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;
bool deleted[100010];
int legs[100010];
vector<int> Adj[100010];
void DFS(int u, int p) {
  if (Adj[u].size() <= 2) {
    deleted[u] = true;
    for (auto &(t1) : (Adj[u])) {
      if (t1 != p) {
        DFS(t1, u);
      }
    }
  }
}
int main() {
  int n;
  scanf("%d", &n);
  for (int(i) = (1); (i) < (n); ++(i)) {
    int a, b;
    scanf("%d%d", &a, &b);
    a--;
    b--;
    Adj[a].push_back(b);
    Adj[b].push_back(a);
  }
  for (int(i) = (0); (i) < (n); ++(i)) {
    if (Adj[i].size() == 1) {
      DFS(i, -1);
    }
  }
  for (int(i) = (0); (i) < (n); ++(i)) {
    for (auto &(t1) : (Adj[i])) {
      if (deleted[t1]) {
        legs[i] = min(legs[i] + 1, 2);
      }
    }
  }
  for (int(i) = (0); (i) < (n); ++(i)) {
    if (!deleted[i]) {
      int count1 = 0;
      for (auto &(t1) : (Adj[i])) {
        if (!deleted[t1] && Adj[t1].size() - legs[t1] > 1) {
          count1++;
        }
      }
      if (count1 > 2) {
        printf("No\n");
        return 0;
      }
    }
  }
  printf("Yes\n");
  return 0;
}
