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.*;
import java.io.*;

public class main
{ 


   
   public static void main(String[] args){
  Reader sc=new Reader(System.in);
  int n=sc.nextInt();
  int parent[]=new int[n+1];
  int min[]=new int[n+1];
  Arrays.fill(min,Integer.MAX_VALUE);
  for(int i=2;i<=n;i++) {
	  parent[i]=sc.nextInt();
  }
  int sum[]=new int[n+1];
  for(int i=1;i<=n;i++) {
	  sum[i]=sc.nextInt();
	  min[parent[i]]=Math.min(min[parent[i]],sum[i]);
  }
  long ans=sum[1];
  for(int i=2;i<=n;i++) {
	  if(sum[i]==-1) {
		  if(min[i]!=Integer.MAX_VALUE) {
			  sum[i]=min[i];
			  if(sum[i]<sum[parent[i]]) {
				  ans=-1;
				  break;
			  }
			  else {
				  ans+=(sum[i]-sum[parent[i]]);
			  }
		  }
	  }
	  else {
		  if(sum[i]<sum[parent[i]]) {
			  ans=-1;
			  break;
		  }
		  else {
			  ans+=(sum[i]-sum[parent[i]]);
		  }
	  }
  }
  System.out.println(ans);
	}
   }
class Reader {
	private InputStream stream;
	private byte[] buf = new byte[1024];
	private int curChar;
	private int numChars;
	private SpaceCharFilter filter;
	
	public Reader(InputStream stream) {
		this.stream = stream;
	}
	
	public int read() {
		if (numChars == -1) {
			throw new InputMismatchException();
		}
		if (curChar >= numChars) {
			curChar = 0;
			try {
				numChars = stream.read(buf);
			} catch (IOException e) {
				throw new InputMismatchException();
			}
			if (numChars <= 0) {
				return -1;
			}
		}
		return buf[curChar++];
	}
	
	public int nextInt() {
		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 String readString() {
		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 double nextDouble() {
		int c = read();
		while (isSpaceChar(c)) {
			c = read();
		}
		int sgn = 1;
		if (c == '-') {
			sgn = -1;
			c = read();
		}
		double res = 0;
		while (!isSpaceChar(c) && c != '.') {
			if (c == 'e' || c == 'E') {
				return res * Math.pow(10, nextInt());
			}
			if (c < '0' || c > '9') {
				throw new InputMismatchException();
			}
			res *= 10;
			res += c - '0';
			c = read();
		}
		if (c == '.') {
			c = read();
			double m = 1;
			while (!isSpaceChar(c)) {
				if (c == 'e' || c == 'E') {
					return res * Math.pow(10, nextInt());
				}
				if (c < '0' || c > '9') {
					throw new InputMismatchException();
				}
				m /= 10;
				res += (c - '0') * m;
				c = read();
			}
		}
		return res * sgn;
	}
	
	public long nextLong() {
		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 boolean isSpaceChar(int c) {
		if (filter != null) {
			return filter.isSpaceChar(c);
		}
		return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
	}
	
	public String next() {
		return readString();
	}
	
	public interface SpaceCharFilter {
		public boolean isSpaceChar(int ch);
	}
}