Path sum is the sum of the numbers on a path in BST. For example the sum of the numbers

  15 + 12 + 14 + 13 = 54

Question: Write a program to find the largest path sum in a given BST.

Input specification
In the first line, you will be given an integer (n) The number of numbers in the BST where 0 ≤ n ≤ 1e4. Then, in the following n lines, you will be given n integers which are between -1e4 and 1e4.

Output specification
Show one number: Largest path sum.