Greg has a weighed directed graph, consisting of n vertices. In this graph any pair of distinct vertices has an edge between them in both directions. Greg loves playing with the graph and now he has invented a new game:  The game consists of n steps.  On the i-th step Greg removes vertex number x_{i} from the graph. As Greg removes a vertex, he also removes all the edges that go in and out of this vertex.  Before executing each step, Greg wants to know the sum of lengths of the shortest paths between all pairs of the remaining vertices. The shortest path can go through any remaining vertex. In other words, if we assume that d(i, v, u) is the shortest path between vertices v and u in the graph that formed before deleting vertex x_{i}, then Greg wants to know the value of the following sum: $\sum_{v, u, v \neq u} d(i, v, u)$. 

Help Greg, print the value of the required sum before each step.


-----Input-----

The first line contains integer n (1 ≤ n ≤ 500) — the number of vertices in the graph.

Next n lines contain n integers each — the graph adjacency matrix: the j-th number in the i-th line a_{ij} (1 ≤ a_{ij} ≤ 10^5, a_{ii} = 0) represents the weight of the edge that goes from vertex i to vertex j.

The next line contains n distinct integers: x_1, x_2, ..., x_{n} (1 ≤ x_{i} ≤ n) — the vertices that Greg deletes.


-----Output-----

Print n integers — the i-th number equals the required sum before the i-th step.

Please, do not use the %lld specifier to read or write 64-bit integers in C++. It is preferred to use the cin, cout streams of the %I64d specifier.


-----Examples-----
Input
1
0
1

Output
0 
Input
2
0 5
4 0
1 2

Output
9 0 
Input
4
0 3 1 1
6 0 400 1
2 4 0 1
1 1 1 0
4 1 2 3

Output
17 23 404 0

```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 = "import sys\nfrom array import array  # noqa: F401\n\nn = int(input())\nmatrix = [array('i', list(map(int, input().split()))) for _ in range(n)]\naa = tuple([int(x) - 1 for x in input().split()])\nans = [''] * n\n\nfor i in range(n-1, -1, -1):\n    x = aa[i]\n\n    for a in range(n):\n        for b in range(n):\n            if matrix[a][b] > matrix[a][x] + matrix[x][b]:\n                matrix[a][b] = matrix[a][x] + matrix[x][b]\n\n    val, overflow = 0, 0\n    for a in aa[i:]:\n        for b in aa[i:]:\n            val += matrix[a][b]\n        if val > 10**9:\n            overflow += 1\n            val -= 10**9\n\n    ans[i] = str(10**9 * overflow + val)\n\nprint(' '.join(ans))\n"
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 13441