal;
import java.math.BigInteger;
import java.util.*;
 
public class Main {
	static final int INF = (int) (1e9 + 10);
	static final int MOD = (int) (1000000007);
 
	// static final int N = (int) (4e5 + 5);
	// static ArrayList<Integer>[] graph;
	// static boolean visited[];
	// static long size[];
 
	public static void main(String[] args) throws NumberFormatException, IOException {
		FastReader sc = new FastReader();
		PrintWriter pr = new PrintWriter(new BufferedWriter(new OutputStreamWriter(System.out)));
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
	    int n = sc.nextInt();
	   // int k = sc.nextInt();
	    int [][] arr = new int [n][3];
	    int [][] dp  = new int [n+1][3];
	    
	    for(int i =0 ; i < n ; i++){
	        arr[i][0] = sc.nextInt();
	        arr[i][1] = sc.nextInt();
	        arr[i][2] = sc.nextInt();
	    }
	    dp[0][0] = arr[0][0];
	    dp[0][1] = arr[0][1];
	    dp[0][2] = arr[0][2];
	    for(int i =1 ; i < n ; i++){
	        int a = Math.max(dp[i-1][1] , dp[i-1][2]);
	        dp[i][0] = a+arr[i][0];
	        a = Math.max(dp[i-1][0], dp[i-1][2]);
	        dp[i][1] = a+ arr[i][1];
	        a = Math.max(dp[i-1][0] , dp[i-1][1]);
	        dp[i][2] = a + arr[i][2];
	        
	    }
	    
	    pr.println(Math.max(dp[n-1][0] , Math.max(dp[n-1][1] , dp[n-1][2])));
		pr.flush();
		pr.close();
	}
	private static boolean possible(long[] arr, int[] f, long mid, long k) {
		long c = 0;
 
		for (int i = 0; i < arr.length; i++) {
			if ((arr[i] * f[f.length - i - 1]) > mid) {
				c += (arr[i] - (mid / f[f.length - i - 1]));
			}
		}
		// System.out.println(mid+" "+c);
		if (c <= k)
			return true;
		return false;
	}
 
	public static int lowerBound(ArrayList<Integer> array, int length, long value) {
		int low = 0;
		int high = length;
		while (low < high) {
			final int mid = (low + high) / 2;
			if (value <= array.get(mid)) {
				high = mid;
			} else {
				low = mid + 1;
			}
		}
		return low;
	}
 
	static class FastReader {
		BufferedReader br;
		StringTokenizer st;
 
		public FastReader() {
			br = new BufferedReader(new InputStreamReader(System.in));
		}
 
		String next() {
			while (st == null || !st.hasMoreElements()) {
				try {
					st = new StringTokenizer(br.readLine());
				} catch (IOException e) {
					e.printStackTrace();
				}
			}
			return st.nextToken();
		}
 
		int nextInt() {
			return Integer.parseInt(next());
		}
 
		long nextLong() {
			return Long.parseLong(next());
		}
 
		double nextDouble() {
			return Double.parseDouble(next());
		}
 
		String nextLine() {
			String str = "";
			try {
				str = br.readLine();
			} catch (IOException e) {
				e.printStackTrace();
			}
			return str;
		}
	}
 
	static long gcd(long a, long b) {
		if (a == 0)
			return b;
		return gcd(b % a, a);
	}
 
	static long lcm(long a, long b) {
		return (a * b) / gcd(a, b);
	}
 
	public static void sortbyColumn(int[][] att, int col) {
		// Using built-in sort function Arrays.sort
		Arrays.sort(att, new Comparator<int[]>() {
 
			@Override
			// Compare values according to columns
			public int compare(final int[] entry1, final int[] entry2) {
 
				// To sort in descending order revert
				// the '>' Operator
				// if (entry1[col] > entry2[col])
				// return 1;
				// else //(entry1[col] >= entry2[col])
				// return -1;
				return new Integer(entry1[col]).compareTo(entry2[col]);
				// return entry1[col].
			}
		}); // End of function call sort().
	}
 
	static class pair {
		int V, I;
 
		pair(int v, int i) {
			V = v;
			I = i;
		}
	}
 
	public static int[] swap(int data[], int left, int right) {
		int temp = data[left];
		data[left] = data[right];
		data[right] = temp;
		return data;
	}
 
	public static int[] reverse(int data[], int left, int right) {
		while (left < right) {
			int temp = data[left];
			data[left++] = data[right];
			data[right--] = temp;
		}
		return data;
	}
 
	public static boolean findNextPermutation(int data[]) {
		if (data.length <= 1)
			return false;
 
		int last = data.length - 2;
		while (last >= 0) {
			if (data[last] < data[last + 1]) {
				break;
			}
			last--;
		}
		if (last < 0)
			return false;
 
		int nextGreater = data.length - 1;
		for (int i = data.length - 1; i > last; i--) {
			if (data[i] > data[last]) {
				nextGreater = i;
				break;
			}
		}
		data = swap(data, nextGreater, last);
		data = reverse(data, last + 1, data.length - 1);
		return true;
	}
 
	static long nCr(long n, long r) {
		if (n == r)
			return 1;
		return fact(n) / (fact(r) * fact(n - r));
	}
 
	static long fact(long n) {
		long res = 1;
		for (long i = 2; i <= n; i++)
			res = res * i;
		return res;
	}
 
	/*
	 * static boolean prime[] = new boolean[1000007];
	 * 
	 * public static void sieveOfEratosthenes(int n) {
	 * 
	 * for (int i = 0; i < n; i++) prime[i] = true; * for (int p = 2; p * p <=
	 * n; p++) { // If prime[p] is not changed, then it is a prime if (prime[p]
	 * == true) { // Update all multiples of p for (int i = p * p; i <= n; i +=
	 * p) prime[i] = false; } }
	 * 
	 * // Print all prime numbers // for(int i = 2; i <= n; i++) // { //
	 * if(prime[i] == true) // System.out.print(i + " "); // } }
	 */
 
	static long power(int a, int n , int modd) {
		long b = (long)a;
		long res = 1;
		while(n>0) {
			if((n&1)==1){
				res = (res*b)%modd;
			}
			b = (b*b)%modd;
			n = n>>1;
		}
		return res;
	}

 
	
	static boolean isPrime(int n) {
		// Corner cases
		if (n <= 1)
			return false;
		if (n <= 3)
			return true;
 
		// This is checked so that we can skip
		// middle five numbers in below loop
		if (n % 2 == 0 || n % 3 == 0)
			return false;
 
		for (int i = 5; i * i <= n; i = i + 6)
			if (n % i == 0 || n % (i + 2) == 0)
				return false;
 
		return true;
	}
 
	public static BigInteger lcmm(String a, String b) {
		BigInteger s = new BigInteger(a);
		BigInteger s1 = new BigInteger(b);
		BigInteger mul = s.multiply(s1);
		BigInteger gcd = s.gcd(s1);
		BigInteger lcm = mul.divide(gcd);
		return lcm;
	}
 
}