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;
int n;
bool used[N];
std::vector<int> tree[N];
void cut(int p, int u) {
  if (!used[u] && (int)tree[u].size() <= 2) {
    used[u] = true;
    for (int v : tree[u]) {
      cut(u, v);
    }
  }
}
int main() {
  scanf("%d", &n);
  for (int i = 0; i < n - 1; ++i) {
    int a, b;
    scanf("%d%d", &a, &b);
    a--;
    b--;
    tree[a].push_back(b);
    tree[b].push_back(a);
  }
  memset(used, 0, sizeof(*used) * n);
  for (int i = 0; i < n; ++i) {
    if ((int)tree[i].size() == 1) {
      cut(-1, i);
    }
  }
  for (int i = 0; i < n; ++i) {
    if ((int)tree[i].size() == 3) {
      int deg = 0;
      for (int v : tree[i]) {
        deg += !used[v] || (int)tree[v].size() >= 3;
      }
      used[i] = deg <= 1;
    }
  }
  bool valid = true;
  for (int i = 0; i < n; ++i) {
    if (!used[i]) {
      int deg = 0;
      for (int v : tree[i]) {
        deg += !used[v];
      }
      valid &= deg <= 2;
    }
  }
  puts(valid ? "Yes" : "No");
  return 0;
}
