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
// LM10: The next Ballon d'Or
import java.util.*;
import java.io.*;
import java.math.*;
public class Main
{
    static class FastReader
    {
        private InputStream mIs;private byte[] buf = new byte[1024];private int curChar,numChars;public FastReader() { this(System.in); }public FastReader(InputStream is) { mIs = is;}
        public int read() {if (numChars == -1) throw new InputMismatchException();if (curChar >= numChars) {curChar = 0;try { numChars = mIs.read(buf);} catch (IOException e) { throw new InputMismatchException();}if (numChars <= 0) return -1; }return buf[curChar++];}
        public String nextLine(){int c = read();while (isSpaceChar(c)) c = read();StringBuilder res = new StringBuilder();do {res.appendCodePoint(c);c = read();}while (!isEndOfLine(c));return res.toString() ;}
        public String next(){int c = read();while (isSpaceChar(c)) c = read();StringBuilder res = new StringBuilder();do {res.appendCodePoint(c);c = read();}while (!isSpaceChar(c));return res.toString();}
        public long l(){int c = read();while (isSpaceChar(c)) c = read();int sgn = 1;if (c == '-') { sgn = -1 ; c = read() ; }long res = 0; do{ if (c < '0' || c > '9') throw new InputMismatchException();res *= 10 ; res += c - '0' ; c = read();}while(!isSpaceChar(c));return res * sgn;}
        public int i(){int c = read() ;while (isSpaceChar(c)) c = read();int sgn = 1;if (c == '-') { sgn = -1 ; c = read() ; }int res = 0;do{if (c < '0' || c > '9') throw new InputMismatchException();res *= 10 ; res += c - '0' ; c = read() ;}while(!isSpaceChar(c));return res * sgn;}
        public double d() throws IOException {return Double.parseDouble(next()) ;}
        public boolean isSpaceChar(int c) { return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1; }
        public boolean isEndOfLine(int c) { return c == '\n' || c == '\r' || c == -1; }
        public void scanIntArr(int [] arr){ for(int li=0;li<arr.length;++li){ arr[li]=i();}}
        public void scanLongArr(long [] arr){for (int i=0;i<arr.length;++i){arr[i]=l();}}
        public void shuffle(int [] arr){ for(int i=arr.length;i>0;--i) { int r=(int)(Math.random()*i); int temp=arr[i-1]; arr[i-1]=arr[r]; arr[r]=temp; } }
    }
    static long ans=0;
    static boolean possible=true;
    public static void main(String[] args)throws IOException {
        /*
inputCopy
5
1 1 1 1
1 -1 -1 -1 -1
outputCopy
1
inputCopy
5
1 2 3 1
1 -1 2 -1 -1
outputCopy
2
inputCopy
3
1 2
2 -1 1
outputCopy
-1
*/
        PrintWriter pw = new PrintWriter(System.out);
        FastReader fr = new FastReader();
        int n=fr.i();
        Node [] nodeArr=new Node[n+1];
        nodeArr[1]=new Node(1,1,nodeArr);
        for(int i=2;i<=n;++i)
        {
            int parent=fr.i();
            nodeArr[i]=new Node(i,parent,nodeArr);
        }
        for(int i=2;i<=n;++i)
        {
            int parent=nodeArr[i].parent;
            nodeArr[parent].childs.add(nodeArr[i]);
        }
        for(int i=1;i<=n;++i)
        {
            nodeArr[i].sum=fr.i();
        }
        ans=0;
        possible=true;
        traversal(nodeArr,1,0);
        if(possible)
            pw.println(ans);
        else
            pw.println(-1);
        pw.flush();
        pw.close();
    }
    public static void traversal(Node [] nodeArr,int id,long sum)
    {
        //System.out.println("sum="+sum+" id="+id);
        if(sum>nodeArr[id].sum && nodeArr[id].sum>=0)
        {
            //System.out.println("id="+id);
            possible=false;
            return;
        }
        if(nodeArr[id].sum<0)
        {
            long min=Long.MAX_VALUE;
            for(Node n:nodeArr[id].childs)
            {
                if(n.sum<sum)
                {
                    possible=false;
                    return;
                }
                min=Math.min(min,n.sum);
            }
            if(min!=Long.MAX_VALUE) {


                nodeArr[id].sum = min;
                // System.out.println("sum="+sum+" min="+min+" id="+id);
                ans += min - sum;
                sum = nodeArr[id].sum;
            }
        }
        else
        {
            ans+=nodeArr[id].sum-sum;
            sum=nodeArr[id].sum;
        }
        for(Node n:nodeArr[id].childs)
        {
            traversal(nodeArr,n.id,sum);
        }
        return;
    }
    static class Node
    {
        int id;
        int parent;
        long sum=0;
        LinkedList<Node> childs;
        Node(int i,int p,Node [] nodeArr)
        {
            id=i;
            parent=p;
            childs=new LinkedList<>();
        }
    }
}