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.io.InputStreamReader;
import java.io.InputStream;
import java.util.ArrayList;

/**
 * Built using CHelper plug-in Actual solution is at the top
 *
 * @author Hieu Le
 */
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);
    TaskD solver = new TaskD();
    solver.solve(1, in, out);
    out.close();
  }

  static class TaskD {
    public void solve(int testNumber, InputReader in, PrintWriter out) {
      int n = in.nextInt();

      TaskD.Node[] nodes = new TaskD.Node[n];
      for (int i = 0; i < n; ++i) nodes[i] = new TaskD.Node();

      for (int i = 1; i < n; ++i) {
        int par = in.nextInt() - 1;
        nodes[i].parent = nodes[par];
        nodes[par].next.add(nodes[i]);
      }

      for (int i = 0; i < n; ++i) nodes[i].sum = in.nextInt();

      nodes[0].value = nodes[0].sum;
      nodes[0].depth = 1;

      for (TaskD.Node child : nodes[0].next) {
        if (!dfs(child)) {
          out.println(-1);
          return;
        }
      }

      long res = 0;
      for (TaskD.Node node : nodes) {
        if (node.value < 0) throw new RuntimeException();
        res += node.value;
      }
      out.println(res);
    }

    private boolean dfs(TaskD.Node node) {
      // Update depth
      node.depth = node.parent.depth + 1;

      // Find current node value
      if (node.depth % 2 == 1) {
        node.value = node.sum - node.parent.parent.sum - node.parent.value;
      } else {
        if (isLeaf(node)) {
          node.value = 0;
        } else {
          node.value = Integer.MAX_VALUE;
          for (TaskD.Node child : node.next) {
            if (child.sum < node.parent.sum) return false;
            node.value = Math.min(node.value, child.sum - node.parent.sum);
          }
        }
      }

      // Recurse
      for (TaskD.Node child : node.next) {
        if (!dfs(child)) return false;
      }
      return true;
    }

    private boolean isLeaf(TaskD.Node node) {
      return node.next.isEmpty();
    }

    static class Node {
      long value = -1;
      int depth = -1;
      long sum = -1;
      TaskD.Node parent = null;
      List<TaskD.Node> next = new ArrayList<>();
    }
  }

  static class InputReader {
    private BufferedReader reader;
    private StringTokenizer tokenizer;
    private static final int BUFFER_SIZE = 32768;

    public InputReader(InputStream stream) {
      reader = new BufferedReader(new InputStreamReader(stream), BUFFER_SIZE);
      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());
    }
  }
}
