Given a binary tree which has T nodes, you need to find the diameter of that binary tree. The diameter of a tree is the number of nodes on the longest path between two leaves in the tree.

Input:
First line contains two integers, T and X, number of nodes in the tree and value of the root.
Next $2\times (T-1)$ lines contain details of nodes.
Each detail of node contains two lines. First lines contains a string and second line contains an integer, which denotes the path of the node and the value of the node respectively.

String consists of only L or R. L denotes left child and R denotes right child. ( Look at the sample explanation for more details )

Output:
Print the diameter of the binary tree.

Constraints:
$1 \le T \le 20$
$1 \le value of nodes \le 20$