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;
int n, root, newroot;
vector<int> v[100100];
void read() {
  int i;
  int x, y;
  scanf("%d", &n);
  for (i = 1; i < n; i++) {
    scanf("%d%d", &x, &y);
    v[x].push_back(y);
    v[y].push_back(x);
  }
}
int solve(int x, int parent) {
  int i, sz;
  int current, level1 = 0, level2 = 0, sublevel1 = 0;
  sz = v[x].size();
  for (i = 0; i < sz; i++) {
    if (v[x][i] == parent) continue;
    current = solve(v[x][i], x);
    if (current == 0) return 0;
    if (current == 1) level1++;
    if (current == 2) level2++;
    if (current == 3) sublevel1++;
  }
  if (level1 <= 1 && level2 == 0 && sublevel1 == 0) return 1;
  if (level1 <= 2 && level2 == 0 && sublevel1 == 0) return 3;
  if (level2 <= 1) return 2;
  if (x == root && level2 == 2) return 420;
  if (x != root) newroot = x;
  return 0;
}
int main() {
  int status;
  read();
  root = newroot = 1;
  status = solve(root, -1);
  if (!status) {
    root = newroot;
    status = solve(root, -1);
  }
  if (!status)
    printf("No\n");
  else
    printf("Yes\n");
}
