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 sys
import random, math
from collections import defaultdict

def dfs(cur):
    global s, ws
    while True:
        for u in dn[cur]:
            if ws[u] == -1:
                m = -1
                for el in dn[u]:
                    if m==-1 or m > ws[el]:
                        m = ws[el]
                if m == -1:
                    ws[u] = ws[cur]
                else:
                    ws[u] = m
            
            if ws[u] >= ws[cur]:
                
                s += ws[u] - ws[cur]
            else:
                print(-1)
                exit()
            if len(dn[cur]) == 1:
                cur = u
                break
            else:
                dfs(u)
        else:
            break
            
        
        
#n,k = [int(__) for __ in raw_input().split()]

n = int(raw_input())
arr = [int(__) for __ in raw_input().split()]
ws = [int(__) for __ in raw_input().split()]

dn = defaultdict(set)

for i in range(len(arr)):
    dn[arr[i]-1].add(i+1)
#print(dn)

s = ws[0]
dfs(0)
print(s)
    