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 inf = 1e9;
int n;
vector<int> g[200500];
int leaf[200500], son[200500], d[200500];
void dfs(int u) {
  leaf[u] = 1;
  for (auto v : g[u]) {
    if (leaf[v]) continue;
    if (d[v] == 2) dfs(v);
  }
}
int main() {
  scanf("%d", &n);
  for (int i = 2; i <= n; i++) {
    int x, y;
    scanf("%d%d", &x, &y);
    g[x].push_back(y);
    g[y].push_back(x);
    d[x]++;
    d[y]++;
  }
  for (int i = 1; i <= n; i++)
    if (d[i] == 1) dfs(i);
  for (int i = 1; i <= n; i++)
    if (d[i] == 3) {
      int p = 3;
      for (auto v : g[i]) {
        if (leaf[v]) p--;
      }
      if (p == 1) son[i] = 1;
    }
  for (int i = 1; i <= n; i++)
    if (son[i] || leaf[i]) {
      for (auto v : g[i]) d[v]--;
    }
  for (int i = 1; i <= n; i++)
    if (!son[i] && !leaf[i] && d[i] > 2) {
      puts("No");
      return 0;
    }
  puts("Yes");
  return 0;
}
