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
from sys import setrecursionlimit
setrecursionlimit(10000000)
import threading
threading.stack_size(67108864)
def main():
    n = int(input())
    a = list(map(int, input().split()))
    s = list(map(int, input().split()))
    u = []
    inf = 10 ** 9 + 1
    for i in range(n):
        u.append([])
    for i in range(n - 1):
        u[a[i] - 1].append(i + 1)
    a = [0] * n
    a[0] = s[0]
    use = [0] * n
    def dfs(v, p, pp):
        use[v] = 1
        if s[v] != -1 and pp != -1:
            s[p] = min(s[p], s[v])
        elif s[v] == -1 and len(u[v]) != 0:
            s[v] = inf
        elif s[v] == -1 and p != -1:
            s[v] = s[p]
        for i in u[v]:
            if use[i] == 0:
                dfs(i, v, p)
    dfs(0, -1, -1)
    #print(s)
    def dfs1(v, p):
        if p != -1:
            a[v] = s[v] - s[p]
        for i in u[v]:
            dfs1(i, v)
    dfs1(0, -1)
    for i in range(n):
        if a[i] < 0:
            print(-1)
            exit()
    print(sum(a))
thread = threading.Thread(target=main)
thread.start()
thread.join()
