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 = "def solve():\n    a = [None] * (n + 1)\n\n    a[1] = s[0]\n    for i in range(2, n + 1):\n        if s[i - 1] == -1:\n            continue\n\n        pi = p[i - 2]\n        pi_er_pi = p[pi - 2]\n\n        if s[i - 1] < s[pi_er_pi - 1]:\n            return -1\n\n        new_value = s[i - 1] - s[pi_er_pi - 1]\n        a[pi] = min(a[pi] if a[pi] is not None else float('inf'), new_value)\n\n    for i in range(2, n + 1):\n        if s[i - 1] == -1:\n            continue\n\n        pi = p[i - 2]\n        pi_er_pi = p[pi - 2]\n\n        a[i] = s[i - 1] - s[pi_er_pi - 1] - a[pi]\n\n    return sum(filter(None, a))\n\n\nn = int(input())\np = list(map(int, input().split()))\ns = list(map(int, input().split()))\nans = solve()\nprint(ans)"
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 13157