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.BufferedWriter;
import java.io.InputStreamReader;
import java.io.OutputStreamWriter;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.List;
import java.util.StringTokenizer;

public class DSumInTheTree {

    public static void main(String[] args) throws Exception {
        PrintWriter writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(System.out)));
        Solution solution = new Solution(new InputReader(), writer);
        solution.solve();
        writer.close();
    }

    public static class Solution {
        private InputReader in;
        private PrintWriter writer;
        private Vertex[] vertices;

        Solution(InputReader input, PrintWriter writer) {
            this.in = input;
            this.writer = writer;
        }

        void solve() throws Exception {
            int n = in.readInt();

            vertices = new Vertex[n+1];

            vertices[1] = new Vertex(-1);
            for(int i = 2; i <= n; i++){
                int parent = in.readInt();
                vertices[i] = new Vertex(parent);
            }

            for(int i = 2; i <= n; i++){
                Vertex vertex = vertices[i];
                vertices[vertex.parent].addChild(i);
            }

            for(int i = 1; i <= n; i++){
                long pathSum = in.readLong();
                vertices[i].pathSum = pathSum;
            }

            rec(vertices[1]);

            rec2(vertices[1], 0);

            long sum = 0;
            for(int i = 1; i <= n; i++){
                sum += vertices[i].value;
            }
            writer.println(sum);
        }

        long rec(Vertex vertex){
            long maxSum = -1;
            for(int child : vertex.children){
                long childMaxSum = rec(vertices[child]);
                if(childMaxSum == -1){
                    continue;
                }

                if(maxSum == -1){
                    maxSum = childMaxSum;
                } else{
                    maxSum = Math.min(maxSum, childMaxSum);
                }
            }
            vertex.maxSum = maxSum;

            if(vertex.pathSum == -1){
                vertex.pathSum = vertex.maxSum;
            }
            if(vertex.maxSum == -1){
                return vertex.pathSum;
            }
            if(vertex.pathSum > vertex.maxSum){
                writer.println(-1);
                writer.close();
                System.exit(0);
            }
            return vertex.pathSum;
        }

        void rec2(Vertex vertex, long pathScore){
            if(vertex.pathSum == -1){
                vertex.value = 0;
            } else{
                vertex.value = vertex.pathSum - pathScore;
            }

            for(int child : vertex.children){
                rec2(vertices[child], pathScore+vertex.value);
            }
        }
    }

    public static class Vertex{
        int parent;
        List<Integer> children;
        long pathSum = -1;
        long maxSum = -1;
        long value = -1;

        Vertex(int parent){
            this.parent = parent;
            children = new ArrayList<>();
        }

        void addChild(int child){
            children.add(child);
        }

    }

    public static class InputReader {
        BufferedReader stdin = new BufferedReader(new InputStreamReader(System.in));
        StringTokenizer st = new StringTokenizer("");

        String readString() throws Exception {
            while (!st.hasMoreTokens()) {
                st = new StringTokenizer(stdin.readLine());
            }
            return st.nextToken();
        }

        long readLong() throws Exception {
            return Long.parseLong(readString());
        }

        int readInt() throws Exception {
            return Integer.parseInt(readString());
        }
    }
}
