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;
template <typename _Ty>
_Ty sq(_Ty k) {
  return k * k;
}
vector<vector<int> > g;
vector<int> freedom;
bool calc(int v, int p = -1) {
  int cntCh[6] = {0};
  for (int i = 0; i < (int)(g[v]).size(); i++) {
    int to = g[v][i];
    if (to == p) continue;
    if (!calc(to, v)) return false;
    cntCh[freedom[to]]++;
  }
  if (cntCh[5] > 0)
    return false;
  else if (cntCh[4] > 0) {
    if (cntCh[4] > 1 || cntCh[3] > 0 || cntCh[2] > 0 || cntCh[1] > 0 ||
        cntCh[0] > 1)
      return false;
    if (cntCh[0] == 1)
      freedom[v] = 5;
    else
      freedom[v] = 4;
  } else if (cntCh[3] > 0) {
    if (cntCh[3] > 1 || cntCh[2] > 0 || cntCh[1] > 0 || cntCh[0] > 2)
      return false;
    if (cntCh[0] == 2)
      freedom[v] = 5;
    else
      freedom[v] = 4;
  } else if (cntCh[2] > 0) {
    if (cntCh[2] > 2)
      return false;
    else if (cntCh[2] == 2)
      freedom[v] = 3;
    else if (cntCh[2] == 1)
      freedom[v] = 2;
  } else if (cntCh[1] > 0) {
    freedom[v] = 2;
  } else if (cntCh[0] > 2) {
    freedom[v] = 2;
  } else if (cntCh[0] == 2) {
    freedom[v] = 1;
  } else {
    freedom[v] = 0;
  }
  return true;
}
int main() {
  int n;
  scanf("%d", &n);
  g.assign(n, vector<int>());
  for (int i = 0; i < n - 1; i++) {
    int a, b;
    scanf("%d%d", &a, &b);
    a--;
    b--;
    g[a].push_back(b);
    g[b].push_back(a);
  }
  freedom.assign(n, 0);
  puts(calc(0) ? "Yes" : "No");
  return 0;
}
