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;
const int N = 1e3 + 20;
vector<vector<int> > children;
int main() {
  int n;
  cin >> n;
  children.resize(n + 1);
  for (int i = 0; i < n - 1; i++) {
    int p;
    cin >> p;
    children[p].push_back(i + 2);
  }
  bool isSpruce = true;
  for (int i = 1; i <= n; i++) {
    if (children[i].size() > 0) {
      int ct_leaf = 0;
      for (auto child : children[i]) {
        if (children[child].size() == 0) ct_leaf++;
      }
      if (ct_leaf < 3) {
        isSpruce = false;
        break;
      }
    }
  }
  if (isSpruce)
    cout << "Yes" << endl;
  else
    cout << "No" << endl;
}