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
//package codeforces.contests.round530;

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

/**
 * @author tainic on Jan 5, 2019
 */
public class D {

    private static boolean LOCAL;
    static {
        try { LOCAL = "aurel".equalsIgnoreCase(System.getenv().get("USER")); } catch (Exception e){}
    }

    private static final String TEST =
        "3\n" +
        "1 2\n" +
        "2 -1 1";

    void solve(InputReader in, PrintWriter out) {
        int n = in.nextInt();
        List<Integer>[] ch = new List[n + 1];
        for (int i = 0; i <= n; i++) {
            ch[i] = new ArrayList<>();
        }
        int[] p = new int[n + 1];
        for (int i = 2; i <= n; i++) {
            int j = in.nextInt();
            p[i] = j;
            ch[j].add(i);
        }
        int[] s = new int[n + 1];
        for (int i = 1; i <= n; i++) {
            s[i] = in.nextInt();
        }

        boolean pos = true;
        int[] h = new int[n + 1];
        Deque<Integer> stack = new ArrayDeque<>();
        stack.add(1);
        long sum = s[1];
        while (!stack.isEmpty()) {
            int u = stack.removeFirst();
            for (int v : ch[u]) {
                stack.addFirst(v);
            }

            h[u] = h[p[u]] + 1;

            if (h[u] % 2 == 1) {
                if (s[u] < 0 || (u != 1 && s[u] < s[p[p[u]]])) {
                    pos = false;
                    break;
                }
            } else if (ch[u].size() > 0) {
                int pu = p[u];
                int max = Integer.MAX_VALUE;
                long sumChU = 0;
                for (int v : ch[u]) {
                    if (s[v] < s[pu]) {
                        pos = false;
                        break;
                    }
                    max = Math.min(max, s[v] - s[pu]);
                    sumChU += s[v];
                }
                if (!pos) {
                    break;
                }
                sum += max + sumChU - ch[u].size() * (max + s[pu]);
            }
        }

        out.println(pos ? sum : -1);
    }

    //region main
    public static void main(String[] args) throws Exception {
        long t = System.currentTimeMillis();

        try (
            InputReader in = new StreamInputReader(!LOCAL ? System.in : new ByteArrayInputStream(TEST.getBytes()));
            PrintWriter out = new PrintWriter(new BufferedOutputStream(System.out, 2048), false)
        ) {
            new D().solve(in, out);
        }

        System.err.println("time: " + (System.currentTimeMillis() - t) + "ms");
    }
    //endregion

    //region fast io
    abstract static class InputReader implements AutoCloseable {

        public abstract int read();

        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 - '0';
                c = read();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

        public long nextLong() {
            int c = read();
            while (isSpaceChar(c)) {
                c = read();
            }
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            long res = 0;
            do {
                if (c < '0' || c > '9') {
                    throw new InputMismatchException();
                }
                res *= 10;
                res += c - '0';
                c = read();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

        public String next() {
            int c = read();
            while (isSpaceChar(c)) {
                c = read();
            }
            StringBuilder res = new StringBuilder();
            do {
                res.appendCodePoint(c);
                c = read();
            } while (!isSpaceChar(c));
            return res.toString();
        }

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

    static class StreamInputReader extends InputReader {

        private InputStream stream;
        private byte[] buf;
        private int curChar, numChars;

        public StreamInputReader(InputStream stream) {
            this(stream, 2048);
        }

        public StreamInputReader(InputStream stream, int bufSize) {
            this.stream = stream;
            this.buf = new byte[bufSize];
        }

        @Override
        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++];
        }

        @Override
        public void close() throws Exception {
            stream.close();
        }

    }
    //endregion

    //region imports
    //endregion

}