Tree with Small Distances

You 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 ≤ n ≤ 2 ⋅ 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 ≤ u_i, v_i ≤ 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).

inputFormat

Input

The first line contains one integer n (2 ≤ n ≤ 2 ⋅ 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 ≤ u_i, v_i ≤ 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.

outputFormat

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).

样例

7
1 2
2 3
3 4
3 5
3 6
3 7

1

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