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.OutputStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.io.BufferedWriter;
import java.util.InputMismatchException;
import java.io.IOException;
import java.util.ArrayList;
import java.io.Writer;
import java.io.OutputStreamWriter;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author sumit
 */
public class Main {
      public static void main(String[] args) {
            InputStream inputStream = System.in;
            OutputStream outputStream = System.out;
            InputReader in = new InputReader(inputStream);
            OutputWriter out = new OutputWriter(outputStream);
            DSumInTheTree solver = new DSumInTheTree();
            solver.solve(1, in, out);
            out.close();
      }

      static class DSumInTheTree {
            ArrayList<Integer>[] list;
            int[] arr;
            int[] sum;
            boolean[] vis;
            int[] pr;

            void dfs(int v, int height) {
                  if (vis[v])
                        return;
                  vis[v] = true;
                  if (height % 2 == 1) {
                        arr[pr[v]] = Math.min(arr[pr[v]], sum[v] - sum[pr[pr[v]]]);
                  }
                  for (int temp : list[v]) {
                        dfs(temp, height + 1);
                  }

            }

            public void solve(int testNumber, InputReader in, OutputWriter out) {
                  int n = in.nextInt();
                  list = new ArrayList[n];
                  arr = new int[n];
                  Arrays.fill(arr, 1000000001);
                  pr = new int[n];
                  for (int i = 0; i < n; i++)
                        list[i] = new ArrayList<>();

                  for (int i = 1; i < n; i++) {
                        int a = in.nextInt() - 1;
                        pr[i] = a;
                        list[a].add(i);
                  }
                  sum = in.nextIntArray(n);
                  arr[0] = sum[0];
                  vis = new boolean[n];
                  vis[0] = true;
                  for (int temp : list[0])
                        dfs(temp, 2);

                  boolean is = true;
                  long su = 0;
                  su += arr[0];
                  for (int i = 1; i < n; i++) {
                        if (arr[i] < 0) {
                              is = false;
                              break;
                        }
                        if (arr[i] == 1000000001 && sum[i] != -1) {
                              arr[i] = sum[i] - sum[pr[pr[i]]] - arr[pr[i]];

                        } else if (arr[i] == 1000000001 && sum[i] == -1) {
                              arr[i] = 0;
                        }
                        su += arr[i];

                  }

                  if (is)
                        out.printLine(su);
                  else
                        out.printLine("-1");


            }

      }

      static class OutputWriter {
            private final PrintWriter writer;

            public OutputWriter(OutputStream outputStream) {
                  writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(outputStream)));
            }

            public OutputWriter(Writer writer) {
                  this.writer = new PrintWriter(writer);
            }

            public void print(Object... objects) {
                  for (int i = 0; i < objects.length; i++) {
                        if (i != 0) {
                              writer.print(' ');
                        }
                        writer.print(objects[i]);
                  }
            }

            public void printLine(Object... objects) {
                  print(objects);
                  writer.println();
            }

            public void close() {
                  writer.close();
            }

            public void printLine(long i) {
                  writer.println(i);
            }

      }

      static class InputReader {
            private InputStream stream;
            private byte[] buf = new byte[1024];
            private int curChar;
            private int numChars;

            public InputReader(InputStream stream) {
                  this.stream = stream;
            }

            public int read() {
                  if (numChars == -1)
                        throw new InputMismatchException();

                  if (curChar >= numChars) {
                        curChar = 0;
                        try {
                              numChars = stream.read(buf);
                        } catch (IOException e) {
                              throw new InputMismatchException();
                        }
                        if (numChars <= 0)
                              return -1;
                  }

                  return buf[curChar++];
            }

            public int nextInt() {
                  int c = read();

                  while (isSpaceChar(c))
                        c = read();

                  int sgn = 1;

                  if (c == '-') {
                        sgn = -1;
                        c = read();
                  }

                  int res = 0;

                  do {
                        if (c < '0' || c > '9')
                              throw new InputMismatchException();

                        res *= 10;
                        res += c & 15;

                        c = read();
                  } while (!isSpaceChar(c));

                  return res * sgn;
            }

            public int[] nextIntArray(int arraySize) {
                  int array[] = new int[arraySize];

                  for (int i = 0; i < arraySize; i++)
                        array[i] = nextInt();

                  return array;
            }

            public boolean isSpaceChar(int c) {
                  return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
            }

      }
}

