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>
#pragma comment(linker, "/STACK:134217728")
using namespace std;
const int MAX_N = 100050;
vector<int> g[MAX_N];
pair<bool, int> dfs(int v, int parent) {
  int upval = -2;
  if (g[v].size() > 3) {
    upval = 0;
  } else if (g[v].size() == 3) {
    upval = -1;
  }
  bool ok = true;
  int ups = 0;
  for (int i = 0; i < g[v].size(); ++i) {
    int u = g[v][i];
    if (u == parent) continue;
    pair<bool, int> res = dfs(u, v);
    if (!res.first) {
      ok = false;
      break;
    }
    if (res.second == -1) {
      upval = 0;
    }
    if (res.second >= 0) {
      if (res.second >= 2) {
        ok = false;
        break;
      }
      upval = 0;
      ++ups;
    }
  }
  if (upval == 0) {
    upval = ups;
  }
  if (upval > 2) {
    ok = false;
  }
  return make_pair(ok, upval);
}
int main() {
  int n;
  scanf("%d", &n);
  for (int i = 0; i < n - 1; ++i) {
    int a, b;
    scanf("%d %d", &a, &b);
    --a;
    --b;
    g[a].push_back(b);
    g[b].push_back(a);
  }
  int rootsize = 0;
  vector<int> maxroots;
  for (int i = 0; i < n; ++i) {
    if (g[i].size() > rootsize) {
      maxroots.clear();
      maxroots.push_back(i);
      rootsize = g[i].size();
    } else if (g[i].size() == rootsize) {
      maxroots.push_back(i);
    }
  }
  bool good = false;
  for (auto root : maxroots) {
    pair<bool, int> res = dfs(root, -1);
    if (res.first) {
      good = true;
      break;
    }
  }
  if (good) {
    cout << "Yes" << endl;
  } else {
    cout << "No" << endl;
  }
  return 0;
}
