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;
typedef struct tagNode {
  int Sum;
  int Cnt;
  long long Link;
  bool flag;
} node;
const int MAXPOINT = 100000;
node point[MAXPOINT];
int main() {
  int n;
  int i, j, k;
  memset(point, 0, sizeof(point));
  scanf("%d", &n);
  for (i = 1; i < n; i++) {
    scanf("%d%d", &j, &k);
    j--;
    k--;
    point[j].Sum++;
    point[j].Cnt++;
    point[j].Link += k;
    point[k].Sum++;
    point[k].Cnt++;
    point[k].Link += j;
  }
  for (i = 0; i < n; i++) {
    if (point[i].Sum == 1) {
      j = i;
      while (point[j].Sum <= 2 && point[j].Cnt == 1) {
        k = (int)point[j].Link;
        point[j].Cnt--;
        point[k].Cnt--;
        point[j].Link -= k;
        point[k].Link -= j;
        j = k;
      }
    }
  }
  for (i = 0; i < n; i++) {
    if (point[i].flag) continue;
    if (point[i].Cnt == 1 && point[i].Sum - point[i].Cnt <= 2) {
      j = i;
      k = (int)point[j].Link;
      point[j].Cnt--;
      point[k].Cnt--;
      point[j].Link -= k;
      point[k].Link -= j;
      point[k].flag = true;
    }
  }
  i = 0;
  for (i = 0; i < n; i++) {
    if (point[i].Cnt == 1) break;
  }
  if (i < n) {
    j = i;
    while (point[j].Cnt == 1) {
      k = (int)point[j].Link;
      point[j].Cnt--;
      point[k].Cnt--;
      point[j].Link -= k;
      point[k].Link -= j;
      j = k;
    }
  }
  j = 1;
  for (i = 0; i < n; i++) {
    if (point[i].Cnt) {
      j = 0;
    }
  }
  if (j) {
    printf("Yes\n");
  } else {
    printf("No\n");
  }
  return 0;
}
