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>
#pragma warning(disable : 4996)
using namespace std;
using ld = long double;
const ld eps = 1e-9;
vector<int> memo;
int kk = -1;
int dfs(const int now, const int from, const vector<vector<int>>& edges) {
  int a = 0;
  int b = 0;
  int c = 0;
  for (auto e : edges[now]) {
    if (e == from)
      continue;
    else {
      int sta = dfs(e, now, edges);
      if (sta == 0)
        c++;
      else if (sta == 1) {
        b++;
      } else if (sta == 2) {
        a++;
      } else if (sta == 3) {
        kk = e;
        throw(false);
      }
    }
  }
  if (a == 0 && b == 0 && c <= 1) {
    return memo[now] = 0;
  } else if (a == 0 && b == 0 && c == 2) {
    return memo[now] = 1;
  } else if (a <= 1) {
    return memo[now] = 2;
  } else if (a == 2) {
    return memo[now] = 3;
  } else {
    throw(false);
  }
}
int main() {
  int N;
  cin >> N;
  memo.resize(N);
  vector<vector<int>> edges(N, vector<int>());
  for (int i = 0; i < N - 1; ++i) {
    int a, b;
    cin >> a >> b;
    a--;
    b--;
    edges[a].push_back(b);
    edges[b].push_back(a);
  }
  bool ok = true;
  try {
    dfs(0, -1, edges);
  } catch (...) {
    ok = false;
  }
  if (kk != -1) {
    ok = true;
    try {
      dfs(kk, -1, edges);
    } catch (...) {
      ok = false;
    }
  }
  if (ok)
    cout << "Yes" << endl;
  else
    cout << "No" << endl;
  return 0;
}
