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>
const int N = 100000 + 10;
int n;
std::vector<int> adj[N];
bool flag[N];
void dfs(int a, int fa = -1) {
  if (adj[a].size() > 2) return;
  flag[a] = true;
  for (int i = 0; i < adj[a].size(); ++i) {
    int b = adj[a][i];
    if (b != fa) dfs(b, a);
  }
}
int main() {
  scanf("%d", &n);
  for (int i = n - 1; i--;) {
    int a, b;
    scanf("%d%d", &a, &b);
    adj[a].push_back(b);
    adj[b].push_back(a);
  }
  for (int i = 1; i <= n; ++i)
    if (adj[i].size() == 1) dfs(i);
  static int cnt[N];
  for (int i = 1; i <= n; ++i)
    for (int j = 0; j < adj[i].size(); ++j) cnt[i] += flag[adj[i][j]];
  for (int i = 1; i <= n; ++i) {
    if (flag[i]) continue;
    int cur = 0;
    for (int j = 0; j < adj[i].size(); ++j) {
      int t = adj[i][j];
      if (!flag[t] && adj[t].size() - std::min(cnt[t], 2) > 1) ++cur;
    }
    if (cur > 2) return puts("No"), 0;
  }
  puts("Yes");
  return 0;
}
