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

// Solution
public class Main {
  private static Scanner in;
  private static PrintWriter out;
  private static final String INPUT = ""; // input file name

  /**
   * Interactive get next command
   */
  static int get(int pos) {
    out.println(pos + 1);
    out.flush();
    return ni();
  }

  static void solve() {
    int n = ni();
    int[][] arr = new int[n][3];

    for (int i = 0; i < n; i++) {
      for (int j = 0; j < 3; j++) {
        arr[i][j] = ni();
      }
    }

//    out.println(Math.max(
//        helper(arr, n - 2, 0, arr[n-1][0]),
//        Math.max(
//            helper(arr, n - 2, 1, arr[n-1][1]),
//            helper(arr, n - 2, 2, arr[n-1][2])
//        )
//    ));

    int[][] dp = new int[n + 1][3];

    // dp[i] = dp[i-1] + max(a[i],b[i],c[i])

    for (int i = 1; i <= n; i++) {
      for (int j = 0; j < 3; j++) {
        // Add arr[i - 1][0] to all the previous 3 dp and check which one is max

        for (int prev = 0; prev < 3; prev++) {
          if (j == prev) continue; // if prev is same, don't add

          dp[i][j] = Math.max(dp[i][j], dp[i - 1][prev] + arr[i - 1][j]);
        }
      }
    }

    out.println(Math.max(
        dp[n][0],
        Math.max(dp[n][1], dp[n][2])
    ));
  }

  static int helper(int[][] arr, int row, int choice, int max) {
    if (row < 0) {
      return max;
    }

    if (choice == 0) {
      return Math.max(
          helper(arr, row - 1, 1, max + arr[row][1]),
          helper(arr, row - 1, 2, max + arr[row][2])
      );
    } else if (choice == 1) {
      return Math.max(
          helper(arr, row - 1, 0, max + arr[row][0]),
          helper(arr, row - 1, 2, max + arr[row][2])
      );
    } else {
      return Math.max(
          helper(arr, row - 1, 0, max + arr[row][0]),
          helper(arr, row - 1, 1, max + arr[row][1])
      );
    }
  }

  public static void main(String[] args) throws Exception {
    long S = System.currentTimeMillis();
    in = INPUT.isEmpty() ? new Scanner(System.in) : new Scanner(INPUT);
    out = new PrintWriter(System.out);

    solve();
    out.flush();
    long G = System.currentTimeMillis();
    tr(G - S + "ms");
  }

  private static int gcd(int a, int b) {
    while (b != 0) {
      int t = b;
      b = a % b;
      a = t;
    }

    return a;
  }

  private static int ni() {
    return Integer.parseInt(in.next());
  }

  private static long nl() {
    return Long.parseLong(in.next());
  }

  // Math Utils
  private static int pi(int num, int pow) {
    int result = 1;

    while (pow > 0) {
      if (pow % 2 == 1) {
        result *= num;
      }

      num *= num;
      pow /= 2;
    }

    return result;
  }

  private static int pim(int num, int pow, int mod) {
    int result = 1;

    while (pow > 0) {
      if (pow % 2 == 1) {
        // keep collecting `odd` num in result
        result = (result * num) % mod;
      }

      num = (num * num) % mod;
      pow /= 2;
    }

    return result;
  }

  private static long pl(long num, long pow) {
    long result = 1;

    while (pow > 0) {
      if (pow % 2 == 1) {
        result *= num;
      }

      num *= num;
      pow /= 2;
    }

    return result;
  }

  private static long plm(long num, long pow, long mod) {
    long result = 1;

    while (pow > 0) {
      if (pow % 2 == 1) {
        // keep collecting `odd` num in result
        result = (result * num) % mod;
      }

      num = (num * num) % mod;
      pow /= 2;
    }

    return result;
  }

  static void tr(Object... o) {
    if (!INPUT.isEmpty())
      out.println(Arrays.deepToString(o));
  }
}