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Description

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.

Samples

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

2

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

0

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

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 $(1, 3)$.