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.io.OutputStream;
import java.util.List;
import java.util.Arrays;
import java.util.InputMismatchException;
import java.io.IOException;
import java.util.ArrayList;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        FastReader in = new FastReader(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, FastReader in, PrintWriter out) {
            Debug debug = new Debug();
            int n = in.nextInt();
            List<Integer>[] g = new List[n];
            for (int i = 0; i < n; ++i) g[i] = new ArrayList<>();
            for (int i = 1; i < n; ++i) {
                int p = in.nextInt() - 1;
                g[p].add(i);
                g[i].add(p);
            }
            long[] s = in.nextLongArray(n);
            long[] a = new long[n];
            int[][] pars = GraphUtils.parents3(g, 0);
            int[] par = pars[0], ord = pars[1], depth = pars[2];

            a[0] = s[0];
            for (int i = 1; i < n; ++i) {
                int cur = ord[i];
                if (depth[cur] % 2 == 0) {
                    a[cur] = s[cur] - s[par[cur]];
                    continue;
                }
                int p = par[cur];
                long min = -2;
                for (Integer next : g[cur]) {
                    if (next == p) continue;
                    if (min == -2 || min > s[next]) min = s[next];
                }
                if (min == -2) min = s[p];
                if (min < s[p]) {
                    out.println(-1);
                    return;
                }
                a[cur] = min - s[p];
                s[cur] = s[p] + a[cur];
            }
            long sum = 0;
            for (long aa : a) sum += aa;
            out.println(sum);
        }

    }

    static class FastReader {
        private InputStream stream;
        private byte[] buf = new byte[8192];
        private int curChar;
        private int pnumChars;

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

        private int pread() {
            if (pnumChars == -1) {
                throw new InputMismatchException();
            }
            if (curChar >= pnumChars) {
                curChar = 0;
                try {
                    pnumChars = stream.read(buf);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }
                if (pnumChars <= 0) {
                    return -1;
                }
            }
            return buf[curChar++];
        }

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

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

        public long[] nextLongArray(int n) {
            long[] array = new long[n];
            for (int i = 0; i < n; i++) {
                array[i] = nextLong();
            }
            return array;
        }

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

    }

    static class Debug {
        PrintWriter out;
        boolean oj;
        boolean system;
        long timeBegin;
        Runtime runtime;

        public Debug(PrintWriter out) {
            oj = System.getProperty("ONLINE_JUDGE") != null;
            this.out = out;
            this.timeBegin = System.currentTimeMillis();
            this.runtime = Runtime.getRuntime();
        }

        public Debug() {
            system = true;
            oj = System.getProperty("ONLINE_JUDGE") != null;
            OutputStream outputStream = System.out;
            this.out = new PrintWriter(outputStream);
            this.timeBegin = System.currentTimeMillis();
            this.runtime = Runtime.getRuntime();
        }

    }

    static class ArrayUtils {
        public static void fill(int[] array, int value) {
            Arrays.fill(array, value);
        }

    }

    static class GraphUtils {
        public static int[][] parents3(List<Integer>[] g, int root) {
            int n = g.length;
            int[] par = new int[n];
            ArrayUtils.fill(par, -1);

            int[] depth = new int[n];
            depth[0] = 0;

            int[] q = new int[n];
            q[0] = root;
            for (int p = 0, r = 1; p < r; p++) {
                int cur = q[p];
                for (int nex : g[cur]) {
                    if (par[cur] != nex) {
                        q[r++] = nex;
                        par[nex] = cur;
                        depth[nex] = depth[cur] + 1;
                    }
                }
            }
            return new int[][]{par, q, depth};
        }

    }
}

