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<set<int> > neighbours;
vector<bool> main_series;
int n;
void reduce(int i) {
  if (neighbours[i].size() == 2) {
    int n1 = *(neighbours[i].begin());
    int n2 = *(std::next(neighbours[i].begin()));
    if (neighbours[n1].size() >= 3 and neighbours[n2].size() >= 3) {
      neighbours[i].insert(0);
      return;
    }
    neighbours[n1].erase(i);
    neighbours[n1].insert(n2);
    neighbours[n2].erase(i);
    neighbours[n2].insert(n1);
    neighbours[i].clear();
  }
}
void do_stuff() {
  for (int i = 1; i <= n; i++) {
    if (main_series[i]) {
      int count = 0;
      for (auto& it : neighbours[i]) {
        if (main_series[it]) {
          count++;
          if (count > 2) {
            cout << "No";
            return;
          }
        }
      }
    }
  }
  cout << "Yes";
}
int main() {
  int a, b;
  cin >> n;
  neighbours.resize(n + 1);
  main_series.resize(n + 1);
  for (int i = 0; i < n - 1; i++) {
    cin >> a >> b;
    neighbours[a].insert(b);
    neighbours[b].insert(a);
  }
  for (int i = 1; i <= n; i++) {
    reduce(i);
  }
  for (int i = 1; i <= n; i++) {
    if (neighbours[i].size() >= 4) {
      main_series[i] = true;
    }
    int count = 0;
    for (auto& it : neighbours[i]) {
      if (neighbours[it].size() >= 3) {
        count++;
        if (count >= 2) {
          main_series[i] = true;
          break;
        }
      }
    }
  }
  do_stuff();
  return 0;
}
