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.util.ArrayList;
import java.util.List;
import java.util.StringTokenizer;

public class TreeSum {
    static List<List<Integer>> tree = new ArrayList<>();
    static long[] sVal;
    static long res = 0;
    static boolean fail = false;

    static long dfs(int root, long prevDist) {
        if (sVal[root] != -1 && sVal[root] < prevDist) {
            fail = true;
            return 0;
        }
        if (sVal[root] == -1) {
            long minChildDefined = Integer.MAX_VALUE;
            long defined = 0;
            for (int n : tree.get(root)) {
                long curChild = dfs(n, prevDist);
                if (curChild != -1) {
                    minChildDefined = Math.min(curChild, minChildDefined);
                    defined++;
                }
            }
            if (defined == 0) {
                return -1;
            }
            res -= defined * minChildDefined;
            res += minChildDefined;
            return minChildDefined;
        } else {
            long rootVal = sVal[root] - prevDist;
            res += rootVal;
            for (int n : tree.get(root)) {
                dfs(n, sVal[root]);
            }
            return rootVal;
        }
    }

    public static void main(String[] args) throws IOException {
        BufferedReader reader = new BufferedReader(new InputStreamReader(System.in));
        int n = Integer.parseInt(reader.readLine());
        int[] parent = new int[n];
        StringTokenizer stringTokenizer = new StringTokenizer(reader.readLine());

        for (int i = 0; i < n; i++) {
            tree.add(new ArrayList<>());
        }

        for (int i = 1; i < n; i++) {
            parent[i] = Integer.parseInt(stringTokenizer.nextToken());
            parent[i]--;
            tree.get(parent[i]).add(i);
        }

        stringTokenizer = new StringTokenizer(reader.readLine());
        sVal = new long[n];
        for (int i = 0; i < n; i++) {
            sVal[i] = Integer.parseInt(stringTokenizer.nextToken());
        }
        dfs(0, 0);
        if (fail) {
            System.out.println(-1);
        } else {
            System.out.println(res);
        }
    }
}
