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>
std::vector<int> g, next, node, type;
int n;
void dfs(int curr, int prev) {
  int c[4] = {};
  for (int i = g[curr]; i != -1; i = next[i]) {
    int v = node[i];
    if (v == prev) continue;
    dfs(v, curr);
    ++c[type[v]];
  }
  if (c[3] > 0 || c[2] >= 2)
    type[curr] = 3;
  else if (c[2] == 1 || c[1] >= 1 || c[0] >= 3)
    type[curr] = 2;
  else if (c[0] == 2)
    type[curr] = 1;
  else
    type[curr] = 0;
}
bool gao(int root) {
  dfs(root, -1);
  for (int i = 0; i < n; ++i) {
    if (i == root) continue;
    if (type[i] == 3) return false;
  }
  int c[4] = {};
  for (int i = g[0]; i != -1; i = next[i]) {
    int v = node[i];
    ++c[type[v]];
  }
  if (c[2] >= 3) return false;
  return true;
}
int main() {
  scanf("%d", &n);
  g = std::vector<int>(n, -1);
  next.clear();
  node.clear();
  for (int i = 1; i < n; ++i) {
    int a, b;
    scanf("%d%d", &a, &b);
    --a;
    --b;
    next.push_back(g[a]);
    g[a] = node.size();
    node.push_back(b);
    next.push_back(g[b]);
    g[b] = node.size();
    node.push_back(a);
  }
  type = std::vector<int>(n, 0);
  bool ans = false;
  for (int i = 0; i < n && i < 10; ++i) {
    if (gao(i)) {
      ans = true;
      break;
    }
  }
  puts(ans ? "Yes" : "No");
  return 0;
}
