Problem Description

It is known that a connected undirected graph with both the number of vertices and edges equal to $n$ contains exactly one loop.

Given such a graph, determine the length of the loop in the graph.

Input Format

The input is given in the following format:

$ n $ $ x_1 $ $ y_1 $ $ ... $ $ x_n $ $ y_n $

• The first line contains an integer $ n $ ($3\ \leq\ n\ \leq\ 100{,}000$), representing the number of vertices in the graph.
• The following $ n $ lines contain the edge information of the graph.
• Each vertex is numbered from $ 1 $ to $ n $, and $ x_i, y_i $ ($1\ \leq\ x_i, y_i\ \leq\ n$) indicate that the $ i $th edge connects the two vertices $ x_i $ and $ y_i $.
• The given graph is guaranteed to be connected and does not contain self-loops or multiple edges.

Output Format

Output the length of the loop in the graph in one line.

End with a newline and do not include any extra characters or blank lines.

Sample Input and Output

Sample Input #1

4
1 2
2 3
3 1
1 4

Sample Output #1

3

Sample Input #2

4
1 2
2 3
3 4
4 1

Sample Output #2

4

Notes/Hints

None

见题面 Input 部分

见题面 Output 部分