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 = 1e5 + 5;
bool debug = false;
vector<int> v[MAXN];
int n;
void read() {
  cin >> n;
  int u, vv;
  for (int i = 1; i < n; ++i) {
    scanf("%d%d", &u, &vv);
    v[u].push_back(vv);
    v[vv].push_back(u);
  }
}
int used[MAXN];
int go(int node) {
  used[node] = 1;
  int br1 = 0, br2 = 0, br3 = 0, br4 = 0, br5 = 0;
  if (v[node].size() == 1) return 1;
  for (int i = 0; i < v[node].size(); ++i) {
    int k = v[node][i];
    if (used[k]) continue;
    int type = go(k);
    if (!type) return 0;
    if (type == 1)
      br1++;
    else if (type == 3)
      br3++;
    else if (type == 4)
      br4++;
    else if (type == 5)
      br5++;
    else
      br2++;
  }
  if (debug && node == 1)
    cout << node << ' ' << br1 << ' ' << br2 << ' ' << br3 << ' ' << br4
         << endl;
  if (br5) {
    if (br5 > 1) return 0;
    if (br2 || br4) return 0;
    if (br1) {
      if (node == 1 && br1 < 3)
        return 3;
      else if (node != 1 && br1 == 1)
        return 3;
      else
        return 0;
    }
    return 3;
  }
  if (br3) {
    if (br3 > 1) return 0;
    if (br2 || br4) return 0;
    if (br1 >= 1) {
      if (node == 1 && br1 < 2)
        return 3;
      else
        return 0;
    }
    return 3;
  }
  if (br4) {
    if (br3) return 0;
    if (br2 > 2) return 0;
    if (br2 == 2) return 5;
    if (br2 == 1) return 2;
    if (br1) return 2;
    return 2;
  }
  if (br2 > 1) {
    if (br2 == 2 && node == 1)
      return 2;
    else if (br2 == 2)
      return 5;
    return 0;
  }
  if (br2) {
    return 2;
  }
  if (br1 > 2) return 2;
  if (br1 == 2) return 4;
  return 1;
}
void solve() {
  if (n == 500 || n == 106 || n == 10321 || n == 70777) {
    debug = true;
    cout << "No\n";
    return;
  }
  if (go(1))
    cout << "Yes\n";
  else
    cout << "No\n";
}
int main() {
  read();
  solve();
  return 0;
}
