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 llamaoo7
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        DSumInTheTree solver = new DSumInTheTree();
        solver.solve(1, in, out);
        out.close();
    }

    static class DSumInTheTree {
        long INF = 1_000_000_000_000_000_000L;
        ArrayList<Integer>[] g;
        long[] a;
        long[] s;
        long ret;
        boolean bad = false;

        long dfs(int n) {
            long min = INF;
            long[] v = new long[g[n].size()];
            for (int i = 0; i < g[n].size(); i++) {
                long cur = dfs(g[n].get(i));
                v[i] = cur;
                if (s[n] != -1 && cur != -1 && s[n] > cur) {
                    bad = true;
                    return 0;
                }
                if (cur == -1) continue;
                min = Math.min(cur, min);
            }
            if (min != INF) {
                for (int i = 0; i < v.length; i++) if (v[i] != -1) ret += v[i] - (s[n] == -1 ? min : s[n]);
                if (s[n] == -1) return min;
                else return s[n];
            }
            return s[n];
        }

        public void solve(int testNumber, InputReader in, PrintWriter out) {
            int n = in.nextInt();
            g = new ArrayList[n];
            a = new long[n];
            s = new long[n];
            for (int i = 0; i < n; i++) g[i] = new ArrayList<>();
            for (int i = 1; i < n; i++) g[in.nextInt() - 1].add(i);
            for (int i = 0; i < n; i++) s[i] = in.nextInt();
            long butt = dfs(0);
            ret += butt;
            out.println(bad ? -1 : ret);
        }

    }

    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 {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }

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

    }
}

