#include <bits/stdc++.h>
using namespace std;
vector<int> v[100005];
bool d[100005];
int s[100005];
void del(int i, int par) {
  if (v[i].size() <= 2) {
    d[i] = true;
    for (int j : v[i])
      if (j != par) del(j, i);
  }
}
int main() {
  int n;
  cin >> n;
  int a, b;
  for (int i = 1; i < n; i++) {
    cin >> a >> b;
    v[a].push_back(b);
    v[b].push_back(a);
  }
  for (int i = 1; i <= n; i++) {
    if (v[i].size() == 1) del(i, 0);
  }
  for (int i = 1; i <= n; i++) {
    for (int j : v[i])
      if (d[j]) s[i] = min(s[i] + 1, 2);
  }
  for (int i = 1; i <= n; i++)
    if (!d[i]) {
      int cnt = 0;
      for (int j : v[i])
        if (!d[j] && v[j].size() - s[j] > 1) cnt++;
      if (cnt > 2) {
        cout << "No\n";
        return 0;
      }
    }
  cout << "Yes\n";
  return 0;
}

### Prompt

Create a solution in CPP for 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> v[100005];
bool d[100005];
int s[100005];
void del(int i, int par) {
  if (v[i].size() <= 2) {
    d[i] = true;
    for (int j : v[i])
      if (j != par) del(j, i);
  }
}
int main() {
  int n;
  cin >> n;
  int a, b;
  for (int i = 1; i < n; i++) {
    cin >> a >> b;
    v[a].push_back(b);
    v[b].push_back(a);
  }
  for (int i = 1; i <= n; i++) {
    if (v[i].size() == 1) del(i, 0);
  }
  for (int i = 1; i <= n; i++) {
    for (int j : v[i])
      if (d[j]) s[i] = min(s[i] + 1, 2);
  }
  for (int i = 1; i <= n; i++)
    if (!d[i]) {
      int cnt = 0;
      for (int j : v[i])
        if (!d[j] && v[j].size() - s[j] > 1) cnt++;
      if (cnt > 2) {
        cout << "No\n";
        return 0;
      }
    }
  cout << "Yes\n";
  return 0;
}

```