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++ (GCC 9.2.1) (judge verdict: Accepted)


// Problem : C - Vacation
// Contest : AtCoder - Educational DP Contest
// URL : https://atcoder.jp/contests/dp/tasks/dp_c?lang=en
// Memory Limit : 1024 MB
// Time Limit : 2000 ms
// Powered by CP Editor (https://github.com/cpeditor/cpeditor)
#define _CRT_SECURE_NO_WARNINGS
#define _USE_MATH_DEFINES
#include<bits/stdc++.h>
#include<unordered_map>
using namespace std;
#define Ma7moud_7amdy                 \
    ios_base::sync_with_stdio(false); \
    cin.tie(NULL);                    \
    cout.tie(NULL)
#define Open_Sesame Open()
#define all(v) ((v).begin()), ((v).end())
#define allr(v) ((v).rbegin()), ((v).rend())
#define clr(arr, x) memset(arr, x, sizeof arr)
#define endl "\n"
#define watch(x) cout << #x << " = " << x << endl;
#define RT(x) return cout << (x), 0;
#define Accepted 0
typedef long long ll;
typedef vector<int> vi;
const int dx[] = { 1, 0, -1, 0, 1, 1, -1, -1 };
const int dy[] = { 0, 1, 0, -1, 1, -1, 1, -1 };
void Open()
{
#ifndef ONLINE_JUDGE 
	freopen("Input.txt", "r", stdin);
	freopen("Output.txt", "w", stdout);
#endif
}
const int mod = ll(1e9 + 7), N = 1e5 + 5;
//“Nobody but you have to believe in your dreams to make them a reality.” ― Germany Kent

struct Vacation {
	int Swim, bugs, homework;
};
int n;
vector<Vacation> v;
//int mem[N][4];
int dp[N][4];
/*int solve(int idx = 0, int prev = 0)
{
	if (idx == n)
		return 0;
	int& ret = mem[idx][prev];
	if (~ret)return ret;
	ret = 0;
	if (prev != 1)
		ret = max(ret, solve(idx + 1, 1) + v[idx].Swim);
	if (prev != 2)
		ret = max(ret, solve(idx + 1, 2) + v[idx].bugs);
	if (prev != 3)
		ret = max(ret, solve(idx + 1, 3) + v[idx].homework);

	return ret;
}*/
int main()
{
	Ma7moud_7amdy;
	Open_Sesame;
	//clr(mem, -1);
	cin >> n;
	v = vector<Vacation>(n);
	for (int i = 0; i < n; i++)
		cin >> v[i].Swim >> v[i].bugs >> v[i].homework;
	//cout << solve() << endl;

	//baseCase
	dp[n][1] = dp[n][2] = dp[n][3] = 0;


	for (int idx = n-1; idx >=0; idx--) {
		int& ret1 = dp[idx][1];
		int& ret2 = dp[idx][2];
		int& ret3 = dp[idx][3];
		ret1 = ret2 = ret2 = 0;;

		ret1 = max(ret1, dp[idx + 1][2] + v[idx].Swim);
		ret1 = max(ret1, dp[idx + 1][3] + v[idx].Swim);

		ret2 = max(ret2, dp[idx + 1][1] + v[idx].bugs);
		ret2 = max(ret2, dp[idx + 1][3] + v[idx].bugs);

		ret3 = max(ret3, dp[idx + 1][1] + v[idx].homework);
		ret3 = max(ret3, dp[idx + 1][2] + v[idx].homework);

	}

	cout << max({ dp[0][1],dp[0][2],dp[0][3] }) << endl;
}