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.Writer;
import java.io.BufferedWriter;
import java.io.OutputStreamWriter;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.io.IOException;
import java.io.InputStream;
import java.math.BigInteger;
import java.util.Arrays;
import java.util.ArrayList;
import java.util.InputMismatchException;
import java.util.*;
import java.io.*;
import java.math.*;

public class Main{
  static class pair{
    int val, idx;
    pair(int a, int b){
      val=a;
      idx=b;
    }
    public String toString(){
      return "(val: "+val+" idx: "+idx+")";
    }
  }

  static class ProblemSolver{
    static int solve(int ar[][], int day, int flag, int [][]dp){
      if(day==ar.length) return 0;
      int ans=0;
      if(dp[day][flag]!=-1) return dp[day][flag];
      if(flag==0){
        int a=solve(ar, day+1, 1, dp)+ar[day][0];
        int b=solve(ar, day+1, 2, dp)+ar[day][1];
        int c=solve(ar, day+1, 3, dp)+ar[day][2];
        ans=Math.max(a, Math.max(b, c));
      }
      if(flag==1){
        int b=solve(ar, day+1, 2, dp)+ar[day][1];
        int c=solve(ar, day+1, 3, dp)+ar[day][2];
        ans=Math.max(b,c);
      }
      if(flag==2){
        int b=solve(ar, day+1, 1, dp)+ar[day][0];
        int c=solve(ar, day+1, 3, dp)+ar[day][2];
        ans=Math.max(b,c);
      }
      if(flag==3){
        int b=solve(ar, day+1, 1, dp)+ar[day][0];
        int c=solve(ar, day+1, 2, dp)+ar[day][1];
        ans=Math.max(b,c);
      }
      dp[day][flag]=ans;
      return ans;
    }
    public void solveTheProblem(InputReader in,OutputWriter out, NumberTheory nt){
      int test=1;//in.nextInt();
      while(test-- >0){
        int n;
        n=in.nextInt();
        int dp[][]= new int[n][4];
        for(int i[]: dp) Arrays.fill(i, -1);
        int ar[][]= new int[n][3];
        ar=in.nextIntMatrix(n, 3);
        System.out.println(solve(ar, 0, 0, dp));
      }
    }
  }

  public static void main(String[] args){
    InputStream inputStream=System.in;
    OutputStream outputStream=System.out;
    InputReader in=new InputReader(inputStream);
    OutputWriter out=new OutputWriter(outputStream);
    NumberTheory nt= new NumberTheory();
    ProblemSolver problemSolver=new ProblemSolver();
    problemSolver.solveTheProblem(in,out, nt);
    out.flush();
    out.close();
  }

  static class InputReader {
    private boolean finished = false;

    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 peek() {
      if (numChars == -1) {
        return -1;
      }
      if (curChar >= numChars) {
        curChar = 0;
        try {
          numChars = stream.read(buf);
        } catch (IOException e) {
          return -1;
        }
        if (numChars <= 0) {
          return -1;
        }
      }
      return buf[curChar];
    }

    public int nextInt() {
      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 long nextLong() {
      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 String nextLine() {
      int c = read();
      while (isSpaceChar(c)) {
        c = read();
      }
      StringBuilder res = new StringBuilder();
      do {
        if (Character.isValidCodePoint(c)) {
          res.appendCodePoint(c);
        }
        c = read();
      } while (!isSpaceChar(c));
      return res.toString();
    }

    public boolean isSpaceChar(int c) {
      if (filter != null) {
        return filter.isSpaceChar(c);
      }
      return isWhitespace(c);
    }

    public static boolean isWhitespace(int c) {
      return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
    }

    private String readLine0() {
      StringBuilder buf = new StringBuilder();
      int c = read();
      while (c != '\n' && c != -1) {
        if (c != '\r') {
          buf.appendCodePoint(c);
        }
        c = read();
      }
      return buf.toString();
    }

    public String readLine() {
      String s = readLine0();
      while (s.trim().length() == 0) {
        s = readLine0();
      }
      return s;
    }

    public String readLine(boolean ignoreEmptyLines) {
      if (ignoreEmptyLines) {
        return readLine();
      } else {
        return readLine0();
      }
    }

    public BigInteger readBigInteger() {
      try {
        return new BigInteger(nextLine());
      } catch (NumberFormatException e) {
        throw new InputMismatchException();
      }
    }

    public char nextCharacter() {
      int c = read();
      while (isSpaceChar(c)) {
        c = read();
      }
      return (char) c;
    }

    public double nextDouble() {
      int c = read();
      while (isSpaceChar(c)) {
        c = read();
      }
      int sgn = 1;
      if (c == '-') {
        sgn = -1;
        c = read();
      }
      double res = 0;
      while (!isSpaceChar(c) && c != '.') {
        if (c == 'e' || c == 'E') {
          return res * Math.pow(10, nextInt());
        }
        if (c < '0' || c > '9') {
          throw new InputMismatchException();
        }
        res *= 10;
        res += c - '0';
        c = read();
      }
      if (c == '.') {
        c = read();
        double m = 1;
        while (!isSpaceChar(c)) {
          if (c == 'e' || c == 'E') {
            return res * Math.pow(10, nextInt());
          }
          if (c < '0' || c > '9') {
            throw new InputMismatchException();
          }
          m /= 10;
          res += (c - '0') * m;
          c = read();
        }
      }
      return res * sgn;
    }

    public boolean isExhausted() {
      int value;
      while (isSpaceChar(value = peek()) && value != -1) {
        read();
      }
      return value == -1;
    }

    public String next() {
      return nextLine();
    }

    public SpaceCharFilter getFilter() {
      return filter;
    }

    public void setFilter(SpaceCharFilter filter) {
      this.filter = filter;
    }

    public interface SpaceCharFilter {
      public boolean isSpaceChar(int ch);
    }
    public int[] nextIntArray(int n){
      int[] array=new int[n];
      for(int i=0;i<n;++i)array[i]=nextInt();
      return array;
    }
    public int[] nextSortedIntArray(int n){
      int array[]=nextIntArray(n);
      Arrays.sort(array);
      return array;
    }
    public ArrayList<Integer> nextIntArrayList(int n){
      ArrayList<Integer> ar= new ArrayList<>();
      for(int i=0;i<n;i++)
      ar.add(nextInt());
      return ar;
    }
    public ArrayList<Long> nextLongArrayList(int n){
      ArrayList<Long> ar= new ArrayList<>();
      for(int i=0;i<n;i++)
      ar.add(nextLong());
      return ar;
    }

    public int[] nextSumIntArray(int n){
      int[] array=new int[n];
      array[0]=nextInt();
      for(int i=1;i<n;++i)array[i]=array[i-1]+nextInt();
      return array;
    }
    public long[] nextLongArray(int n){
      long[] array=new long[n];
      for(int i=0;i<n;++i)array[i]=nextLong();
      return array;
    }
    public long[] nextSumLongArray(int n){
      long[] array=new long[n];
      array[0]=nextInt();
      for(int i=1;i<n;++i)array[i]=array[i-1]+nextInt();
      return array;
    }
    public long[] nextSortedLongArray(int n){
      long array[]=nextLongArray(n);
      Arrays.sort(array);
      return array;
    }
    public int[][] nextIntMatrix(int n,int m){
      int[][] matrix=new int[n][m];
      for(int i=0;i<n;++i)
      for(int j=0;j<m;++j)
      matrix[i][j]=nextInt();
      return matrix;
    }

    public int[][] nextIntMatrix(int n){
      return nextIntMatrix(n,n);
    }

    public long[][] nextLongMatrix(int n,int m){
      long[][] matrix=new long[n][m];
      for(int i=0;i<n;++i)
      for(int j=0;j<m;++j)
      matrix[i][j]=nextLong();
      return matrix;
    }

    public long[][] nextLongMatrix(int n){
      return nextLongMatrix(n,n);
    }

    public char[][] nextCharMatrix(int n,int m){
      char[][] matrix=new char[n][m];
      for(int i=0;i<n;++i)
      matrix[i]=next().toCharArray();
      return matrix;
    }

    public char[][] nextCharMatrix(int n){
      return nextCharMatrix(n,n);
    }
  }

  static class OutputWriter {
    private final PrintWriter writer;

    public OutputWriter(OutputStream outputStream) {
      writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(outputStream)));
    }

    public OutputWriter(Writer writer) {
      this.writer = new PrintWriter(writer);
    }

    // public void print(char[] array) {
    //     writer.print(array);
    // }

    public void print(Object... objects) {
      for (int i = 0; i < objects.length; i++) {
        if (i != 0) {
          writer.print(' ');
        }
        writer.print(objects[i]);
      }
    }

    public void print(int[] array) {
      for (int i = 0; i < array.length; i++) {
        if (i != 0) {
          writer.print(' ');
        }
        writer.print(array[i]);
      }
    }

    public void print(double[] array) {
      for (int i = 0; i < array.length; i++) {
        if (i != 0) {
          writer.print(' ');
        }
        writer.print(array[i]);
      }
    }

    public void print(long[] array) {
      for (int i = 0; i < array.length; i++) {
        if (i != 0) {
          writer.print(' ');
        }
        writer.print(array[i]);
      }
    }

    public void print(char[] array) {
      for (int i = 0; i < array.length; i++) {
        if (i != 0) {
          writer.print(' ');
        }
        writer.print(array[i]);
      }
    }

    public void print(String[] array) {
      for (int i = 0; i < array.length; i++) {
        if (i != 0) {
          writer.print(' ');
        }
        writer.print(array[i]);
      }
    }

    public void print(int[][] matrix){
      for(int i=0;i<matrix.length;++i){
        println(matrix[i]);
      }
    }

    public void print(double[][] matrix){
      for(int i=0;i<matrix.length;++i){
        println(matrix[i]);
      }
    }

    public void print(long[][] matrix){
      for(int i=0;i<matrix.length;++i){
        println(matrix[i]);
      }
    }

    public void print(char[][] matrix){
      for(int i=0;i<matrix.length;++i){
        println(matrix[i]);
      }
    }

    public void print(String[][] matrix){
      for(int i=0;i<matrix.length;++i){
        println(matrix[i]);
      }
    }

    public void println(int[] array) {
      print(array);
      writer.println();
    }

    public void println(double[] array) {
      print(array);
      writer.println();
    }

    public void println(long[] array) {
      print(array);
      writer.println();
    }

    // public void println(char[] array) {
    //     print(array);
    //     writer.println();
    // }

    public void println(String[] array) {
      print(array);
      writer.println();
    }

    public void println() {
      writer.println();
    }

    public void println(Object... objects) {
      print(objects);
      writer.println();
    }

    public void print(char i) {
      writer.print(i);
    }

    public void println(char i) {
      writer.println(i);
    }

    public void println(char[] array) {
      writer.println(array);
    }

    public void printf(String format, Object... objects) {
      writer.printf(format, objects);
    }

    public void close() {
      writer.close();
    }

    public void flush() {
      writer.flush();
    }

    public void print(long i) {
      writer.print(i);
    }

    public void println(long i) {
      writer.println(i);
    }

    public void print(int i) {
      writer.print(i);
    }

    public void println(int i) {
      writer.println(i);
    }

    public void separateLines(int[] array) {
      for (int i : array) {
        println(i);
      }
    }
  }
  static class NumberTheory{

    /**
    * Modular Arithmetic:
    *  1. (a+b)%c=(a%c+b%c)%c
    *  2. (a*b)%c=(a%c*b%c)%c
    *  3. (a-b)%c=(a%c-b%c+c)%c
    *  4. (a/b)%c=(a%c*(b^-1)%c)%c -- (b^-1 is multiplicative modulo inverse)
    */
    //Modular Addition
    public int modularAddition(int a,int b,int MOD){
      return (a%MOD+b%MOD)%MOD;
    }
    public long modularAddition(long a,long b,long MOD){
      return (a%MOD+b%MOD)%MOD;
    }
    //Modular Multiplication
    public int modularMultiplication(int a,int b,int MOD){
      return ((a%MOD)*(b%MOD))%MOD;
    }
    public long modularMultiplication(long a,long b,long MOD){
      return ((a%MOD)*(b%MOD))%MOD;
    }
    //Modular Subtraction
    public int modularSubtraction(int a,int b,int MOD){
      return (a%MOD-b%MOD+MOD)%MOD;
    }
    public long modularSubtraction(long a,long b,long MOD){
      return (a%MOD-b%MOD+MOD)%MOD;
    }

    /**
    * Binary Exponentiation
    */
    public int binaryExponentiation(int x,int n){
      if(n==0)return 1;
      else if(n%2==0)return binaryExponentiation(x*x,n/2);
      else return x*binaryExponentiation(x*x,(n-1)/2);
    }
    public long binaryExponentiation(long x,long n){
      long result=1;
      while(n>0){
        if(n%2==1)result*=x;
        x=x*x;
        n/=2;
      }
      return result;
    }

    /**
    * Modular Exponentiation
    */
    public int modularExponentiation(int x,int n,int MOD){
      if(n==0)return 1%MOD;
      else if(n%2==0)return modularExponentiation(modularMultiplication(x,x,MOD),n/2,MOD);
      else return modularMultiplication(x,modularExponentiation(modularMultiplication(x,x,MOD),(n-1)/2,MOD),MOD);
    }
    public long modularExponentiation(long x,long n,long MOD){
      long result=1;
      while(n>0){
        if(n%2==1)result=modularMultiplication(result,x,MOD);
        x=modularMultiplication(x,x,MOD);
        n/=2;
      }
      return result;
    }

    /**
    * Factorial of a number
    */
    public long factorials(long n){
      if(n==0)return 1;
      return n*factorials(n-1);
    }

    /**
    * Prime factors of a number
    */
    public ArrayList<Integer> distinctPrimeFactors(int n){
      ArrayList<Integer> factorials=new ArrayList<>();
      int limit=(int)Math.sqrt(n);
      if(n%2==0){
        factorials.add(2);
        while(n%2==0)n/=2;
      }
      for(int i=3;i<=limit;i+=2){
        if(n%i==0){
          factorials.add(i);
          while(n%i==0)n/=i;
        }
      }
      if(n>2)factorials.add(n);
      return factorials;
    }

    public ArrayList<Long> distinctPrimeFactors(long n){
      ArrayList<Long> factorials=new ArrayList<>();
      long limit=(long)Math.sqrt(n);
      if(n%2==0){
        factorials.add((long)2);
        while(n%2==0)n/=2;
      }
      for(long i=3;i<=limit;i+=2){
        if(n%i==0){
          factorials.add(i);
          while(n%i==0)n/=i;
        }
      }
      if(n>2)factorials.add(n);
      return factorials;
    }

    public ArrayList<Integer> primeFactors(int n){
      ArrayList<Integer> factorials=new ArrayList<>();
      int limit=(int)Math.sqrt(n);
      if(n%2==0){
        factorials.add(2);
        while(n%2==0)n/=2;
      }
      for(int i=3;i<=limit;i+=2){
        if(n%i==0){
          factorials.add(i);
          while(n%i==0)n/=i;
        }
      }
      if(n>2)factorials.add(n);
      return factorials;
    }

    public ArrayList<Long> primeFactors(long n){
      ArrayList<Long> factorials=new ArrayList<>();
      long limit=(long)Math.sqrt(n);
      if(n%2==0){
        factorials.add((long)2);
        while(n%2==0)n/=2;
      }
      for(long i=3;i<=limit;i+=2){
        if(n%i==0){
          factorials.add(i);
          while(n%i==0)n/=i;
        }
      }
      if(n>2)factorials.add(n);
      return factorials;
    }

    /**
    * Combination: nCr
    */
    //Naive version
    //(n,r)=(n-1,r-1)+(n-1,r) for r!=0 or r!=n
    //(n,0)=(n,n)=1
    public int binomialCoefficientRecursive(int n,int k){
      if(k==0 || k==n)return 1;//base case
      return binomialCoefficientRecursive(n-1,k-1)+binomialCoefficientRecursive(n-1,k);//recursion
    }

    //Dynamic Programming version(Uses bottom up approach to fill the table)
    //Time complexity: O(n*k)
    //Space complexity: O(n*k)
    public long binomialCoefficientIterative(int n,int k){
      long[][] C=new long[n+1][k+1];
      for(int i=0;i<=n;++i){
        for(int j=0;j<=Math.min(n,k);++j){
          if(j==0 || j==i)C[i][j]=1;
          else C[i][j]=C[i-1][j-1]+C[i-1][j];
        }
      }
      return C[n][k];
    }

    //Pascal's Triangle version(Space efficient program)
    //Time complexity: O(n*k)
    //Space complexity: O(k)
    public long nCr(int n,int r){
      int[] C=new int[r+1];
      C[0]=1;//nC0=1
      for(int i=1;i<=n;++i)
      for(int j=Math.min(i,r);j>0;--j)
      C[j]=C[j]+C[j-1];
      return C[r];
    }

    /**
    * Catlan number:
    *  - Time complexity: O(n*n)
    *  - Auxiliary space: O(n)
    *
    *  NOTE: Time complexity could be reduced to O(n) but it is
    *        possible if and only if n is small or else there is
    *        a chance of getting an overflow. To decrease the time
    *        complexity to O(n) just remember nCr=nCn-r
    */
    public long catlanNumber(int n){
      long[] catlan=new long[n+1];
      catlan[0]=catlan[1]=1;
      for(int i=2;i<=n;++i)
      for(int j=0;j<i;++j)
      catlan[i]+=catlan[j]*catlan[i-1-j];

      return catlan[n];
    }

    /**
    * Greatest Common Divisor(GCD)
    *  - It is also known as Highest Common Factor(HCF)
    *  - Time complexity: log(min(a,b))
    *  - Auxiliary Space: O(1)
    */
    public int gcd(int a,int b){
      if(b==0)return a;
      return gcd(b,a %b);
    }

    public long gcd(long a,long b){
      if(b==0)return a;
      return gcd(b,a%b);
    }

    /**
    * Extended Euclid's Algorithm:
    *  - ax+by=gcd(a,b)
    *  - Time complexity:
    *  -
    */


    /**
    * Least Common Multiple(LCM):
    *  - Time complexity: log(min(a,b))
    *  - Auxiliary Space: O(1)
    */
    public long lcm(long a,long b){
      return (a*b)/gcd(a,b);
    }

  }
}
//
//                       "8,        .m8"
//                        I8Im    ,mI8"
//                        ,8I""I8,mI8m
//             "I8mm,    ,I8    I8 "I8,          ,m"
//                "I88I88I8m ,I8"   "I8""==mm ,mI8"
//        ___    ,mI8"    "8I8"      I8,  ,mI8I8"
//   .,mI8I8I8I8I88,      ,m8"      ,I8I8I8I888"
// "I8Im,       "I88,    ,8"      ,II8"     "88,
//    `"I8,        "I8, ,8"     ,I8"         "I8,
//       "I8m       "I888      ,I8"           "I8,
//         "8m        "I8      88"              "I8,
//          I8,        I8      88                 "I8,
//           88,       I8,     "I8                 "I8
//           "I8,      "I8,     "I8,                I8;.
//            "I8,      "I8,      "I8        .,mmmI8888888m,.
//              I8,      "I8,      I8,  .mI8I88"""". .. "I8888
//              "I8,      "I8      mI8I88"". . . . . .,m8"   "8
//               I8m,  __ ;I8   ,II88" . . . . .,;miI88"
//               "I88I8I88I88,,I88" . . . ,mmiiI8888"
//                ,I8". . ."I8I8". . . mi888888888"
//              ,I8 . . . .,I88I. . .i88888888888"
//             I8. . . .,mII88Ima. .i88888888888"
//            ,8"..,mI88I88I88I8Imi888888888888"
//            I8.,I8I"""        ""II88888888888
//           ;I8I8"                  ""I8888888
//           ""                         "I88888
//                                        "I888
//                                         "I88,
//                                          "I88
//                                           "88,
//                                            I88,              ______   __
//                           ______           "I88__        .mI88I88I88I88I88,
//                      .,mI88I88I88, ,mI88,   I88"""     ,mI8". . . . "I8,..8,
//                    ,I888' . . . "I88.\ "8,  I88      ,I8". . . .  / :;I8 \ 8,
//                  .mI8' . . .  / .:"I8.\ 88  "88,    ,8". . .  / .;mI8I8I8,\ 8
//                 ,I8'. . .  / . .:;,I8I8I888  I88   ,8". .  / .:mI8"'   "I8,:8
//                ,I8'. . . / . .:;,mI8"  `"I88 I88   I8. .  / .m8"         "I8I
//               ,I8 . .  / . .:;,mI8"      "I88888   88,.  / ,m8            "8'
//               I8'. .  / . .;,mI8"          "II888 ,I8I8,.,I8"
//               I8 . . / . .,mI8"              I8888888' """
//               `I8,.  / ;,mI8"                 II888
//                "I8I, /,mI8"                 __I888
//                  "I8888"                   """I88
//                    ""                         I88
//                                               I88__
//                                               I88"""
//                                               I88
//                                               I88
//                                             __I88
//                                            """I88
//                                               I88
//                                               I88
//                                               I88__
//                                               I88"""
//                                               I88
//                                        BITSY  ___  CHUCK