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;
void dfs(int node, vector<int> adj[], vector<int>& visit, int arr[]) {
  int c = 0;
  visit[node] = 1;
  for (int i = 0; i < adj[node].size(); i++) {
    int child = adj[node][i];
    if (visit[child] == 0 && adj[child].size() != 0) {
      dfs(child, adj, visit, arr);
    } else
      c++;
  }
  arr[node] = c;
}
int main() {
  int n;
  cin >> n;
  vector<int> adj[n + 1];
  for (int i = 2; i <= n; i++) {
    int a;
    cin >> a;
    adj[a].push_back(i);
  }
  vector<int> visit(n + 1, 0);
  int arr[n + 1];
  memset(arr, 0, sizeof(arr));
  dfs(1, adj, visit, arr);
  int flag = 0;
  for (int i = 1; i <= n; i++) {
    if (arr[i] == 1 || arr[i] == 2 || (arr[i] == 0 && adj[i].size() >= 1)) {
      flag = 1;
      break;
    }
  }
  if (flag == 0)
    cout << "Yes";
  else
    cout << "No";
  return 0;
}