The National Genealogical Society (NGS) is a non governmental organization dedicated to assisting its members in genealogical research. Elections for the Executive Board of the Society are currently underway.

All members of the NGS are eligible voters, each having a number of votes equal to the rank level of his or her officially registered genealogical tree. The rank level of a tree depends on its size and shape, and is statutorily defined as follows:

"[...] is to be obtained by rounding down to the nearest integer, the average height of all complete paths included in the tree. A complete path is an ascending path connecting the root to a leaf. The height of a path is the number of its nodes."

The following tree contains 3 complete paths: two of height 3 and one of height 4. The rank level of this tree is therefore (3+3+4)/3 = 3, hence the number of votes of Mary John is 3.

Write a program that calculates the rank level of a given genealogical tree.

Input

The input contains a genealogical tree, organized according to the following recursive rules.

• The empty tree is represented by a line containing a single dot (".").

• A non-empty tree is represented using multiple consecutive lines:
  • the first line contains the root of the tree (a name);
  • the following lines contain the left subtree;
  • the next lines contain the right subtree.

The output consists of a single line that contains the rank level of the tree (an integer).

Sample Input

Mary John
Thomas John
Efstration John
.
.
Diamantina Kaskabas
.
.
Sarah Sally
.
Mary Ann
John Smith
.
.
.

3