The Triangle

Figure 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 greater than 1 but less or equal 100.

• The numbers in the triangle, all integers, are between 0 and 99.

Input

First given the number of rows in triangle. Next rows describe the triangle itself.

Output

Print the maximum sum from top to the base of triangle.

Examples