You are given an unweighted, undirected tree. Write a program to find a vertex set of minimum size in this tree such that each edge has as least one of its end-points in that set.

Input

The first line of the input file contains one integer N – number of nodes in the tree (0 < N ≤ 100000). Next N-1 lines contain N-1 edges of that tree – Each line contains a pair (u, v) means there is an edge between node u and node v (1 ≤ u,v ≤ N).

Output

Print number of nodes in the satisfied vertex set on one line.

Example 1

Input:
3
1 2
1 3

Output:
1

Explanation

The set can be {1}

Example 2

Input:
3
1 2
2 3
Output:
1

Explanation

The set can be {2}