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E. Tree with Small Distances

time limit per test

1 secondmemory limit per test

256 megabytesinput

standard inputoutput

standard outputYou are given an undirected tree consisting of $$$n$$$ vertices. An undirected tree is a connected undirected graph with $$$n - 1$$$ edges.

Your task is to add the minimum number of edges in such a way that the length of the shortest path from the vertex $$$1$$$ to any other vertex is at most $$$2$$$. Note that you are not allowed to add loops and multiple edges.

Input

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

The following $$$n - 1$$$ lines contain edges: edge $$$i$$$ is given as a pair of vertices $$$u_i, v_i$$$ ($$$1 \le u_i, v_i \le n$$$). It is guaranteed that the given edges form a tree. It is guaranteed that there are no loops and multiple edges in the given edges.

Output

Print a single integer — the minimum number of edges you have to add in order to make the shortest distance from the vertex $$$1$$$ to any other vertex at most $$$2$$$. Note that you are not allowed to add loops and multiple edges.

Examples

Input

7

1 2

2 3

2 4

4 5

4 6

5 7

Output

2

Input

7

1 2

1 3

2 4

2 5

3 6

1 7

Output

0

Input

7

1 2

2 3

3 4

3 5

3 6

3 7

Output

1

Note

The tree corresponding to the first example: The answer is $$$2$$$, some of the possible answers are the following: $$$[(1, 5), (1, 6)]$$$, $$$[(1, 4), (1, 7)]$$$, $$$[(1, 6), (1, 7)]$$$.

The tree corresponding to the second example: The answer is $$$0$$$.

The tree corresponding to the third example: The answer is $$$1$$$, only one possible way to reach it is to add the edge $$$(1, 3)$$$.

Codeforces (c) Copyright 2010-2020 Mike Mirzayanov

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