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.io.*;
import java.util.*;
import static java.lang.Math.*;

public class B {
    static int uid = 0;
    private static class Node {
        Node parent;
        int index = uid++;
        ArrayList<Node> children = new ArrayList<>();
        void addChild(Node n) {
            children.add(n);
        }
        boolean leaf() {
            return children.isEmpty();
        }
        public String toString() {
            return ""+index;
        }
    }
    public static void main(String[] args) {
        Scanner input = new Scanner();
        StringBuilder output = new StringBuilder();

        int n = input.nextInt();
        Node[] nodes = new Node[n];
        for (int i = 0; i < n; i++) {
            nodes[i] = new Node();
        }

        for (int i = 1; i < n; i++) {
            int p = input.nextInt()-1;
            // nodes[i].parent = nodes[p];
            nodes[p].addChild(nodes[i]);
        }
        // System.err.println(nodes[0].children);

        System.out.println(spruce(nodes[0]) ? "Yes" : "No");
    }
    private static boolean spruce(Node n) {
        if (n.leaf()) {
            return true;
        }
        int count = 0;
        boolean res = true;
        for (Node e : n.children) {
            if (e.leaf()) {
                count++;
            } else {
                res &= spruce(e);
            }
        }
        return count >= 3 && res;
    }

    private static class Scanner {
        BufferedReader br; StringTokenizer st;
        public Scanner(Reader in) { br = new BufferedReader(in); }
        public Scanner() { this(new InputStreamReader(System.in)); }
        String next() {
            while (st == null || !st.hasMoreElements()) {
                try { st = new StringTokenizer(br.readLine());
                } catch (IOException e) { e.printStackTrace(); } }
            return st.nextToken(); }
        int nextInt() { return Integer.parseInt(next()); }
        long nextLong() { return Long.parseLong(next()); }
        double nextDouble() { return Double.parseDouble(next()); }
        String readNextLine() {
            String str = "";
            try { str = br.readLine();
            } catch (IOException e) { e.printStackTrace(); }
            return str; }
        int[] readIntArray(int n) {
            int[] a = new int[n];
            for (int idx = 0; idx < n; idx++) { a[idx] = nextInt(); }
            return a; }
        long[] readLongArray(int n) {
            long[] a = new long[n];
            for (int idx = 0; idx < n; idx++) { a[idx] = nextLong(); }
            return a; }
    } // end Scanner
}