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 solve() {
  int n, i, cnt, j, f = 0;
  cin >> n;
  vector<int> g[n + 1];
  for (i = 2; i < n + 1; i++) {
    int first;
    cin >> first;
    g[first].push_back(i);
  }
  for (i = 1; i < n + 1; i++) {
    if ((int)g[i].size()) {
      if ((int)g[i].size() < 3) {
        f = 1;
        goto l;
      }
      cnt = 0;
      for (j = 0; j < (int)g[i].size(); j++)
        if ((int)g[g[i][j]].size() == 0) cnt++;
      if (cnt < 3) {
        f = 1;
        goto l;
      }
    }
  }
l:
  if (f)
    cout << "No";
  else
    cout << "Yes";
}
int main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  cout.tie(0);
  int t = 1;
  while (t--) {
    solve();
  }
  return 0;
}