Kingdom Roadmap

The Kingdom consists of n cities connected by n − 1 roads in such a way that there is exactly one route between any two cities. In other words, the cities and roads form a tree.

The King is a busy man and constantly travels from city to city. Unfortunately, during one of his journeys a road was damaged and needed serious repairs, and as a result the King could not reach his destination in time.

After the incident the King decided to improve the reliability of the road network. The improved network must withstand the loss of any single road: even if one road becomes unusable, there must still be a path between every pair of cities. Because the budget is limited, the number of newly built roads must be as small as possible.

Determine the minimum number of new roads that must be built so that every pair of cities remains connected even if any one road becomes unusable.

The first line contains an integer n — the number of cities in the kingdom (2 ≤ n ≤ 100 000).

Each of the following n − 1 lines contains two integers uᵢ and vᵢ — the two cities connected by the i-th road (1 ≤ uᵢ, vᵢ ≤ n).

Print a single integer — the minimum number of new roads that must be built so that every pair of cities stays connected even if any single road becomes unusable.