Limak is a little bear who learns to draw. People usually start with houses, fences and flowers but why would bears do it? Limak lives in the forest and he decides to draw a tree.

Recall that tree is a connected graph consisting of n vertices and n - 1 edges.

Limak chose a tree with n vertices. He has infinite strip of paper with two parallel rows of dots. Little bear wants to assign vertices of a tree to some n distinct dots on a paper so that edges would intersect only at their endpoints — drawn tree must be planar. Below you can see one of correct drawings for the first sample test.

<image>

Is it possible for Limak to draw chosen tree?

Input

The first line contains single integer n (1 ≤ n ≤ 105).

Next n - 1 lines contain description of a tree. i-th of them contains two space-separated integers ai and bi (1 ≤ ai, bi ≤ n, ai ≠ bi) denoting an edge between vertices ai and bi. It's guaranteed that given description forms a tree.

Output

Print "Yes" (without the quotes) if Limak can draw chosen tree. Otherwise, print "No" (without the quotes).

Examples

Input

8
1 2
1 3
1 6
6 4
6 7
6 5
7 8


Output

Yes


Input

13
1 2
1 3
1 4
2 5
2 6
2 7
3 8
3 9
3 10
4 11
4 12
4 13


Output

No
import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.StringTokenizer;
import java.io.IOException;
import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author Bat-Orgil
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        TaskC solver = new TaskC();
        solver.solve(1, in, out);
        out.close();
    }

    static class TaskC {
        static ArrayList<Integer>[] G;
        static boolean[] del;
        static int[] leg;

        static void dfs(int node, int par) {
            if (G[node].size() <= 2) {
                del[node] = true;
                for (int i = 0; i < G[node].size(); i++) {
                    int c = G[node].get(i);
                    if (c != par) {
                        dfs(c, node);
                    }
                }
            }
        }

        public void solve(int testNumber, InputReader in, PrintWriter out) {
            int n = in.nextInt();
            G = new ArrayList[n];
            for (int i = 0; i < n; i++) {
                G[i] = new ArrayList();
            }
            for (int i = 0; i < (n - 1); i++) {
                int a = in.nextInt() - 1;
                int b = in.nextInt() - 1;
                G[a].add(b);
                G[b].add(a);
            }
            del = new boolean[n];
            leg = new int[n];
            for (int i = 0; i < n; i++) {
                if (G[i].size() == 1) {
                    dfs(i, -1);
                }
            }

            for (int i = 0; i < n; i++) {
                int c = 0;
                for (int j = 0; j < G[i].size(); j++) {
                    if (del[G[i].get(j)]) c++;
                }
                c = Math.min(2, c);
                leg[i] = c;
            }

            for (int i = 0; i < n; i++) {
                int count = 0;

                for (int j = 0; j < G[i].size(); j++) {
                    int neighbor = G[i].get(j);
                    if (!del[neighbor] && (G[neighbor].size() - leg[neighbor] > 1)) {
                        count++;
                    }
                }
                if (count > 2) {
                    out.println("No");
                    return;
                }
            }
            out.println("Yes");


        }

    }

    static class InputReader {
        public BufferedReader reader;
        public StringTokenizer tokenizer;

        public InputReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream), 32768);
            tokenizer = null;
        }

        public String next() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }

        public int nextInt() {
            return Integer.parseInt(next());
        }

    }
}

