Mitya has a rooted tree with n vertices indexed from 1 to n, where the root has index 1. Each vertex v initially had an integer number a_v ≥ 0 written on it. For every vertex v Mitya has computed s_v: the sum of all values written on the vertices on the path from vertex v to the root, as well as h_v — the depth of vertex v, which denotes the number of vertices on the path from vertex v to the root. Clearly, s_1=a_1 and h_1=1.

Then Mitya erased all numbers a_v, and by accident he also erased all values s_v for vertices with even depth (vertices with even h_v). Your task is to restore the values a_v for every vertex, or determine that Mitya made a mistake. In case there are multiple ways to restore the values, you're required to find one which minimizes the total sum of values a_v for all vertices in the tree.

Input

The first line contains one integer n — the number of vertices in the tree (2 ≤ n ≤ 10^5). The following line contains integers p_2, p_3, ... p_n, where p_i stands for the parent of vertex with index i in the tree (1 ≤ p_i < i). The last line contains integer values s_1, s_2, ..., s_n (-1 ≤ s_v ≤ 10^9), where erased values are replaced by -1.

Output

Output one integer — the minimum total sum of all values a_v in the original tree, or -1 if such tree does not exist.

Examples

Input


5
1 1 1 1
1 -1 -1 -1 -1


Output


1


Input


5
1 2 3 1
1 -1 2 -1 -1


Output


2


Input


3
1 2
2 -1 1


Output


-1
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.util.List;
import java.util.StringTokenizer;

/**
 * Created by Katushka on 02.02.2020.
 */
public class SumInTheTree {

    private static class Node {
        int num;
        long weight;

        Node parent;
        int parentNum;

        long sum;
        long minSum = Long.MAX_VALUE;

        List<Node> children = new ArrayList<>();

        public Node(int num, int weight, int parentNum) {
            this.num = num;
            this.weight = weight;
            this.parentNum = parentNum;
        }

        public void setSum(long sum) {
            this.sum = sum;
            minSum = sum;
        }
    }

    public static void main(String[] args) {
        InputReader in = new InputReader(System.in);

        int n = in.nextInt();
        List<Node> allNodes = new ArrayList<>();
        allNodes.add(new Node(1, -1, -1));
        for (int i = 2; i <= n; i++) {
            allNodes.add(new Node(i, -1, in.nextInt()));
        }
        for (int i = 2; i <= n; i++) {
            Node node = allNodes.get(i - 1);
            Node parent = allNodes.get(node.parentNum - 1);
            node.parent = parent;
            parent.children.add(node);
        }

        for (int i = 1; i <= n; i++) {
            Node node = allNodes.get(i - 1);
            node.setSum(in.nextInt());
            if (i == 1) {
                node.weight = node.sum;
            }
        }

        if (solve(allNodes.get(0))) {
            System.out.println(getSum(allNodes.get(0)));
        } else {
            System.out.println("-1");
        }
    }

    private static long getSum(Node node) {
        long sum = 0;
        if (node.weight != -1) {
            sum += node.weight;
        } else {
            sum += (node.minSum - node.parent.minSum);
        }

        for (Node child : node.children) {
            sum += getSum(child);
        }
        return sum;
    }

    private static boolean solve(Node node) {
        if (node.parent != null) {
            if (node.parent.sum != -1) {
                if (node.sum != -1) {
                    if (node.sum < node.parent.sum) {
                        return false;
                    }
                    node.weight = node.parent.sum - node.sum;
                } else {
                    node.minSum = node.parent.sum;
                }
            } else {
                if (node.sum != -1) {
                    if (node.sum < node.parent.minSum) {
                        return false;
                    }
                }
            }
        }

        for (Node child : node.children) {
            if (!solve(child)) {
                return false;
            }
        }

        if (node.sum == -1) {
            if (node.children.isEmpty()) {
                node.weight = 0;
                node.setSum(node.parent.sum);
            } else {
                long maxSum = Long.MAX_VALUE;

                for (Node child : node.children) {
                    maxSum = Math.min(child.sum, maxSum);
                }

                node.setSum(maxSum);
            }
        }
        return true;
    }

    private static class InputReader {
        public BufferedReader reader;
        public StringTokenizer tokenizer;

        public InputReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream), 32768);
            tokenizer = null;
        }

        public String next() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    final String str = reader.readLine();
                    tokenizer = new StringTokenizer(str);
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }

        public String nextString() {
            try {
                return reader.readLine();
            } catch (IOException e) {
                throw new RuntimeException(e);
            }
        }

        public int nextInt() {
            return Integer.parseInt(next());
        }

        public long nextLong() {
            return Long.parseLong(next());
        }

        public char nextChar() {
            return next().charAt(0);
        }
    }
}
