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 double PI = acos(-1.0);
const double EPS = 1e-6;
const int STATE_COUNT = 9;
enum State {
  O = 0,
  I = 1,
  V = 2,
  W = 3,
  F1 = 4,
  F2 = 5,
  F2I = 6,
  F3 = 7,
  GG = 8
};
const State TRANSFORM[STATE_COUNT][STATE_COUNT] = {
    {O, I, V, W, F1, F2, F2I, F3, GG},     {I, V, W, F1, F1, F2, F3, GG, GG},
    {V, W, W, F1, F1, F2, GG, GG, GG},     {W, F1, F1, F2, F2, GG, GG, GG, GG},
    {F1, F1, F1, F2, F2, GG, GG, GG, GG},  {F2, F2, F2, GG, GG, GG, GG, GG, GG},
    {F2I, F3, GG, GG, GG, GG, GG, GG, GG}, {F3, GG, GG, GG, GG, GG, GG, GG, GG},
    {GG, GG, GG, GG, GG, GG, GG, GG, GG}};
const string s[STATE_COUNT] = {"O",  "I",   "V",  "W", "F1",
                               "F2", "F2I", "F3", "GG"};
vector<int> G[100005];
State DFS(int u, int father) {
  vector<State> states;
  for (int v : G[u])
    if (v != father) states.emplace_back(DFS(v, u));
  sort((states).begin(), (states).end());
  reverse((states).begin(), (states).end());
  State now = O;
  for (State st : states) now = TRANSFORM[now][st];
  ;
  if (now == O)
    now = I;
  else if (now == V and ((int)(states).size()) == 1)
    now = W;
  else if (now == F2)
    now = F2I;
  else if (now == F2I)
    now = F3;
  return now;
}
static void UnitTest() {
  for (int i = 0; i < STATE_COUNT; i++)
    for (int j = i + 1; j < STATE_COUNT; j++)
      assert(TRANSFORM[i][j] == TRANSFORM[j][i]);
}
int main() {
  { ; };
  { ; };
  UnitTest();
  int n;
  scanf("%d", &n);
  for (int i = 1; i < n; i++) {
    int a, b;
    scanf("%d %d", &a, &b);
    G[a].emplace_back(b);
    G[b].emplace_back(a);
  };
  for (int i = 1; i <= n; i++) {
    ;
    for (int v : G[i])
      ;
    ;
  };
  State res = O;
  for (int s = 1; s <= n; s++)
    if (((int)(G[s]).size()) == 1) {
      ;
      res = DFS(s, s);
      break;
    }
  bool ok = (res != GG);
  puts(ok ? "Yes" : "No");
  return 0;
}
