Problem:
Score : 900 points

Problem Statement

We have a tree with N vertices.
The vertices are numbered 0 through N - 1, and the i-th edge (0 ≤ i < N - 1) comnnects Vertex a_i and b_i.
For each pair of vertices u and v (0 ≤ u, v < N), we define the distance d(u, v) as the number of edges in the path u-v.

It is expected that one of the vertices will be invaded by aliens from outer space.
Snuke wants to immediately identify that vertex when the invasion happens.
To do so, he has decided to install an antenna on some vertices.

First, he decides the number of antennas, K (1 ≤ K ≤ N).
Then, he chooses K different vertices, x_0, x_1, ..., x_{K - 1}, on which he installs Antenna 0, 1, ..., K - 1, respectively.
If Vertex v is invaded by aliens, Antenna k (0 ≤ k < K) will output the distance d(x_k, v).
Based on these K outputs, Snuke will identify the vertex that is invaded.
Thus, in order to identify the invaded vertex no matter which one is invaded, the following condition must hold:

For each vertex u (0 ≤ u < N), consider the vector (d(x_0, u), ..., d(x_{K - 1}, u)). These N vectors are distinct.

Find the minumum value of K, the number of antennas, when the condition is satisfied.

Constraints

2 ≤ N ≤ 10^5

0 ≤ a_i, b_i < N

The given graph is a tree.

Input

Input is given from Standard Input in the following format:

N
a_0 b_0
a_1 b_1
:
a_{N - 2} b_{N - 2}

Output

Print the minumum value of K, the number of antennas, when the condition is satisfied.

Sample Input 1

5
0 1
0 2
0 3
3 4

Sample Output 1

2

For example, install an antenna on Vertex 1 and 3.
Then, the following five vectors are distinct:

(d(1, 0), d(3, 0)) = (1, 1)

(d(1, 1), d(3, 1)) = (0, 2)

(d(1, 2), d(3, 2)) = (2, 2)

(d(1, 3), d(3, 3)) = (2, 0)

(d(1, 4), d(3, 4)) = (3, 1)

Sample Input 2

2
0 1

Sample Output 2

1

For example, install an antenna on Vertex 0.

Sample Input 3

10
2 8
6 0
4 1
7 6
2 3
8 6
6 9
2 4
5 8

Sample Output 3

3

For example, install an antenna on Vertex 0, 4, 9.

Solution in Java8 (OpenJDK 1.8.0) (judge verdict: Wrong Answer)

import java.util.ArrayList;
import java.util.Collections;
import java.util.Scanner;
import java.util.SplittableRandom;

public class Main {
  static long startTime = System.currentTimeMillis();
  static Scanner sc = new Scanner(System.in);
  static ArrayList<ArrayList<Integer>> nei = new ArrayList<>();
  static int[] visited;
  static int vc;

  public static void main(String[] args) {
    int N = sc.nextInt();
    visited = new int[N];
    for (int i = 0; i < N; i++) {
      nei.add(new ArrayList<>());
    }
    for (int i = 0; i < N - 1; i++) {
      int A = Integer.parseInt(sc.next());
      int B = Integer.parseInt(sc.next());
      nei.get(A).add(B);
      nei.get(B).add(A);
    }
    ArrayList<Integer> cand = new ArrayList<>();
    ArrayList<Integer> other = new ArrayList<>();
    for (int i = 0; i < N; i++) {
      if (nei.get(i).size() == 1) {
        cand.add(i);
      } else {
        other.add(i);
      }
    }
    int ans = N;
    SplittableRandom rnd = new SplittableRandom();
    Collections.shuffle(cand);
    Collections.shuffle(other);
    for (int i = 0; i < cand.size(); i++) {
      if (System.currentTimeMillis() - startTime > 1800) break;
      int start = cand.get(i);
      ans = Math.min(ans, count(start));
    }
    for (int i = 0; i < other.size(); i++) {
      if (System.currentTimeMillis() - startTime > 1800) break;
      int start = other.get(i);
      ans = Math.min(ans, count(start));
    }
    System.out.println(ans);
  }

  static int count(int s) {
    ++vc;
    int ret = 1;
    ArrayList<Integer> cur = new ArrayList<>();
    ArrayList<Integer> next = new ArrayList<>();
    cur.add(s);
    visited[s] = vc;
    while (!cur.isEmpty()) {
      ret = Math.max(ret, cur.size());
      for (int c : cur) {
        for (int n : nei.get(c)) {
          if (visited[n] == vc) continue;
          next.add(n);
          visited[n] = vc;
        }
      }
      ArrayList<Integer> tmp = cur;
      cur = next;
      next = tmp;
      next.clear();
    }
    return ret;
  }

}