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.*;
import java.util.ArrayList;
import java.util.List;
import java.util.StringTokenizer;

public class D {

    public static void main(String[] args) {
        InputReader in = new InputReader(System.in);
        PrintWriter out = new PrintWriter(System.out);
        Solver solver = new Solver();
        solver.solve(in, out);
        out.close();
    }

    private static class Solver {

        private List<List<Integer>> g;
        private int[] a;
        private int[] s;
        private boolean exi;

        private int min(int a, int b) {
            return a > b ? b : a;
        }

        private void dfs(int v) {
            if (g.get(v).size() == 0) {
                if (s[v] == -1) a[v] = 0;
                return;
            }
            if (s[v] == -1) {
                int min = s[g.get(v).get(0)];
                for (int i = 1; i < g.get(v).size(); i++) {
                    min = min(min, s[g.get(v).get(i)]);
                }
                if (min < a[v]) {
                    exi = false;
                    return;
                }
                a[v] = min - a[v];
                for (int u : g.get(v)) {
                    a[u] = s[u] - min;
                    dfs(u);
                }
            } else {
                for (int u : g.get(v)) {
                    a[u] = s[v];
                    dfs(u);
                }
            }
        }

        private void solve(InputReader in, PrintWriter out) {
            int n = in.nextInt();

            g = new ArrayList<>();
            for (int i = 0; i <= n; i++) g.add(new ArrayList<>());
            a = new int[n + 1];
            s = new int[n + 1];

            for (int i = 2; i <= n; i++) {
                g.get(in.nextInt()).add(i);
            }

            for (int i = 1; i <= n; i++) {
                s[i] = in.nextInt();
            }

            exi = true;
            a[1] = s[1];
            dfs(1);

            long sum = 0;
            for (int i = 1; i <= n; i++) {
                sum += a[i];
            }

            out.println(exi ? sum : -1);
        }
    }

    private static class InputReader {
        private static BufferedReader br;
        private static StringTokenizer st;

        public InputReader(InputStream stream) {
            br = new BufferedReader(new InputStreamReader(stream));
        }

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

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

        public double nextDouble() {
            return Double.parseDouble(next());
        }

        public String nextLine() {
            String s = "";
            try {
                s = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return s;
        }

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