You are given a tree with $n$ vertices. You are allowed to modify the structure of the tree through the following multi-step operation:

1. Choose three vertices $a$, $b$, and $c$ such that $b$ is adjacent to both $a$ and $c$.
2. For every vertex $d$ other than $b$ that is adjacent to $a$, remove the edge connecting $d$ and $a$ and add the edge connecting $d$ and $c$.
3. Delete the edge connecting $a$ and $b$ and add the edge connecting $a$ and $c$.

As an example, consider the following tree:

The following diagram illustrates the sequence of steps that happen when we apply an operation to vertices $2$, $4$, and $5$:

It can be proven that after each operation, the resulting graph is still a tree.

Find the minimum number of operations that must be performed to transform the tree into a star. A star is a tree with one vertex of degree $n - 1$, called its center, and $n - 1$ vertices of degree $1$.

The first line contains an integer $n$ ($3 \le n \le 2 \cdot 10^5$)  — the number of vertices in the tree.

The $i$-th of the following $n - 1$ lines contains two integers $u_i$ and $v_i$ ($1 \le u_i, v_i \le n$, $u_i \neq v_i$) denoting that there exists an edge connecting vertices $u_i$ and $v_i$. It is guaranteed that the given edges form a tree.

Print a single integer  — the minimum number of operations needed to transform the tree into a star.

It can be proven that under the given constraints, it is always possible to transform the tree into a star using at most $10^{18}$ operations.