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 = 100 * 1000 + 10;
set<int> v[maxn];
int d[maxn], mark[maxn], mark2[maxn];
int get_id(const set<int> &s, int id) {
  set<int>::iterator it = s.begin();
  for (int i = 0; i < id; ++i) it++;
  return *it;
}
bool is_good(const set<int> &s) {
  for (int i = 0; i < 2; ++i)
    if (v[get_id(s, i)].size() <= 2) return true;
  return false;
}
void print(int x) {
  cout << x << "::" << endl;
  for (auto i : v[x])
    cout << i << ": " << v[i].size() << " " << mark[i] << endl;
}
int main() {
  int n;
  cin >> n;
  for (int i = 0; i < n - 1; ++i) {
    int fi, se;
    cin >> fi >> se;
    v[fi].insert(se);
    v[se].insert(fi);
  }
  for (int i = 1; i <= n; ++i)
    if (v[i].size() == 2) {
      if (is_good(v[i])) {
        v[get_id(v[i], 0)].insert(get_id(v[i], 1));
        v[get_id(v[i], 1)].insert(get_id(v[i], 0));
        v[get_id(v[i], 0)].erase(i);
        v[get_id(v[i], 1)].erase(i);
        v[i].clear();
      }
    }
  for (int i = 1; i <= n; ++i)
    if (v[i].size() == 1) mark[i] = 1;
  for (int i = 1; i <= n; ++i)
    if (v[i].size() == 3) {
      int cnt = 0;
      for (int j = 0; j < 3; ++j)
        if (mark[get_id(v[i], j)] == 1) cnt++;
      if (cnt >= 2) mark2[i] = 1;
    }
  for (int i = 1; i <= n; ++i)
    if (mark2[i] == 1) mark[i] = 1;
  for (int i = 1; i <= n; ++i) {
    set<int>::iterator it = v[i].begin();
    int cnt = 0;
    while (cnt <= 2 && it != v[i].end()) {
      if (mark[*it] == 0) {
        cnt++;
      }
      it++;
    }
    if (cnt > 2) {
      cout << "No" << endl;
      return 0;
    }
  }
  cout << "Yes" << endl;
  return 0;
}
