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 int N = 1e5 + 5;
vector<int> a[N];
int mark[N], mark2[N];
int getparent(int x, int y) {
  if (((int)(a[x]).size()) == 1) {
    return y == -1 ? a[x][0] : 0;
  }
  if (((int)(a[x]).size()) == 2) {
    return y == -1 ? 0 : a[x][0] + a[x][1] - y;
  }
  return 0;
}
int main(void) {
  int n;
  scanf("%d", &n);
  for (int i = 1; i < n; i++) {
    int x, y;
    scanf("%d%d", &x, &y);
    a[x].push_back(y);
    a[y].push_back(x);
  }
  for (int i = 1; i <= n; i++) {
    if (((int)(a[i]).size()) == 1 && mark[i] == 0) {
      int x = i, y = -1, z;
      mark[x] = 1;
      while ((z = getparent(x, y)) > 0) {
        if (((int)(a[z]).size()) > 2) break;
        mark[z] = 1;
        y = x;
        x = z;
      }
    }
  }
  int d[3] = {}, ok = 1;
  for (int i = 1; i <= n; i++) {
    if (mark[i] == 0) {
      int deg = 0;
      for (__typeof((a[i]).begin()) it = (a[i]).begin(); it != (a[i]).end();
           ++it)
        if (mark[*it] == 0) ++deg;
      if (deg == 1 && ((int)(a[i]).size()) <= 3) mark2[i] = 1;
    }
  }
  for (int i = 1; i <= n; i++) mark[i] |= mark2[i];
  for (int i = 1; i <= n; i++) {
    if (mark[i] == 0) {
      int deg = 0;
      for (__typeof((a[i]).begin()) it = (a[i]).begin(); it != (a[i]).end();
           ++it)
        if (mark[*it] == 0) ++deg;
      if (deg <= 2)
        ++d[deg];
      else
        ok = 0;
    }
  }
  if (d[1] > 2) ok = 0;
  puts(ok ? "Yes" : "No");
  return 0;
}
