7
          3   8
        8   1   0
      2   7   4   4
    4   5   2   6   5     (Figure 1)

Figure 1 shows a number triangle.

Write a program that calculates the highest sum of numbers passed on a route that starts at the top and ends somewhere on the base.

• Each step can go either diagonally down to the left or diagonally down to the right.
• The number of rows in the triangle is ~> 1~ but ~\le 100~.
• The numbers in the triangle, all integers, are between ~0~ and ~99~.

Input Specification

The first line of input will contain an integer ~N~. The ~i^{th}~ of the next ~N~ lines will contain ~i~ space-separated integers, denoting the values of the triangle.

Output Specification

The highest sum as required by the problem statement.

Sample Input

5
7
3 8
8 1 0
2 7 4 4
4 5 2 6 5

Sample Output

30