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.util.*;

public class D {

    static List<Integer>[] childList;

    static int[] sums;
    static Stack<Pr> dfsStack = new Stack<>();

    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);

        int n = sc.nextInt();
        childList = new List[n+1]; // use elems 1->n
        for (int i = 0 ; i <= n; i++) childList[i] = new ArrayList<>();

        for (int i = 2; i <= n; i++) {
            int parent = sc.nextInt();
            childList[parent].add(i);
        }

        sums = new int[n+1];

        for (int i = 1; i <= n; i++) sums[i] = sc.nextInt();

        dfsStack.push(new Pr(1, 0));

        try {
            while (!dfsStack.isEmpty()) {
                Pr x = dfsStack.pop();
                dfs(x.index, x.sum);
            }
            System.out.println(total);
        } catch (Exception e) {
            System.out.println(-1); return;
        }

    }

    static class Pr {
        int index, sum;

        public Pr(int index, int sum) {
            this.index = index;
            this.sum = sum;
        }
    }

    static long total = 0;

    private static void dfs(int curr, int parentSum) throws Exception {
        if (sums[curr] == -1) {
            // need to fill
            int best = Integer.MIN_VALUE;
            for (int child : childList[curr]) {
                if (sums[child] < parentSum) throw new Exception();
                else {
                    best = Math.max(best, parentSum - sums[child]);
                }
            }
            if (best == Integer.MIN_VALUE) best = 0;
            best = -best; // obtain best value
            sums[curr] = parentSum + best;
            total += best;

            for (int child : childList[curr]) {
                dfsStack.push(new Pr(child, sums[curr]));
            }

        } else {
            total += sums[curr] - parentSum;
            for (int child : childList[curr]) {
                dfsStack.push(new Pr(child, sums[curr]));
            }
        }
    }

}
