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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.Reader;
import java.util.*;
public class D {
    static ArrayList<Integer>[] graph;
    static int[] sums;
    static int[] vals;
    public static void main(String[] args) {
        FastScanner scanner = new FastScanner();
        int N = scanner.nextInt();
        graph = new ArrayList[N];
        for(int i = 0; i < N; i++) {
            graph[i] = new ArrayList<>();
        }
        for(int i = 1; i < N; i++) {
            int p = scanner.nextInt()-1;
            graph[p].add(i);
        }
        sums = new int[N];
        for(int i = 0; i < N; i++) {
            sums[i] = scanner.nextInt();
        }
        vals = new int[N];
        vals[0] = sums[0];
        dfs(0, 0, 1);
        long sum = 0;
        for(int i = 0; i < N; i++) {
            sum+=(long)vals[i];
        }
        System.out.println(sum);
    }
    public static void dfs(int cur, int parent, int depth) {
        if (depth%2==0) {
            int min = Integer.MAX_VALUE;
            for(int edge: graph[cur]) {
                if (sums[edge] < sums[parent]) {
                    System.out.println(-1);
                    System.exit(0);
                }
                else min = Math.min(sums[edge]-sums[parent], min);
            }
            vals[cur] = min == Integer.MAX_VALUE ? 0: min;
            for(int edge: graph[cur]) {
                vals[edge] = sums[edge]-sums[parent] - vals[cur];
            }
        }
        for(int edge : graph[cur]) {
            dfs(edge, cur, depth+1);
        }
    }
    public static class FastScanner {
        BufferedReader br;
        StringTokenizer st;
        public FastScanner(Reader in) {
            br = new BufferedReader(in);
        }
        public FastScanner() {
            this(new InputStreamReader(System.in));
        }
        String next() {
            while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }
        int nextInt() {
            return Integer.parseInt(next());
        }
        long nextLong() {
            return Long.parseLong(next());
        }
        double nextDouble() {
            return Double.parseDouble(next());
        }
        String readNextLine() {
            String str = "";
            try {
                str = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }
        int[] readIntArray(int n) {
            int[] a = new int[n];
            for (int idx = 0; idx < n; idx++) {
                a[idx] = nextInt();
            }
            return a;
        }
    }
}