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 C# (Mono 4.6.2.0) (judge verdict: Accepted)

using System;
using System.Collections.Generic;
using System.Linq;

class Program
{
    static void Main(string[] args)
    {
        var N = sc.ReadInt();
        var ABC = new long[N, 3];
        for (int i = 0; i < N; i++)
        {
            ABC[i, 0] = sc.ReadInt();
            ABC[i, 1] = sc.ReadInt();
            ABC[i, 2] = sc.ReadInt();
        }

        // i日目に行動jを行う場合にによって得られる幸福度の最大値
        // N+1日目は存在しないが配列外参照を行わないように0で入れておく
        var dp = new long[N + 1, 3];
        // 最終日から順番に見る
        for (int i = N - 1; i >= 0; i--)
        {
            // 活動jを行う(0:A, 1:B, 3:C)
            for (int j = 0; j < 3; j++)
            {
                // 例えば活動aを行う場合は、翌日にa以外を行う。
                // 「翌日bを行う場合の幸福度 + 今日活動aを行った幸福度」と
                // 「翌日cを行う場合の幸福度 + 今日活動aを行った幸福度」
                // 以上2パターンのうち大きいほうをi日目に活動aを行った場合の最大値とする
                var res1 = dp[i + 1, (j + 1) % 3] + ABC[i, (j + 1) % 3];
                var res2 = dp[i + 1, (j + 2) % 3] + ABC[i, (j + 2) % 3];
                dp[i, j] = Math.Max(res1, res2);
            }
        }

        // DP[0, j] には初日に3パターンの活動を行う場合の幸福の最大値が入っている
        var ans = Math.Max(dp[0, 0], Math.Max(dp[0, 1], dp[0, 2]));
        Console.WriteLine(ans);
    }

    static string[,] DP;
    static string S;
    static string T;

    static int MOD = (int)1e9 + 7;
    static int INF = (int)1e7 + 1;
    static long LINF = (long)1e13 + 1;
    static Random Rand = new Random();
    static Scanner sc = new Scanner();

    static long Gcd(long a, long b)
    {
        var v = new[] { a, b };
        while (v[1] != 0) { v = new[] { v[1], v[0] % v[1] }; }
        return v[0];
    }
    static long Lcm(long a, long b)
    {
        return a / Gcd(a, b) * b;
    }
    static bool IsPrime(long num)
    {
        if (num < 2) return false;
        else if (num == 2) return true;
        else if (num % 2 == 0) return false;

        double sqrtNum = Math.Sqrt(num);
        for (int i = 3; i <= sqrtNum; i += 2)
        {
            if (num % i == 0)
            {
                return false;
            }
        }
        return true;
    }
    static List<long> PrimeFactors(long n)
    {
        var res = new List<long>();
        var tmp = n;
        for (long x = 2; x * x <= n; x++)
        {
            while (tmp % x == 0)
            {
                tmp /= x;
                res.Add(x);
            }
        }
        if (tmp != 1) res.Add(tmp);
        return res;
    }
    static long[] Divisor(long n)
    {
        var res = new List<long>();
        for (int i = 1; i * i <= n; i++)
        {
            if (n % i == 0)
            {
                res.Add(i);
                if (i * i != n) res.Add(n / i);
            }
        }
        return res.ToArray();
    }
    static Result[] ListAll<T1, T2, Result>(IEnumerable<T1> a, IEnumerable<T2> b, Func<T1, T2, Result> f)
    {
        Result[] res = new Result[a.Count() * b.Count()];
        var i = 0;
        foreach (var v in a)
            foreach (var w in b)
                res[i++] = f(v, w);
        return res;
    }
    static IEnumerable<Result> ListAll<T1, T2, Result>(IEnumerable<T1> a, IEnumerable<T2> b, Func<T1, T2, Result> f, Func<T1, T2, bool> s)
    {
        foreach (var v in a)
        {
            foreach (var w in b)
                if (s(v, w)) yield return f(v, w);
        }
    }
    static List<long> Facs = new List<long>() { 1 };
    static long Fac(int n)
    {
        for (int i = Facs.Count; i <= n; i++)
        {
            Facs.Add(i * Facs[i - 1]);
        }
        return Facs[n];
    }
    static long nCr(int n, int r)
    {
        if (n < r) return 0;
        if (n == r) return 1;
        var res = Fac(n);
        res /= Fac(r);
        res /= Fac(n - r);
        return res;
    }
}

public struct ModInt
{
    public const long Mod = (int)1e9 + 7;
    public long num;
    public ModInt(long n) { num = n; }
    public override string ToString() { return num.ToString(); }
    public static ModInt operator +(ModInt l, ModInt r) { l.num += r.num; if (l.num >= Mod) l.num -= Mod; return l; }
    public static ModInt operator -(ModInt l, ModInt r) { l.num -= r.num; if (l.num < 0) l.num += Mod; return l; }
    public static ModInt operator *(ModInt l, ModInt r) { return new ModInt(l.num * r.num % Mod); }
    public static implicit operator ModInt(long n) { n %= Mod; if (n < 0) n += Mod; return new ModInt(n); }
    public static ModInt Pow(ModInt v, long k) { return Pow(v.num, k); }
    public static ModInt Pow(long v, long k)
    {
        long ret = 1;
        for (k %= Mod - 1; k > 0; k >>= 1, v = v * v % Mod)
            if ((k & 1) == 1) ret = ret * v % Mod;
        return new ModInt(ret);
    }
    public static ModInt Inverse(ModInt v) { return Pow(v, Mod - 2); }
}
public class BinomialCoefficient
{
    public ModInt[] fact, ifact;
    public BinomialCoefficient(int n)
    {
        fact = new ModInt[n + 1];
        ifact = new ModInt[n + 1];
        fact[0] = 1;
        for (int i = 1; i <= n; i++)
            fact[i] = fact[i - 1] * i;
        ifact[n] = ModInt.Inverse(fact[n]);
        for (int i = n - 1; i >= 0; i--)
            ifact[i] = ifact[i + 1] * (i + 1);
        ifact[0] = ifact[1];
    }
    public ModInt this[int n, int r]
    {
        get
        {
            if (n < 0 || n >= fact.Length || r < 0 || r > n) return 0;
            return fact[n] * ifact[n - r] * ifact[r];
        }
    }
    public ModInt RepeatedCombination(int n, int k)
    {
        if (k == 0) return 1;
        return this[n + k - 1, k];
    }
}

class Debug
{
    public static void Dump<T>(T[,] array)
    {
        Console.WriteLine();
        var h = array.GetLength(0);
        var w = array.GetLength(1);

        for (int r = 0; r < h; r++)
        {
            for (int c = 0; c < w; c++)
            {
                Console.Write(array[r, c]);
                Console.Write(" ");
            }
            Console.WriteLine();
        }
        Console.WriteLine();
    }
    public static void Dump<T>(T[] array)
    {
        Console.WriteLine();
        Console.WriteLine(string.Join(" ", array));
        Console.WriteLine();
    }
}

class Scanner
{
    string[] S = new string[0];
    int Index = 0;
    char[] Separators = new char[] { ' ' };

    public string Next()
    {
        if (this.Index < this.S.Length) return this.S[this.Index++];
        var line = "";
        while (line == "") line = Console.ReadLine();
        this.S = line.Split(this.Separators, StringSplitOptions.RemoveEmptyEntries);
        if (this.S.Length == 0) return this.Next();
        this.Index = 0;
        return this.S[this.Index++];
    }

    public string ReadStr()
    {
        return this.Next();
    }

    public char ReadChar()
    {
        return this.Next()[0];
    }

    public int ReadInt()
    {
        return int.Parse(this.Next());
    }

    public uint ReadUInt()
    {
        return uint.Parse(this.Next());
    }

    public long ReadLong()
    {
        return long.Parse(this.Next());
    }

    public int[] ReadIntArray(int n)
    {
        var array = new int[n];
        for (int i = 0; i < array.Length; i++)
        {
            array[i] = this.ReadInt();
        }
        return array;
    }

    public long[] ReadLongArray(int n)
    {
        var array = new long[n];
        for (int i = 0; i < array.Length; i++)
        {
            array[i] = this.ReadLong();
        }
        return array;
    }

    public char[] ReadCharArray(int n)
    {
        var array = new char[n];
        for (int i = 0; i < array.Length; i++)
        {
            array[i] = this.ReadChar();
        }
        return array;
    }

    public string[] ReadStrArray(int n)
    {
        var array = new string[n];
        for (int i = 0; i < array.Length; i++)
        {
            array[i] = this.ReadStr();
        }
        return array;
    }
}

static class Permutation<T>
{
    private static void Search(List<T[]> perms, Stack<T> stack, T[] a)
    {
        int N = a.Length;
        if (N == 0)
        {
            perms.Add(stack.Reverse().ToArray());
        }
        else
        {
            var b = new T[N - 1];
            Array.Copy(a, 1, b, 0, N - 1);
            for (int i = 0; i < a.Length; ++i)
            {
                stack.Push(a[i]);
                Search(perms, stack, b);
                if (i < b.Length) { b[i] = a[i]; }
                stack.Pop();
            }
        }
    }
    public static List<T[]> All(params T[] source)
    {
        var perms = new List<T[]>();
        Search(perms, new Stack<T>(), source);
        return perms;
    }
}

class HashMap<K, V> : Dictionary<K, V> where V : new()
{
    private V DefaltValue = new V();
    public HashMap() { }
    public HashMap(V defaultValue)
    {
        this.DefaltValue = new V();
    }
    new public V this[K i]
    {
        get
        {
            V v;
            return TryGetValue(i, out v) ? v : base[i] = this.DefaltValue;
        }
        set { base[i] = value; }
    }
}

class Vector<T> : List<T> where T : new()
{
    public Vector() { }
    public Vector(int count, T defaultValue)
    {
        for (int i = 0; i < count; i++)
        {
            this.Add(defaultValue);
        }
    }
}

class PriorityQueue<T> where T : IComparable<T>
{
    public readonly T[] Array;
    public readonly bool Greater;
    public int Count { get; private set; } = 0;

    public PriorityQueue(int capacity, bool greater = true)
    {
        this.Array = new T[capacity];
        this.Greater = greater;
    }

    public void Enqueue(T item)
    {
        this.Array[this.Count] = item;
        this.Count += 1;
        this.UpHeap();
    }

    public T Dequeue()
    {
        this.Swap(0, this.Count - 1);
        this.Count -= 1;
        this.DownHeap();

        return this.Array[this.Count];
    }

    public T Peek()
    {
        return this.Array[0];
    }

    private void UpHeap()
    {
        var n = this.Count - 1;
        while (n != 0)
        {
            var parent = (n - 1) / 2;

            if (this.Array[n].CompareTo(this.Array[parent]) > 0)
            {
                this.Swap(n, parent);
                n = parent;
            }
            else
            {
                break;
            }
        }
    }

    private void DownHeap()
    {
        var parent = 0;
        while (true)
        {
            var child = 2 * parent + 1;
            if (child > this.Count - 1) break;

            if (child < this.Count - 1 && this.Compare(this.Array[child], this.Array[child + 1]) < 0)
            {
                child += 1;
            }

            if (this.Compare(this.Array[parent], this.Array[child]) < 0)
            {
                this.Swap(parent, child);
                parent = child;
            }
            else
            {
                break;
            }
        }
    }

    private int Compare(T a, T b)
    {
        var c = a.CompareTo(b);
        if (!this.Greater)
        {
            c = -c;
        }
        return c;
    }

    private void Swap(int a, int b)
    {
        var tmp = this.Array[a];
        this.Array[a] = this.Array[b];
        this.Array[b] = tmp;
    }
}

class UnionFind
{
    public int[] Parents { get; set; }
    public UnionFind(int n)
    {
        this.Parents = new int[n];
        for (int i = 0; i < n; i++)
        {
            this.Parents[i] = i;
        }
    }
    public int Find(int x)
    {
        if (this.Parents[x] != x)
        {
            this.Parents[x] = Find(this.Parents[x]);
        }
        return this.Parents[x];
    }
    public bool Same(int x, int y)
    {
        return this.Find(x) == this.Find(y);
    }
    public int Union(int x, int y)
    {
        var xroot = this.Find(x);
        var yroot = this.Find(y);
        if (xroot != yroot) this.Parents[xroot] = yroot;
        return yroot;
    }
}
static class Algorithm
{
    static int binarySearch<T>(IList<T> a, T v, IComparer<T> cmp, bool islb)
    {
        var l = 0;
        var r = a.Count - 1;
        while (l <= r)
        {
            var m = (l + r) / 2;
            var res = cmp.Compare(a[m], v);
            if (res < 0 || (res == 0 && !islb)) l = m + 1;
            else r = m - 1;
        }
        return l;
    }
    public static int LowerBound<T>(this IList<T> a, T v, Comparison<T> f) { return binarySearch(a, v, Comparer<T>.Create(f), true); }
    public static int LowerBound<T>(this IList<T> a, T v) { return binarySearch(a, v, Comparer<T>.Default, true); }
    public static int UpperBound<T>(this IList<T> a, T v, Comparison<T> cmp) { return binarySearch(a, v, Comparer<T>.Create(cmp), false); }
    public static int UpperBound<T>(this IList<T> a, T v) { return binarySearch(a, v, Comparer<T>.Default, false); }
}