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.util.ArrayList;
import java.util.List;
import java.util.Scanner;

public class Wuyouwulv {
    private static final int maxn = 100010;
    private static ArrayList<Integer> g[];
    private static int[] legs = new int[maxn];
    private static int[] degree = new int[maxn];
    private static boolean[] del = new boolean[maxn];
    
    private static void dfs(int u, int pa) {
        int sz = g[u].size();
        if(sz > 2) {
            legs[u] ++;
            return;
        }
        del[u] = true;
        for(int v : g[u]) {
            if(v == pa) continue;
            dfs(v, u);
        }
    }
    
    public static void main(String[] args) {
        Scanner in = new Scanner(System.in);
        while(in.hasNext()) {
            int n = in.nextInt();
            g = new ArrayList[n];
            for(int i=0;i<n;i++) g[i] = new ArrayList<Integer>();
            for(int i=1;i<n;i++) {
                int u , v;
                u = in.nextInt() - 1;
                v = in.nextInt() - 1;
                g[u].add(v);
                g[v].add(u);
                degree[u] ++;
                degree[v] ++;
            }
            for(int i=0;i<n;i++) {
                if(!del[i] && degree[i] == 1) {
                    dfs(i, -1);
                }
            }
            for(int u=0;u<n;u++) {
                if(!del[u] && degree[u] - Math.min(legs[u], 2) > 1) {
                    int cnt = 0;
                    for(int v : g[u]) {
                        if(!del[v] && degree[v] - Math.min(legs[v], 2) > 1) {
                            cnt ++;
                            if(cnt > 2) {
                                System.out.println("No");
                                return;
                            }
                        }
                    }
                }
            }
            System.out.println("Yes");
            return;
        }
    }
}