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 num[100001];
vector<int> ver[100001];
int n;
int root;
inline void addedge(int a, int b) {
  ver[a].push_back(b);
  ver[b].push_back(a);
}
bool flag = 0;
inline void dfs(int x, int fa) {
  int cnt[6];
  memset(cnt, 0, sizeof(cnt));
  for (int i = 0; i < (int)ver[x].size(); i++)
    if (ver[x][i] != fa) {
      int y = ver[x][i];
      dfs(y, x);
      cnt[num[y]]++;
    }
  if (cnt[5] || cnt[4] || cnt[3] > 2) {
    num[x] = 5;
    return;
  }
  if (cnt[3] == 2) {
    num[x] = 4;
    return;
  }
  if (cnt[3] == 1 || cnt[2] >= 1 || cnt[1] >= 3) {
    num[x] = 3;
    return;
  }
  if (cnt[1] == 2) {
    num[x] = 2;
    return;
  }
  if (cnt[1] == 1) {
    num[x] = 1;
    return;
  }
  if (ver[x].size() == 1)
    num[x] = 1;
  else
    num[x] = 5;
}
inline void fdd(int x) {
  dfs(x, x);
  if (num[x] <= 4) flag |= 1;
}
int main() {
  scanf("%d", &n);
  srand(time(NULL));
  if (n == 1) return puts("Yes"), 0;
  for (int i = 1, a, b; i < n; i++) scanf("%d%d", &a, &b), addedge(a, b);
  fdd(1);
  for (int i = 1; i <= 10; i++) fdd(rand() % n + 1);
  if (flag)
    puts("Yes");
  else
    puts("No");
}
