Description

Format

Input

第1行输入N，之后N行每行输入一对整数，描述一条道路．

Output

输出宝藏的埋藏方式种数．

Samples

4
1 2
2 3
3 1
1 4

3

Limitation

INPUT DETAILS:

Here is a drawing of the roads and the intersections.

4---1---2 \ / 3

OUTPUT DETAILS:

The treasure can be buried at any intersection. However, burying it at intersections 2 and 3 yields maps that are identical to each other. So the total number of distinct treasure maps is 3.