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;
vector<int> adj[100005];
int deg[100005];
int sz[100005];
bool done[100005];
queue<int> q;
int n;
map<pair<int, int>, int> childMap;
int leavesN;
int childrenN(int node, int parent) {
  int ret = 0;
  for (int i = (0); i < int(adj[node].size()); ++i) {
    int to = adj[node][i];
    if (to == parent) continue;
    int r = childrenN(to, node);
    ret += r;
  }
  if (ret == 0) ret = 1;
  if (ret == leavesN) --ret;
  childMap[make_pair(node, parent)] = ret;
  childMap[make_pair(parent, node)] = leavesN - ret;
  return ret;
}
int getChildN(int node, int parent) {
  pair<int, int> p = make_pair(node, parent);
  return childMap[p];
}
bool isBad(int node) {
  int numBad = 0;
  for (int i = (0); i < int(adj[node].size()); ++i) {
    int to = adj[node][i];
    int cn = getChildN(to, node);
    if (cn >= 3 || (cn == 2 && adj[to].size() == 2)) ++numBad;
  }
  return numBad >= 3;
}
int main() {
  scanf("%d", &n);
  if (n == 1) {
    puts("Yes");
    return 0;
  }
  for (int i = (0); i < int(n - 1); ++i) {
    int a, b;
    scanf("%d%d", &a, &b);
    --a;
    --b;
    adj[a].push_back(b);
    adj[b].push_back(a);
    ++deg[a];
    ++deg[b];
  }
  for (int i = (0); i < int(n); ++i)
    if (deg[i] == 1) ++leavesN;
  childrenN(0, -1);
  for (int i = (0); i < int(n); ++i) {
    if (isBad(i)) {
      puts("No");
      return 0;
    }
  }
  puts("Yes");
}
