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;
class Graph {
  int V;
  list<int> *adjList;
  int a[1000];

 public:
  Graph(int v) {
    V = v;
    for (int i = 1; i <= v; i++) a[i] = 1;
    adjList = new list<int>[V];
  }
  void addEdge(int u, int w) {
    adjList[u].push_back(w);
    a[u] = 0;
  }
  bool check() {
    bool possible = true;
    for (int i = 1; i <= V; i++) {
      long int sum = 0;
      if (a[i] == 0) {
        for (int node : adjList[i]) {
          sum += a[node];
        }
        if (sum < 3) {
          possible = false;
          return false;
        }
      }
    }
    if (possible) {
      return true;
    }
  }
};
int main() {
  int n, t;
  cin >> n;
  Graph g(n);
  for (int i = 2; i <= n; i++) {
    cin >> t;
    g.addEdge(t, i);
  }
  if (g.check()) {
    cout << "Yes";
  } else
    cout << "No";
  return 0;
}