1099_D. Sum in the tree
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
```python
import sys
def getAndParseInt(num=1):
    string = (sys.stdin.readline()).strip()
    if num==1:
        return int(string)
    else:
        return [int(part) for part in string.split()]

def getAndParseString(num=1,delim=" "):
    string = (sys.stdin.readline()).strip()
    if num==1:
        return string
    else:
        return [part for part in string.split(delim)]

n = getAndParseInt()
parents = getAndParseInt(2)
sums = getAndParseInt(2)

pc_list = [[0,[]] for i in range(n)]
a_list = [0]*(n)
a_list[0] = sums[0]
for vertex,parent in enumerate(parents):
    pc_list[vertex+1][0] = parent-1
    pc_list[parent-1][1].append(vertex+1)

stack = [(0,0)]
invalid = False
while stack and not invalid:
    cur_vertex,child_num = stack.pop()
    parent = pc_list[cur_vertex][0]
    cur_list = pc_list[cur_vertex][1]
    if not cur_list and sums[cur_vertex]==-1:
        a_list[cur_vertex] = 0
    elif sums[cur_vertex]==-1 and child_num==0:
        min_sum = min([sums[child] for child in cur_list])
        if min_sum < sums[parent]:
            invalid = True
            break
        else:
            a_list[cur_vertex] = min_sum - sums[parent]
    elif sums[cur_vertex]!=-1 and cur_vertex!=0 and child_num==0:
        grandparent = pc_list[parent][0]
        a_list[cur_vertex] = sums[cur_vertex] - a_list[parent]
        a_list[cur_vertex]+=-sums[grandparent]
    if child_num<len(cur_list):
        stack.append((cur_vertex,child_num+1))
        stack.append((cur_list[child_num],0))

if invalid:
    print(-1)
else:
    print(sum(a_list))





```