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.*;
import java.awt.Point;
import java.math.BigInteger;

public class tree {
	
	static ArrayList<Integer> children[];
	static long[] weight;
	
	public static void main(String[] args) throws Exception {
		FastIO sc = new FastIO(System.in);
		PrintWriter pw = new PrintWriter(System.out);
		
		int N = sc.nextInt();
		
		children = new ArrayList[N];
		for(int i = 0; i < N; i++) children[i] = new ArrayList<Integer>();
		
		weight = new long[N];
		
		for(int i = 1; i < N; i++) {
			children[sc.nextInt()-1].add(i);
		}
		for(int i = 0; i < N; i++) {
			weight[i] = sc.nextInt();
		}
		
		dfs1(0, 0);
		dfs2(0);
		
		long sum = 0;
		for(long i : weight) sum += i;
		
		pw.println(sum);
		pw.close();
	}
	
	static void dfs2(int vert) {
		if(weight[vert] == -1) {
			long min = Long.MAX_VALUE;
			for(int child : children[vert]) {
				min = Math.min(min, weight[child]);
			}
			
			if(min == Long.MAX_VALUE) weight[vert] = 0;
			else {
				weight[vert] = min;
				for(int child : children[vert]) {
					weight[child] -= min;
				}
			}
		}
		
		for(int child : children[vert]) {
			dfs2(child);
		}
	}
	
	static void dfs1(int vert, long w) {
		long currentWeight = weight[vert];
		if(weight[vert] != -1) {
			if(w > weight[vert]) nahG();
			
			weight[vert] -= w;
		}
		
		for(int child : children[vert]) dfs1(child, Math.max(w, currentWeight));
	}
	
	static void nahG() {
		System.out.println(-1);
		System.exit(0);
	}

	static class FastIO {

		//Is your Fast I/O being bad?

		InputStream dis;
		byte[] buffer = new byte[1 << 17];
		int pointer = 0;

		public FastIO(String fileName) throws Exception {
			dis = new FileInputStream(fileName);
		}

		public FastIO(InputStream is) throws Exception {
			dis = is;
		}

		int nextInt() throws Exception {
			int ret = 0;

			byte b;
			do {
				b = nextByte();
			} while (b <= ' ');
			boolean negative = false;
			if (b == '-') {
				negative = true;
				b = nextByte();
			}
			while (b >= '0' && b <= '9') {
				ret = 10 * ret + b - '0';
				b = nextByte();
			}

			return (negative) ? -ret : ret;
		}

		long nextLong() throws Exception {
			long ret = 0;

			byte b;
			do {
				b = nextByte();
			} while (b <= ' ');
			boolean negative = false;
			if (b == '-') {
				negative = true;
				b = nextByte();
			}
			while (b >= '0' && b <= '9') {
				ret = 10 * ret + b - '0';
				b = nextByte();
			}

			return (negative) ? -ret : ret;
		}

		byte nextByte() throws Exception {
			if (pointer == buffer.length) {
				dis.read(buffer, 0, buffer.length);
				pointer = 0;
			}
			return buffer[pointer++];
		}

		String next() throws Exception {
			StringBuffer ret = new StringBuffer();

			byte b;
			do {
				b = nextByte();
			} while (b <= ' ');
			while (b > ' ') {
				ret.appendCodePoint(b);
				b = nextByte();
			}

			return ret.toString();
		}

	}
}
