Problem Statement

You are given a tree with $N$ vertices rooted at vertex $1$. Using this tree and $1$ piece, you perform the following operations.

1. First, choose $1$ vertex and place the piece on it.
2. Repeatedly move the piece to a vertex on which it has never been placed. Here, counting the move right after the initial placement of the piece as the $1$st move, on odd-numbered moves the piece is moved to "a vertex that is an ancestor of the vertex where the piece currently is", and on even-numbered moves it is moved to "a vertex that is a descendant of the vertex where the piece currently is".
3. If there is no vertex to which the piece can be moved, the operations end.

Your score is the number of vertices on which the piece has been placed during this series of operations, performed only once until it ends. Find the maximum score you can obtain.
Here, among the $N-1$ edges of the tree with $N$ vertices, the $i$-th edge connects $A_i$ and $B_i$ given in the input. Also, for vertices $u$, $v$, both "$u$ is an ancestor of $v$" and "$v$ is a descendant of $u$" mean that "$u$ lies on the shortest path connecting $1$ and $v$".

Input

$N$
$A_1\ B_1$
$A_2\ B_2$
...
$A_{N-1}\ B_{N-1}$

• $1\leq N\leq 10^5$
• $1\leq A_i,B_i\leq N$ $(1\leq i\leq N-1)$
• The given graph is a tree
• All inputs are integers

Output

Output the maximum score you can obtain as an integer. Print a newline at the end.

Sample