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>
const short Max = 100000;
using namespace std;
short a[1010];
short father[1010];
short flag2[1010];
int main() {
  short n;
  while (cin >> n) {
    memset(a, 0, sizeof(a));
    memset(father, 0, sizeof(father));
    memset(flag2, 0, sizeof(flag2));
    short temp;
    for (short i = 2; i <= n; i++) {
      cin >> temp;
      a[temp]++;
      if (a[temp]) {
        flag2[temp] = 1;
      }
      father[i] = temp;
      if (father[temp] != 0) {
        a[father[temp]]--;
        father[temp] = 0;
      }
    }
    short flag = 0;
    for (short i = 1; i <= n && flag == 0; i++) {
      if (a[i] < 3 && a[i] > 0) {
        flag = 1;
      } else if (a[i] == 0 && flag2[i] == 1) {
        flag = 1;
      }
    }
    if (flag == 1) {
      cout << "NO" << endl;
    } else
      cout << "YES" << endl;
  }
  return 0;
}