#include <bits/stdc++.h>
using namespace std;
vector<int> ke[123456];
bool del[123456];
int legs[123456];
int n;
void dfs(int a, int par) {
  if (ke[a].size() <= 2) {
    del[a] = true;
    for (int b = 0; b < ke[a].size(); b++)
      if (ke[a][b] != par) dfs(ke[a][b], a);
  }
}
int main() {
  cin >> n;
  for (int i = 1; i < n; i++) {
    int a, b;
    cin >> a >> b;
    ke[a].push_back(b);
    ke[b].push_back(a);
  }
  for (int a = 1; a <= n; ++a)
    if (ke[a].size() == 1) dfs(a, 0);
  for (int a = 1; a <= n; ++a)
    for (int i = 0; i < ke[a].size(); i++)
      if (del[ke[a][i]]) legs[a] = min(legs[a] + 1, 2);
  for (int a = 1; a <= n; ++a)
    if (!del[a]) {
      int cnt = 0;
      for (int b = 0; b < ke[a].size(); b++)
        if (!del[ke[a][b]] && ke[ke[a][b]].size() - legs[ke[a][b]] > 1) ++cnt;
      if (cnt > 2) {
        cout << "No";
        return 0;
      }
    }
  cout << "Yes";
  return 0;
}

### Prompt

Your task is to create a cpp solution to 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;
vector<int> ke[123456];
bool del[123456];
int legs[123456];
int n;
void dfs(int a, int par) {
  if (ke[a].size() <= 2) {
    del[a] = true;
    for (int b = 0; b < ke[a].size(); b++)
      if (ke[a][b] != par) dfs(ke[a][b], a);
  }
}
int main() {
  cin >> n;
  for (int i = 1; i < n; i++) {
    int a, b;
    cin >> a >> b;
    ke[a].push_back(b);
    ke[b].push_back(a);
  }
  for (int a = 1; a <= n; ++a)
    if (ke[a].size() == 1) dfs(a, 0);
  for (int a = 1; a <= n; ++a)
    for (int i = 0; i < ke[a].size(); i++)
      if (del[ke[a][i]]) legs[a] = min(legs[a] + 1, 2);
  for (int a = 1; a <= n; ++a)
    if (!del[a]) {
      int cnt = 0;
      for (int b = 0; b < ke[a].size(); b++)
        if (!del[ke[a][b]] && ke[ke[a][b]].size() - legs[ke[a][b]] > 1) ++cnt;
      if (cnt > 2) {
        cout << "No";
        return 0;
      }
    }
  cout << "Yes";
  return 0;
}

```