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.ByteArrayInputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.*;

public class Main {
    static InputStream is;
    static PrintWriter out;
    static String INPUT = "";

    static void solve() {
        int N = ni();
        long[][] happy = new long[100010][3];

        for (int i = 0; i < N; i++) {
            for (int j = 0; j < 3; j++) {
                happy[i][j] = nl();
            }
        }

        long[][] dp = new long[100010][3];

        for (int i = 0; i < N; i++) {
            for (int j = 0; j < 3; j++) {
                for (int k = 0; k < 3; k++) {
                    if (j == k) {
                        continue;
                    }
                    dp[i + 1][k] = Math.max(dp[i + 1][k], dp[i][j] + happy[i][k]);
                }
            }
        }

        long res = 0;
        for (int j = 0; j < 3; j++) {
            res = Math.max(res, dp[N][j]);
        }
        out.println(res);

    }

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

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

    private static boolean eof() {
        if(lenbuf == -1)return true;
        int lptr = ptrbuf;
        while(lptr < lenbuf)if(!isSpaceChar(inbuf[lptr++]))return false;

        try {
            is.mark(1000);
            while(true){
                int b = is.read();
                if(b == -1){
                    is.reset();
                    return true;
                }else if(!isSpaceChar(b)){
                    is.reset();
                    return false;
                }
            }
        } catch (IOException e) {
            return true;
        }
    }

    private static byte[] inbuf = new byte[1024];
    static int lenbuf = 0, ptrbuf = 0;

    private static int readByte() {
        if(lenbuf == -1)throw new InputMismatchException();
        if(ptrbuf >= lenbuf){
            ptrbuf = 0;
            try { lenbuf = is.read(inbuf); } catch (IOException e) { throw new InputMismatchException(); }
            if(lenbuf <= 0)return -1;
        }
        return inbuf[ptrbuf++];
    }

    private static boolean isSpaceChar(int c) { return !(c >= 33 && c <= 126); }

    private static int skip() { int b; while((b = readByte()) != -1 && isSpaceChar(b)); return b; }

    private static double nd() { return Double.parseDouble(ns()); }
    private static char nc() { return (char)skip(); }

    private static String ns() {
        int b = skip();
        StringBuilder sb = new StringBuilder();
        while(!(isSpaceChar(b))){
            sb.appendCodePoint(b);
            b = readByte();
        }
        return sb.toString();
    }

    private static char[] ns(int n) {
        char[] buf = new char[n];
        int b = skip(), p = 0;
        while(p < n && !(isSpaceChar(b))){
            buf[p++] = (char)b;
            b = readByte();
        }
        return n == p ? buf : Arrays.copyOf(buf, p);
    }

    private static char[][] nm(int n, int m) {
        char[][] map = new char[n][];
        for(int i = 0;i < n;i++)map[i] = ns(m);
        return map;
    }

    private static int[] na(int n) {
        int[] a = new int[n];
        for(int i = 0;i < n;i++)a[i] = ni();
        return a;
    }

    private static int ni() {
        int num = 0, b;
        boolean minus = false;
        while((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'));
        if(b == '-'){
            minus = true;
            b = readByte();
        }

        while(true){
            if(b >= '0' && b <= '9'){
                num = num * 10 + (b - '0');
            }else{
                return minus ? -num : num;
            }
            b = readByte();
        }
    }

    private static long nl() {
        long num = 0;
        int b;
        boolean minus = false;
        while((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'));
        if(b == '-'){
            minus = true;
            b = readByte();
        }

        while(true){
            if(b >= '0' && b <= '9'){
                num = num * 10 + (b - '0');
            }else{
                return minus ? -num : num;
            }
            b = readByte();
        }
    }

    private static void tr(Object... o) { if(INPUT.length() != 0)System.out.println(Arrays.deepToString(o)); }

    // Union-Find
    // https://algs4.cs.princeton.edu/15uf/UF.java.html
    public static class UnionFind {
        private int count = 0;
        private int[] parent, rank;

        public UnionFind(int n) {
            count = n;
            parent = new int[n];
            rank = new int[n];
            for (int i = 0; i < n; i++) {
                parent[i] = i;
            }
        }

        public int find(int p) {
            while (p != parent[p]) {
                parent[p] = parent[parent[p]];
                p = parent[p];
            }
            return p;
        }

        public void union(int p, int q) {
            int rootP = find(p);
            int rootQ = find(q);
            if (rootP ==rootQ) return;
            if (rank[rootQ] > rank[rootP]) {
                parent[rootP] = rootQ;
            } else {
                parent[rootQ] = rootP;
                if (rank[rootP] == rank[rootQ]) {
                    rank[rootP]++;
                }
            }
            count--;
        }

        public int count() {
            return count;
        }

        public void print() {
            out.println("Parent:");
            for (int i : parent) {
                out.print(i);
                out.print(" ");
            }
            out.println();
            out.println("Rank:");
            for (int i : rank) {
                out.print(i);
                out.print(" ");
            }
            out.println();
        }
    }

    // Dijkstra
    // Return min distance from start to end O(ElogV) (negative cost is prohibited)
    // edge is int[3] array {from,to,cost}
    // edges is edge list from specific node
    // all_edges is Map<from node number,edges>
    static int dijkstra(Map<Integer,List<int[]>> all_edges,int start,int end,int max_node_number) {
        int[] distance = new int[max_node_number + 1];
        Arrays.fill(distance, -1);
        PriorityQueue<int[]> p_que = new PriorityQueue<>((a,b) -> ((distance[a[0]] + a[2]) - (distance[b[0]] + b[2])));
        distance[start] = 0;
        List<int[]> edges = all_edges.get(start);
        p_que.addAll(edges);
        while (distance[end] < 0) {
            int[] nearest_edge = p_que.poll();
            assert nearest_edge != null;
            if (distance[nearest_edge[1]] < 0) {
                distance[nearest_edge[1]] = distance[nearest_edge[0]] + nearest_edge[2];
                if (all_edges.containsKey(nearest_edge[1])) {
                    edges = all_edges.get(nearest_edge[1]);
                    for (int[] edge : edges) {
                        if (distance[edge[1]] < 0) p_que.add(edge);
                    }
                }
            }
        }
        return distance[end];
    }

    // Enumerate primes in [2, n] with O(n log log n)
    public static List<Integer> sieveOfEratosthenes(int n) {
        boolean[] isPrime = new boolean[n+1];
        Arrays.fill(isPrime, true);
        for (int i = 2; i * i <= n; i++) {
            if (isPrime[i]) {
                for (int j = i + i; j <= n; j += i) {
                    isPrime[j] = false;
                }
            }
        }
        List<Integer> primes = new ArrayList<>();
        for (int i = 2; i <= n; i++) {
            if (isPrime[i]) {
                primes.add(i);
            }
        }
        return primes;
    }

    // Count divisor
    public static int countDivisor(int n) {
        int[] list = new int[n + 1];
        Arrays.fill(list, 0);
        int num = n;
        for (int i = 2; i <= n; i++) {
            while (num % i == 0) {
                list[i] = list[i] + 1;
                num /= i;
            }
        }
        int ans = 1;
        for (int i : list) {
            ans *= (i + 1);
        }
        return ans;
    }
}