#include <bits/stdc++.h>
using namespace std;
const int N = 100005;
vector<int> mat[N];
int cnt[N];
bool del[N];
void dfs(int k, int fat) {
  if (mat[k].size() >= 3)
    cnt[k]++;
  else {
    del[k] = true;
    for (auto v : mat[k])
      if (v != fat) dfs(v, k);
  }
}
int main() {
  ios::sync_with_stdio(false);
  int n;
  cin >> n;
  for (int i = 1; i < n; i++) {
    int u, v;
    cin >> u >> v;
    mat[u].push_back(v);
    mat[v].push_back(u);
  }
  for (int i = 1; i <= n; i++)
    if (mat[i].size() == 1) dfs(i, 0);
  for (int i = 1; i <= n; i++)
    if (!del[i]) {
      int now = 0;
      for (auto v : mat[i])
        if (!del[v]) now += mat[v].size() - min(cnt[v], 2) > 1;
      if (now > 2) {
        cout << "No\n";
        return 0;
      }
    }
  cout << "Yes\n";
  return 0;
}

### Prompt

In CPP, your task is to solve the following problem:

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

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
const int N = 100005;
vector<int> mat[N];
int cnt[N];
bool del[N];
void dfs(int k, int fat) {
  if (mat[k].size() >= 3)
    cnt[k]++;
  else {
    del[k] = true;
    for (auto v : mat[k])
      if (v != fat) dfs(v, k);
  }
}
int main() {
  ios::sync_with_stdio(false);
  int n;
  cin >> n;
  for (int i = 1; i < n; i++) {
    int u, v;
    cin >> u >> v;
    mat[u].push_back(v);
    mat[v].push_back(u);
  }
  for (int i = 1; i <= n; i++)
    if (mat[i].size() == 1) dfs(i, 0);
  for (int i = 1; i <= n; i++)
    if (!del[i]) {
      int now = 0;
      for (auto v : mat[i])
        if (!del[v]) now += mat[v].size() - min(cnt[v], 2) > 1;
      if (now > 2) {
        cout << "No\n";
        return 0;
      }
    }
  cout << "Yes\n";
  return 0;
}

```