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.IOException;
import java.io.InputStreamReader;
import java.util.*;

public class Main {

    private FastScanner scanner = new FastScanner();

    public static void main(String[] args) {
        new Main().solve();
    }

    List<List<Integer>> gr = new ArrayList<>();

    int s[], a[];

    void dfs(int v, int p) {
        if (s[v] == -1) {
            if (!gr.get(v).isEmpty()) {
                int t = Integer.MAX_VALUE;

                for (int next : gr.get(v)) {
                    t = Math.min(s[next], t);
                }
                a[v] = t - s[p];
            } else {
                a[v] = 0;
            }
        } else {
            if (p != -1) {
                a[v] = s[v] - s[p];
            } else {
                a[v] = s[v];
            }
        }
        if (p != -1) {
            s[v] = s[p] + a[v];
        }

        for (int next : gr.get(v)) {
            dfs(next, v);
        }
    }

    private void solve() {
        int n = scanner.nextInt();

        for (int i = 0; i < n; i++) {
            gr.add(new ArrayList<>());
        }

        for (int i = 1; i < n; i++) {
            int u = scanner.nextInt();
            gr.get(u - 1).add(i);
        }

        s = new int[n];
        a = new int[n];

        for (int i = 0; i < n; i++) {
            s[i] = scanner.nextInt();
        }

        dfs(0, -1);

        for (int i = 0; i < n; i++) {
            if (a[i] < 0) {
                System.out.println(-1);
                return;
            }
        }

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

        System.out.println(ans);
    }

    public static final <T> void swap(T[] a, int i, int j) {
        T t = a[i];
        a[i] = a[j];
        a[j] = t;
    }

    class Pair implements Comparable<Pair> {
        int a, i;

        public Pair(int a, int i) {
            this.a = a;
            this.i = i;
        }

        @Override
        public int compareTo(Pair o) {
            return this.a - o.a;
        }
    }

    long gcd(long a, long b) {
        if (b != 0) {
            return gcd(b, a % b);
        }
        return a;
    }


    class FastScanner {
        public BufferedReader reader;
        public StringTokenizer tokenizer;

        public FastScanner() {
            reader = new BufferedReader(new InputStreamReader(System.in), 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());
        }

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

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

        public String nextLine() {
            try {
                return reader.readLine();
            } catch (IOException e) {
                throw new RuntimeException(e);
            }
        }
    }
}