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;
const int MAXN = 101010, d = 0;
int n, parent[MAXN], nlin[MAXN], nbilin[MAXN], nc[MAXN];
vector<int> adj[MAXN];
bool linear[MAXN], bilinear[MAXN], vis[MAXN];
bool good = true;
void get(int node) {
  nc[node] = parent[node] == 0 ? adj[node].size() : adj[node].size() - 1;
  if (nlin[node] == nc[node]) {
    linear[node] = nc[node] <= 1;
    bilinear[node] = nc[node] == 2;
  } else {
    linear[node] = false;
    bilinear[node] = false;
  }
}
void get_slow(int node) {
  nlin[node] = 0;
  nbilin[node] = 0;
  for (int i = 0; i < adj[node].size(); ++i) {
    if (adj[node][i] == parent[node]) continue;
    if (linear[adj[node][i]])
      nlin[node]++;
    else if (bilinear[adj[node][i]])
      nbilin[node]++;
  }
  get(node);
}
void dfs2(int node) {
  vis[node] = true;
  if (d) cout << "dfs2 " << node << " " << parent[node] << endl;
  int n_special = 0;
  for (int i = 0; i < adj[node].size(); ++i) {
    if (!linear[adj[node][i]] && !bilinear[adj[node][i]]) {
      n_special++;
    }
    if (d)
      cout << adj[node][i] << ": " << linear[adj[node][i]] << " "
           << bilinear[adj[node][i]] << endl;
  }
  if (d)
    cout << "for " << node << " vals are " << nlin[node] << " " << nbilin[node]
         << " " << n_special << " " << nc[node] << endl;
  if (n_special > 2) good = false;
  for (int i = 0; i < adj[node].size(); ++i) {
    if (adj[node][i] != parent[node] && !vis[adj[node][i]]) {
      parent[adj[node][i]] = 0;
      parent[node] = adj[node][i];
      if (linear[adj[node][i]]) nlin[node]--;
      if (bilinear[adj[node][i]]) nbilin[node]--;
      get(node);
      if (linear[node]) nlin[adj[node][i]]++;
      if (bilinear[node]) nbilin[adj[node][i]]++;
      get(adj[node][i]);
      dfs2(adj[node][i]);
      parent[node] = 0;
      parent[adj[node][i]] = node;
      if (linear[node]) nlin[adj[node][i]]--;
      if (bilinear[node]) nbilin[adj[node][i]]--;
      get(adj[node][i]);
      if (linear[adj[node][i]]) nlin[node]++;
      if (bilinear[adj[node][i]]) nbilin[node]++;
      get(node);
    }
  }
}
void dfs(int node) {
  for (int i = 0; i < adj[node].size(); ++i) {
    if (adj[node][i] != parent[node]) {
      parent[adj[node][i]] = node;
      dfs(adj[node][i]);
    }
  }
  get_slow(node);
}
int main() {
  scanf("%d", &n);
  for (int i = 0; i < n - 1; ++i) {
    int a, b;
    scanf("%d %d", &a, &b);
    adj[a].push_back(b);
    adj[b].push_back(a);
  }
  dfs(1);
  dfs2(1);
  if (good)
    printf("Yes\n");
  else
    printf("No\n");
  return 0;
}
