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;
int n;
vector<vector<int> > v(100005);
bool vis[100005];
int meh[100005] = {0};
int solve(int node) {
  if (v[node].size() > 1) meh[node]++;
  if (v[node].size() > 2) return node;
  vis[node] = 1;
  for (int i = 0; i < v[node].size(); i++) {
    int cur = v[node][i];
    if (!vis[cur] && v[cur].size() > 1) return solve(cur);
  }
}
int main() {
  scanf("%d", &n);
  int x, y;
  memset(vis, 0, sizeof vis);
  for (int i = 1; i < n; i++) {
    scanf("%d%d", &x, &y);
    v[x].push_back(y);
    v[y].push_back(x);
  }
  for (int i = 1; i <= n; i++) {
    if (v[i].size() == 1) {
      solve(i);
    }
  }
  for (int i = 1; i <= n; i++) {
    if (vis[i]) continue;
    int cntr = 0;
    for (int j = 0; j < v[i].size(); j++) {
      int cur = v[i][j];
      if (v[cur].size() - min(2, meh[cur]) > 1) cntr++;
    }
    if (cntr > 2) {
      puts("No");
      return 0;
    }
  }
  puts("Yes");
  return 0;
}
