treeBottom

You are given a recursive notation of a binary tree: each node of a tree is represented as a set of three elements:

value of the node;
left subtree;
right subtree.

So, a tree can be written as (value left_subtree right_subtree). It is guaranteed that 1 ≤ value ≤ 10⁹. If a node doesn’t exist then it is represented as an empty set: (). For example, here is a representation of a tree in the given picture: (2 (7 (2 () ()) (6 (5 () ()) (11 () ()))) (5 () (9 (4 () ()) ())))

Your task is calculate the sum of nodes that are the most distant from the tree root.

In the notation of a node its value and subtrees are separated by exactly one space character.

Example

For tree = "(2 (7 (2 () ()) (6 (5 () ()) (11 () ()))) (5 () (9 (4 () ()) ())))" the output should be treeBottom(tree) = 5+ 11 + 4 = 20

Input/Output

[execution time limit] 0.5 seconds
[input] string tree

Guaranteed constraints:
9 ≤ tree.length ≤ 1000.
[output] array.integer
- the sum of nodes that are the most distant from the tree root.