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
#include <bits/stdc++.h>
using namespace std;
vector<int> adj[100010], c[100010], par[100010], leaf;
int vis[100010], mark[100010], lab[100010], cnt[100010];
void dfs(int v) {
  vis[v] = 1;
  for (int i = 0; i < adj[v].size(); i++) {
    if (vis[adj[v][i]]) continue;
    dfs(adj[v][i]);
    c[v].push_back(adj[v][i]);
  }
}
void label(int cur, int prev) {
  if (adj[cur].size() > 2) return;
  lab[cur] = 1;
  for (int i = 0; i < adj[cur].size(); i++) {
    if (adj[cur][i] == prev) continue;
    label(adj[cur][i], cur);
  }
}
int main() {
  int n, u, v;
  cin >> n;
  if (n <= 3) {
    cout << "Yes" << endl;
    return 0;
  }
  for (int i = 0; i < n - 1; i++) {
    cin >> u >> v;
    adj[u].push_back(v);
    adj[v].push_back(u);
  }
  int root;
  for (int i = 1; i <= n; i++) {
    if (adj[i].size() > 1) {
      root = i;
      dfs(i);
      break;
    }
  }
  dfs(root);
  for (int i = 1; i <= n; i++) {
    if (adj[i].size() >= 2) mark[i] = 1;
    if (adj[i].size() == 1) leaf.push_back(i);
  }
  for (int i = 0; i < leaf.size(); i++) label(leaf[i], -1);
  for (int i = 1; i <= n; i++) {
    for (int j = 0; j < adj[i].size(); j++) {
      cnt[i] += lab[adj[i][j]];
    }
  }
  int cur;
  for (int i = 1; i <= n; i++) {
    if (lab[i]) continue;
    cur = 0;
    for (int j = 0; j < adj[i].size(); j++) {
      if (lab[adj[i][j]]) continue;
      if (adj[adj[i][j]].size() > cnt[adj[i][j]] + 1 or
          adj[adj[i][j]].size() >= 4)
        cur++;
    }
    if (cur > 2) {
      cout << "No" << endl;
      return 0;
    }
  }
  cout << "Yes" << endl;
  return 0;
}
