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
class Node:
    def __init__(self):
        self.curV = None
        self.totV = None
        self.children = []
        self.parent = None
        

N = int(input())

relations = list(map(int, input().split()))
totValues = list(map(int, input().split()))

allNodes = []
for n in range(N + 1):
    node = Node()
    allNodes.append(node)
for i in range(len(relations)):
    allNodes[relations[i]].children.append(i + 2)
    allNodes[i + 2].parent = relations[i]

for i in range(0, len(totValues)):
    allNodes[i + 1].totV = totValues[i]
allNodes[1].curV = totValues[0]
allNodes[0].curV = 0


curChildren = allNodes[1].children.copy()

isFine = True
while curChildren != [] and isFine:
    newChildren = []
    
    for c in curChildren:
        child = allNodes[c]
        if child.totV == -1:
            if child.children != []:
                curMin = allNodes[child.children[0]].totV
                for grandC in child.children:
                    curMin = min(allNodes[grandC].totV, curMin)
                if curMin < allNodes[child.parent].totV:
                    isFine = False
                    break
                child.totV = curMin
                child.curV = child.totV - allNodes[child.parent].totV
                newChildren += child.children
            else:
                child.totV = allNodes[child.parent].totV
                child.curV = 0
                
                
        else:
            if child.totV < allNodes[child.parent].totV:
                isFine = False
                break
            else:
                child.curV = -allNodes[child.parent].totV + child.totV

                newChildren += child.children
    curChildren = newChildren.copy()
if isFine:
    ans = 0
    for a in allNodes:
        ans += a.curV
    print(ans)
else:
    print(-1)
    
                
'''
4
1 2 2
1 -1 3 3


8
1 2 3 1 1 6 6
1 -1 2 -1 -1 -1 3 3
'''