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.*;
import java.math.BigInteger;
import java.util.Map.Entry;

import static java.lang.Math.*;

public class D extends PrintWriter {

    boolean setA(int u, long sp, List<Integer>[] tree, long[] a, long[] s) {
        a[u] = s[u] - sp;
        if (a[u] < 0) {
            return false;
        }
        for (int v : tree[u]) {
            if (!setS(v, s[u], tree, a, s)) {
                return false;
            }
        }
        return true;
    }

    boolean setS(int u, long sp, List<Integer>[] tree, long[] a, long[] s) {
        if (tree[u].isEmpty()) {
            return true;
        }

        long min = Integer.MAX_VALUE;

        for (int v : tree[u]) {
            min = min(min, s[v] - sp);
        }

        if (min < 0) {
            return false;
        }

        a[u] = min;

        long su = sp + min;
        for (int v : tree[u]) {
            if (!setA(v, su, tree, a, s)) {
                return false;
            }
        }
        return true;
    }

    void run() {
        int n = nextInt();

        List<Integer>[] tree = new List[n];
        for (int i = 0; i < n; i++) {
            tree[i] = new ArrayList<>();
        }

        for (int u = 1; u < n; u++) {
            int v = nextInt() - 1;
            tree[v].add(u);
        }

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

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

        if (setA(0, 0, tree, a, s)) {
            long sum = 0;
            for (int i = 0; i < n; i++) {
                sum += a[i];
            }
            println(sum);
        } else {
            println(-1);
        }
    }

    void skip() {
        while (hasNext()) {
            next();
        }
    }

    int[][] nextMatrix(int n, int m) {
        int[][] matrix = new int[n][m];
        for (int i = 0; i < n; i++)
            for (int j = 0; j < m; j++)
                matrix[i][j] = nextInt();
        return matrix;
    }

    String next() {
        while (!tokenizer.hasMoreTokens())
            tokenizer = new StringTokenizer(nextLine());
        return tokenizer.nextToken();
    }

    boolean hasNext() {
        while (!tokenizer.hasMoreTokens()) {
            String line = nextLine();
            if (line == null) {
                return false;
            }
            tokenizer = new StringTokenizer(line);
        }
        return true;
    }

    int[] nextArray(int n) {
        int[] array = new int[n];
        for (int i = 0; i < n; i++) {
            array[i] = nextInt();
        }
        return array;
    }

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

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

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

    String nextLine() {
        try {
            return reader.readLine();
        } catch (IOException err) {
            return null;
        }
    }

    public D(OutputStream outputStream) {
        super(outputStream);
    }

    static BufferedReader reader;
    static StringTokenizer tokenizer = new StringTokenizer("");
    static Random rnd = new Random();
    static boolean OJ;

    public static void main(String[] args) throws IOException {
        OJ = System.getProperty("ONLINE_JUDGE") != null;
        D solution = new D(System.out);
        if (OJ) {
            reader = new BufferedReader(new InputStreamReader(System.in));
            solution.run();
        } else {
            reader = new BufferedReader(new FileReader(new File(D.class.getName() + ".txt")));
            long timeout = System.currentTimeMillis();
            while (solution.hasNext()) {
                solution.run();
                solution.println();
                solution.println("----------------------------------");
            }
            solution.println("time: " + (System.currentTimeMillis() - timeout));
        }
        solution.close();
        reader.close();
    }
}