Problem: Consider a rooted tree. A rooted tree has one special vertex called the root. All edges are directed from the root. Vertex u is called a child of vertex v and vertex v is called a parent of vertex u if there exists a directed edge from v to u. A vertex is called a leaf if it doesn't have children and has a parent.

Let's call a rooted tree a spruce if its every non-leaf vertex has at least 3 leaf children. You are given a rooted tree, check whether it's a spruce.

The definition of a rooted tree can be found [here](https://goo.gl/1dqvzz).

Input

The first line contains one integer n — the number of vertices in the tree (3 ≤ n ≤ 1 000). Each of the next n - 1 lines contains one integer pi (1 ≤ i ≤ n - 1) — the index of the parent of the i + 1-th vertex (1 ≤ pi ≤ i).

Vertex 1 is the root. It's guaranteed that the root has at least 2 children.

Output

Print "Yes" if the tree is a spruce and "No" otherwise.

Examples

Input

4
1
1
1


Output

Yes


Input

7
1
1
1
2
2
2


Output

No


Input

8
1
1
1
1
3
3
3


Output

Yes

Note

The first example:

<image>

The second example:

<image>

It is not a spruce, because the non-leaf vertex 1 has only 2 leaf children.

The third example:

<image>

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
vector<vector<int> > V(1002);
int COUNT(int i);
int SEL(int i);
int main() {
  int n, i, j;
  vector<int> dist;
  cin >> n;
  for (i = 1; i <= n; i++) {
    V[i].push_back(0);
  }
  int temp;
  for (i = 0; i < n - 1; i++) {
    cin >> temp;
    if (V[temp].size() == 1) {
      dist.push_back(temp);
    }
    V[temp].push_back(i + 2);
  }
  int count;
  for (j = 0; j < dist.size(); j++) {
    i = dist[j];
    count = COUNT(i);
    if (count == 0) {
      cout << "No";
      return 0;
    }
  }
  cout << "Yes";
  return 0;
}
int COUNT(int i) {
  int j, temp, count = 0;
  for (j = 1; j < V[i].size(); j++) {
    temp = V[i][j];
    if (V[temp].size() == 1) {
      count++;
    }
    if (count == 3) {
      return 1;
    }
  }
  return 0;
}