Vacation

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.

Examples

Input

3 10 40 70 20 50 80 30 60 90

Output

210

Input

1 100 10 1

Output

100

Input

7 6 7 8 8 8 3 2 5 2 7 8 6 4 6 8 2 3 4 7 5 1

Output

46

inputFormat

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

outputFormat

Output

Print the maximum possible total points of happiness that Taro gains.

Examples

Input

3 10 40 70 20 50 80 30 60 90

Output

210

Input

1 100 10 1

Output

100

Input

7 6 7 8 8 8 3 2 5 2 7 8 6 4 6 8 2 3 4 7 5 1

Output

46

样例

3
10 40 70
20 50 80
30 60 90

210