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;
vector<vector<int>> g;
bool stopэ = 0;
int fail = -1;
vector<int> w;
void p(int v) {
  if (fail == -1) fail = v;
}
int dfs(int v, int f) {
  vector<int> d(5, 0);
  for (int i = 0; i < g[v].size(); ++i)
    if (g[v][i] != f) ++d[dfs(g[v][i], v)];
  if (d[4]) {
    if (d[4] > 1 || d[3] || d[2] || d[1]) stopэ = 1, p(v);
    if (d[0] > 1) stopэ = 1, p(v);
    if (d[0] == 1 && v) stopэ = 1, p(v);
    w[v] = 4;
    return 4;
  }
  if (d[3]) {
    if (d[3] > 1) stopэ = 1, p(v);
    if (d[2] || d[1]) stopэ = 1, p(v);
    if (d[0] > 1) stopэ = 1, p(v);
    w[v] = 4;
    return 4;
  }
  if (d[2]) {
    if (d[2] > 2) stopэ = 1, p(v);
    if (d[2] == 2) {
      w[v] = 3;
      return 3;
    }
    w[v] = 2;
    return 2;
  }
  if (d[1]) {
    w[v] = 2;
    return 2;
  }
  if (d[0] > 2) {
    w[v] = 2;
    return 2;
  }
  if (d[0] == 2) {
    w[v] = 1;
    return 1;
  }
  w[v] = 0;
  return 0;
}
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  int n;
  cin >> n;
  g.resize(n);
  w.resize(n);
  vector<int> q(n);
  for (int i = 0; i < n; ++i) q[i] = i;
  random_shuffle(q.begin(), q.end());
  for (int i = 0; i < n - 1; ++i) {
    int a, b;
    cin >> a >> b;
    --a;
    --b;
    a = q[a];
    b = q[b];
    g[a].push_back(b);
    g[b].push_back(a);
  }
  dfs(0, 0);
  cout << (stopэ ? "No" : "Yes") << "\n";
}
