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 $a_v \ge 0$ 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 ($2 \le n \le 10^5$). 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 ($1 \le p_i < i$). The last line contains integer values $s_1$, $s_2$, ..., $s_n$ ($-1 \le s_v \le 10^9$), 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

USER_FILENAME = "<user_code>"
import sys, json, builtins
import math, heapq, bisect, itertools, functools, collections, statistics, fractions, decimal, operator, array, random, re, string, os, pathlib
try:
    import resource as _res
except Exception:
    _res = None
from collections import Counter, defaultdict, deque, OrderedDict
from functools import lru_cache, reduce
from itertools import accumulate, permutations, combinations, product
from math import gcd, ceil, floor, sqrt
from decimal import Decimal
try:
    from typing import *
except Exception:
    pass
try:
    sys.setrecursionlimit(1_000_000)
except Exception:
    pass
try:
    import site as _site
    try:
        _sys_sites = _site.getsitepackages() if hasattr(_site, "getsitepackages") else []
        for _p in _sys_sites:
            if _p and _p not in sys.path:
                sys.path.append(_p)
    except Exception:
        pass
    try:
        _usp = _site.getusersitepackages()
        if isinstance(_usp, str):
            _usp = [_usp]
        for _p in _usp:
            if _p and _p not in sys.path:
                sys.path.append(_p)
    except Exception:
        pass
except Exception:
    pass

ns = {"__name__": "__main__"}
for _k, _v in list(globals().items()):
    if not _k.startswith("_"):
        ns[_k] = _v
_CODE = 'from collections import deque,defaultdict\nn=int(input())\ng=defaultdict(list)\na=list(map(int,input().split()))\nfor i in range(n-1):\n    g[a[i]].append(i+2)\n    g[i+2].append(a[i])\ns=list(map(int,input().split()))\nvisited=[False]*(n+1)\nq=deque();q.append(1);visited[1]=True\nval=[0]*(n+1);val[1]=s[0]\n#print(val)\nwhile len(q)>0:\n    v=q.popleft()\n    b=[]\n    for i in g[v]:\n        if not visited[i]:\n            if s[v-1]==-1:\n                b.append(s[i-1])\n            else:\n                if v>1:\n                    val[v]=s[v-1]-s[g[v][0]-1]\n            q.append(i)\n            visited[i]=True\n    if b!=[] and not all([x>=s[g[v][0]-1] for x in b]):\n        print(-1)\n        return\n    elif b!=[]:\n        val[v]=min(b)-s[g[v][0]-1]\n        s[v-1]=val[v]+s[g[v][0]-1]\n    else:\n        if s[v-1]!=-1 and v>1:\n            val[v]=s[v-1]-s[g[v][0]-1]\n    \n\n\nprint(sum(val))\n'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: