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 <class T>
ostream &operator<<(ostream &os, const vector<T> &vec) {
  os << '{';
  for (int i = (0), __i = (((int)(vec).size())); i < __i; i++) {
    os << vec[i];
    if (i + 1 != ((int)(vec).size())) os << ',';
  }
  os << '}';
  return os;
}
template <class T1, class T2>
ostream &operator<<(ostream &os, const pair<T1, T2> &par) {
  os << '(' << par.first << ',' << par.second << ')';
  return os;
}
int gcd(int x, int y) { return y ? gcd(y, x % y) : abs(x); }
template <class T>
T sqr(T x) {
  return x * x;
}
bool used[100010];
int legs[100010];
int main() {
  ios::sync_with_stdio(false);
  int n;
  cin >> n;
  vector<vector<int>> edge(n);
  for (int i = (0), __i = (n - 1); i < __i; i++) {
    int u, v;
    cin >> u >> v;
    --u;
    --v;
    edge[u].push_back(v);
    edge[v].push_back(u);
  }
  queue<int> leaf;
  for (int i = (0), __i = (n); i < __i; i++) {
    if (((int)(edge[i]).size()) == 1) leaf.push(i);
  }
  while (!leaf.empty()) {
    int u = leaf.front();
    leaf.pop();
    used[u] = true;
    for (int v : edge[u]) {
      if (used[v]) continue;
      if (((int)(edge[v]).size()) < 3)
        leaf.push(v);
      else
        legs[v]++;
    }
  }
  for (int i = (0), __i = (n); i < __i; i++) {
    if (used[i]) continue;
    int neighbours = 0;
    for (int j : edge[i]) {
      if (used[j]) continue;
      if (((int)(edge[j]).size()) - min(2, legs[j]) > 1) neighbours++;
    }
    if (neighbours > 2) {
      cout << "No";
      return 0;
    }
  }
  cout << "Yes";
  return 0;
}
