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.util.*;
import java.io.*;

public class P1099D {

  private static void solve() {
    int n = nextInt();

    int[] v = new int[n];

    Map<Integer, List<Integer>> m = new HashMap<>();

    for (int i = 1; i < n; i++) {
      int p = nextInt() - 1;
      m.computeIfAbsent(p, (k) -> new ArrayList<>()).add(i);
    }

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

    v[0] = s[0];

    boolean valid = bfs(m, v, s);


    if (valid) {
      long sum = 0;
      for (int i = 0; i < n; i++) {
        sum += Math.max(0, v[i]);
      }

      System.out.println(sum);
    } else {
      System.out.println(-1);
    }
  }

  private static boolean bfs(Map<Integer, List<Integer>> m, int[] v, int[] s) {
    Queue<int[]> queue = new LinkedList<>();

    queue.offer(new int[] {0, -1});

    while (!queue.isEmpty()) {
      int[] first = queue.poll();

      int cur = first[0];
      int par = first[1];

      if (s[cur] == -1) {
        List<Integer> list = m.get(cur);
        if (list != null) {
          int min = Integer.MAX_VALUE;

          for (Integer c : list) {
            min = Math.min(min, s[c]);
          }
          s[cur] = min;
        } else {
          s[cur] = s[par];
        }
      }

      if (par != -1) {
        v[cur] = s[cur] - s[par];
        if (v[cur] < 0) {
          return false;
        }
      }

      List<Integer> list = m.get(cur);

      if (list != null) {
        for (Integer c : list) {
          queue.offer(new int[] { c, cur });
        }
      }

    }

    return true;
  }

  private static void run() {
    br = new BufferedReader(new InputStreamReader(System.in));
    out = new PrintWriter(System.out);

    solve();

    out.close();
  }

  private static StringTokenizer st;
  private static BufferedReader br;
  private static PrintWriter out;

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

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

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

  public static void main(String[] args) {
    run();
  }
}