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.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.StringTokenizer;
import java.io.IOException;
import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author Washoum
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        inputClass in = new inputClass(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        DSumInTheTree solver = new DSumInTheTree();
        solver.solve(1, in, out);
        out.close();
    }

    static class DSumInTheTree {
        static long res;
        static boolean oui;
        static DSumInTheTree.Node[] graph;
        static boolean[] visited;

        static void dfs(int a, int depth) {
            visited[a] = true;
            if (depth % 2 == 1 && depth > 1 && graph[a].value < graph[graph[graph[a].parent].parent].value) {
                oui = false;
            }
            if (depth % 2 == 1 && depth > 1) res += (graph[a].value - graph[graph[graph[a].parent].parent].value);
            if (depth == 1) res += graph[0].value;
            int min = Integer.MAX_VALUE;
            if (depth % 2 == 0) {
                for (int i = 0; i < graph[a].edges.size(); i++) {
                    if (graph[a].edges.get(i) != graph[a].parent && graph[graph[a].edges.get(i)].value < min)
                        min = graph[graph[a].edges.get(i)].value;
                }
                if (min != Integer.MAX_VALUE) {
                    res -= (graph[a].edges.size() - 2) * (min - graph[graph[a].parent].value);
                }
            }
            for (int i = 0; i < graph[a].edges.size(); i++) {
                if (!visited[graph[a].edges.get(i)])
                    dfs(graph[a].edges.get(i), depth + 1);
            }
        }

        public void solve(int testNumber, inputClass sc, PrintWriter out) {
            int n = sc.nextInt();
            graph = new DSumInTheTree.Node[n];
            visited = new boolean[n];
            graph[0] = new DSumInTheTree.Node();
            graph[0].parent = -1;
            graph[0].edges = new ArrayList<>();
            int x;
            res = 0;
            oui = true;
            for (int i = 1; i < n; i++) {
                x = sc.nextInt() - 1;
                graph[i] = new DSumInTheTree.Node();
                graph[i].edges = new ArrayList<>();
                graph[i].parent = x;
                graph[i].edges.add(x);
                graph[x].edges.add(i);
            }

            for (int i = 0; i < n; i++) {
                x = sc.nextInt();
                graph[i].value = (x > 0) ? x : 0;
            }

            dfs(0, 1);
            if (oui)
                out.println(res);
            else
                out.println(-1);
        }

        static class Node {
            int parent;
            int value;
            ArrayList<Integer> edges;

        }

    }

    static class inputClass {
        BufferedReader br;
        StringTokenizer st;

        public inputClass(InputStream in) {

            br = new BufferedReader(new InputStreamReader(in));
        }

        public String next() {
            while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

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

    }
}

