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
input = sys.stdin.readline
from collections import deque

def bfs():
    q = deque([0])
    a[0] = s[0]
    visited = [False]*n
    visited[0] = True
    
    while q:
        v = q.popleft()
        
        for nv in G[v]:
            if visited[nv]:
                continue
            
            visited[nv] = True
            
            if s[nv]==-1:
                l = []
                
                for nnv in G[nv]:
                    if v==nnv:
                        continue
                    
                    l.append(s[nnv])

                if len(l)==0:
                    s[nv] = s[v]
                else:
                    s[nv] = min(l)
                
                a[nv] = s[nv]-s[v]
                q.append(nv)
            else:
                a[nv] = s[nv]-s[v]
                q.append(nv)

n = int(input())
p = list(map(int, input().split()))
s = list(map(int, input().split()))
G = [[] for _ in range(n)]

for i in range(n-1):
    G[i+1].append(p[i]-1)
    G[p[i]-1].append(i+1)

a = [0]*n
bfs()

if min(a)>=0:
    print(sum(a))
else:
    print(-1)