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.List;
import java.util.StringTokenizer;
import java.io.IOException;
import java.io.BufferedReader;
import java.util.LinkedList;
import java.io.InputStreamReader;
import java.io.InputStream;

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

    static class D {
        Node[] nodes;
        int[] s;
        int[] a;
        boolean possible = true;

        void dfs(int v, int sum) {
            int min = Integer.MAX_VALUE;
            if (s[v] != -1) {
                if (s[v] < sum) {
                    possible = false;
                }
                sum = s[v];
            }
            for (int u : nodes[v].children) {
                dfs(u, sum);
                if (s[v] == -1)
                    min = Math.min(s[u], min);
            }
            if (s[v] == -1) {
                if (min == Integer.MAX_VALUE)
                    a[v] = 0;
                else {

                    a[v] = min - sum;
                    for (int u : nodes[v].children) {
                        a[u] = s[u] - sum - a[v];
                    }
                }
            }

        }

        public void solve(int testNumber, FastScanner in, PrintWriter out) {
            int n = in.ni();
            nodes = new Node[n];
            for (int i = 0; i < n; i++) {
                nodes[i] = new Node(i, -1);
            }
            for (int i = 1; i < n; i++) {
                int p = in.ni() - 1;
                nodes[i].p = p;
                nodes[p].children.add(i);

            }
            s = in.na(n);
            a = new int[n];
            a[0] = s[0];
            dfs(0, s[0]);
            if (possible) {
                long ans = 0;
                for (int i = 0; i < n; i++) {
                    ans += a[i];
                }
                out.println(ans);
            } else {
                out.println(-1);
            }

        }

        class Node {
            int v;
            int p;
            List<Integer> children;

            public Node(int v, int p) {
                this.v = v;
                this.p = p;
                children = new LinkedList<>();
            }

        }

    }

    static class FastScanner {
        private BufferedReader in;
        private StringTokenizer st;

        public FastScanner(InputStream stream) {
            in = new BufferedReader(new InputStreamReader(stream));
        }

        public String ns() {
            while (st == null || !st.hasMoreTokens()) {
                try {
                    String rl = in.readLine();
                    if (rl == null) {
                        return null;
                    }
                    st = new StringTokenizer(rl);
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return st.nextToken();
        }

        public int ni() {
            return Integer.parseInt(ns());
        }

        public int[] na(int n) {
            int[] a = new int[n];
            for (int i = 0; i < n; i++) a[i] = ni();
            return a;
        }

    }
}

