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.util.stream.IntStream;
import java.lang.reflect.Array;
import java.util.ArrayList;
import java.math.BigDecimal;
import java.nio.charset.Charset;
import java.util.StringTokenizer;
import java.io.OutputStreamWriter;
import java.io.OutputStream;
import java.util.stream.LongStream;
import java.io.BufferedWriter;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.UncheckedIOException;
import java.util.Objects;
import java.util.List;
import java.io.Writer;
import java.io.BufferedReader;
import java.io.InputStream;

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

    static class ASumInTheTree {
        private static int n;
        private static int[] p;
        private static List<List<Integer>> list;
        private static long[] s;

        public void solve(int testNumber, LightScanner in, LightWriter out) {
            n = in.ints();
            list = new ArrayList<>(n);
            for (int i = 0; i < n; i++) {
                list.add(new ArrayList<>());
            }
            p = new int[n];
            for (int i = 1; i < n; i++) {
                int pa = in.ints() - 1;
                list.get(pa).add(i);
                p[i] = pa;
            }
            s = in.longs(n);

            for (int i = 0; i < n; i++) {
                if (s[i] >= 0 || list.get(i).isEmpty()) {
                    continue;
                }
                long min = 1_000_000_000L;
                for (int c : list.get(i)) {
                    min = Math.min(min, s[c]);
                }
                s[i] = min;
            }


            //out.enableDebug();
            out.debug("s", s);

            long ans = s[0];
            for (int i = 1; i < n; i++) {
                if (s[i] == -1) {
                    continue;
                }
                long d = s[i] - s[p[i]];
                if (d < 0) {
                    out.ans(-1).ln();
                    return;
                }
                ans += d;
            }
            out.ans(ans).ln();
        }

    }

    static class LightWriter implements AutoCloseable {
        private static final String DEBUG_PREFIX = "\\e[30;41;1m[ DEBUG ] \\e[m";
        private static final String DEBUG_KEY_SEPARATOR = "= ";
        private static final int DEFAULT_DOUBLE_ACC = 9;
        private final Writer out;
        private boolean autoflush = false;
        private boolean debug = false;
        private boolean breaked = true;

        public LightWriter(Writer out) {
            this.out = out;
        }

        public LightWriter(OutputStream out) {
            this(new BufferedWriter(new OutputStreamWriter(out, Charset.defaultCharset())));
        }

        public LightWriter print(char c) {
            try {
                out.write(c);
                breaked = false;
            } catch (IOException ex) {
                throw new UncheckedIOException(ex);
            }
            return this;
        }

        public LightWriter print(String s) {
            try {
                out.write(s, 0, s.length());
                breaked = false;
            } catch (IOException ex) {
                throw new UncheckedIOException(ex);
            }
            return this;
        }

        public LightWriter ans(String s) {
            if (!breaked) {
                print(' ');
            }
            return print(s);
        }

        public LightWriter ans(double x, int n) {
            if (!breaked) {
                print(' ');
            }
            if (x < 0) {
                print('-');
                x = -x;
            }
            x += Math.pow(10, -n) / 2;
            print(Long.toString((long) x)).print('.');
            x -= (long) x;
            for (int i = 0; i < n; i++) {
                x *= 10;
                print((char) ('0' + ((int) x)));
                x -= (int) x;
            }
            return this;
        }

        public LightWriter ans(double x) {
            return ans(x, DEFAULT_DOUBLE_ACC);
        }

        public LightWriter ans(BigDecimal x) {
            return ans(x == null ? "null" : x.toPlainString());
        }

        public LightWriter ans(long l) {
            return ans(Long.toString(l));
        }

        public LightWriter ans(int i) {
            return ans(Integer.toString(i));
        }

        public LightWriter ans(Object obj) {
            return ans(Objects.toString(obj));
        }

        private LightWriter ansNonArray(Object obj) {
            if (obj.getClass() == Double.class) {
                return ans((double) obj);
            } else if (obj.getClass() == BigDecimal.class) {
                return ans((BigDecimal) obj);
            } else {
                return ans(obj);
            }
        }

        public LightWriter ln() {
            breaked = true;
            print(System.lineSeparator());
            if (autoflush) {
                try {
                    out.flush();
                } catch (IOException ex) {
                    throw new UncheckedIOException(ex);
                }
            }
            return this;
        }

        public LightWriter debug(String key, Object obj) {
            if (!debug) {
                return this;
            }
            if (obj == null) {
                return ans("null").ln();
            } else if (obj.getClass().isArray()) {
                int len = Array.getLength(obj);
                if (obj.getClass().getComponentType().isArray()) {
                    for (int i = 0; i < len; i++) {
                        debug(key + "[" + i + "]", Array.get(obj, i));
                    }
                } else {
                    print(DEBUG_PREFIX).print(key).print(DEBUG_KEY_SEPARATOR);
                    for (int i = 0; i < len; i++) {
                        Object elem = Array.get(obj, i);
                        ansNonArray(elem);
                    }
                    ln();
                }
            } else {
                print(DEBUG_PREFIX).print(key).print(DEBUG_KEY_SEPARATOR).ansNonArray(obj).ln();
            }
            return this;
        }

        public void close() {
            try {
                out.close();
            } catch (IOException ex) {
                throw new UncheckedIOException(ex);
            }
        }

    }

    static class LightScanner {
        private BufferedReader reader = null;
        private StringTokenizer tokenizer = null;

        public LightScanner(InputStream in) {
            reader = new BufferedReader(new InputStreamReader(in));
        }

        public String string() {
            if (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new UncheckedIOException(e);
                }
            }
            return tokenizer.nextToken();
        }

        public int ints() {
            return Integer.parseInt(string());
        }

        public long longs() {
            return Long.parseLong(string());
        }

        public long[] longs(int length) {
            return IntStream.range(0, length).mapToLong(x -> longs()).toArray();
        }

    }
}

