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;
template <typename A, size_t N, typename T>
void Fill(A (&array)[N], const T &val) {
  std::fill((T *)array, (T *)(array + N), val);
}
template <class T>
inline bool chmax(T &a, T b) {
  if (a < b) {
    a = b;
    return true;
  }
  return false;
}
template <class T>
inline bool chmin(T &a, T b) {
  if (a > b) {
    a = b;
    return true;
  }
  return false;
}
int n;
vector<vector<int>> g;
vector<int> c;
vector<int> p;
bool ng;
int dfs(int id, int pre) {
  int t = 0;
  for (auto x : g[id]) {
    if (x != pre) {
      t += dfs(x, id);
    }
  }
  if (t == 0 && p[id]) {
    return 1;
  }
  if (t == 1 && p[id]) {
    return 1;
  }
  if (t == 2) {
    return 4;
  }
  if (t == 3) {
    ng = 1;
    return 4;
  }
  if (t >= 5) {
    ng = 1;
    return t;
  }
  if (t == 4 && p[id]) {
    ng = 1;
    return t;
  }
  return t;
}
int main() {
  cin >> n;
  g.resize(n);
  c.resize(n);
  for (int i = 0; i < (int)(n - 1); ++i) {
    int a, b;
    cin >> a >> b;
    a--;
    b--;
    c[a]++;
    c[b]++;
    g[a].push_back(b);
    g[b].push_back(a);
  }
  priority_queue<pair<int, int>, vector<pair<int, int>>,
                 greater<pair<int, int>>>
      pq;
  for (int i = 0; i < (int)(n); ++i) {
    pq.push(make_pair(c[i], i));
  }
  vector<int> v(n);
  p.resize(n);
  vector<bool> flag(n);
  while (!pq.empty()) {
    auto x = pq.top();
    pq.pop();
    if (c[x.second] != x.first) continue;
    int id = x.second;
    if (p[id]) continue;
    if (c[id] == 1) {
      if (v[id] <= 1) {
        for (auto y : g[id]) {
          if (flag[y]) continue;
          c[y]--;
          pq.push(make_pair(c[y], y));
          v[y]++;
        }
      } else if (v[id] == 2) {
        for (auto y : g[id]) {
          if (flag[y]) continue;
          c[y]--;
          pq.push(make_pair(c[y], y));
          p[y] = 1;
        }
      } else {
        p[id] = 1;
      }
      flag[id] = 1;
    }
  }
  dfs(0, -1);
  if (ng) {
    cout << "No\n";
  } else {
    cout << "Yes\n";
  }
  return 0;
}
