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 JAVA):

Solution:
import java.util.*;

public class Solution {

    private static Scanner sc;

    public static void main(String[] args) throws Exception {
        sc = new Scanner(System.in);

        int n = sc.nextInt();

        int[] tree = new int[n-1];

        for (int i = 0; i < tree.length; i++) {
            tree[i] = sc.nextInt() - 1;
        }

        if (isSpruce(n, tree))
            System.out.println("Yes");
        else
            System.out.println("No");

        // test(null);
    }

    public static boolean isSpruce(int n, int[] tree) {
        boolean ans = true;

        HashMap<Integer, List<Integer>> map = new HashMap<>();

        for (int i = 1; i <= n - 1; ++i) {
            int tmp = tree[i-1];
            List<Integer> list = map.get(Integer.valueOf(tmp));
            if (list == null) {
                list = new ArrayList<>();
            }
            list.add(i);
            map.put(tmp, list);
        }

        loop:
        for (int i = 0; i < n; i++) {
            List<Integer> list = map.get(Integer.valueOf(i));
            if (list != null) {
                int count = list.size();
                for (Integer c : list) {
                    if (map.containsKey(c)) {
                        --count;
                    }
                }
                if (count < 3) {
                    ans = false;
                    break loop;
                }
            }
        }

        return ans;
    }

    public static void test(String args[]) {
        System.out.println(isSpruce(4, new int[]{0,0,0}));

        System.out.println(isSpruce(7, new int[]{0,0,0,1,1,1}));

        System.out.println(isSpruce(8, new int[]{0,0,0,0,2,2,2}));
    }
}