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;
int n;
vector<int> adjlist[100005];
int degrees[100005];
bool eliminated[100005];
int legs[100005];
vector<int> toiter;
void find3(int node) {
  if (degrees[node] < 3) {
    eliminated[node] = true;
    for (vector<int>::iterator iter = adjlist[node].begin();
         iter != adjlist[node].end(); iter++) {
      if (!eliminated[(*iter)]) {
        find3((*iter));
      }
    }
  } else {
    legs[node]++;
    return;
  }
}
int main() {
  cin >> n;
  int end1, end2;
  for (int i = 0; i < n - 1; i++) {
    cin >> end1 >> end2;
    adjlist[end1].push_back(end2);
    adjlist[end2].push_back(end1);
    degrees[end1]++;
    degrees[end2]++;
  }
  for (int i = 1; i <= n; i++) {
    if (degrees[i] == 1) {
      toiter.push_back(i);
    }
  }
  for (vector<int>::iterator iter = toiter.begin(); iter != toiter.end();
       iter++) {
    find3((*iter));
  }
  bool sol = true;
  for (int i = 1; i <= n; i++) {
    int criticalcnt = 0;
    if (!eliminated[i]) {
      for (vector<int>::iterator iter = adjlist[i].begin();
           iter != adjlist[i].end(); iter++) {
        if (!eliminated[(*iter)] &&
            degrees[(*iter)] - min(2, legs[(*iter)]) > 1) {
          criticalcnt++;
        }
      }
    }
    if (criticalcnt > 2) {
      sol = false;
    }
  }
  if (sol) {
    cout << "Yes" << endl;
  } else {
    cout << "No" << endl;
  }
}
