There is a row of m houses in a small city, each house must be painted with one of the n colors (labeled from 1 to n), some houses that has been painted last summer should not be painted again.
A neighborhood is a maximal group of continuous houses that are painted with the same color. (For example: houses = [1,2,2,3,3,2,1,1] contains 5 neighborhoods  [{1}, {2,2}, {3,3}, {2}, {1,1}]).
Given an array houses, an m * n matrix cost and an integer target where:

houses[i]: is the color of the house i, 0 if the house is not painted yet.
cost[i][j]: is the cost of paint the house i with the color j+1.

Return the minimum cost of painting all the remaining houses in such a way that there are exactly target neighborhoods, if not possible return -1.
 
Example 1:
Input: houses = [0,0,0,0,0], cost = [[1,10],[10,1],[10,1],[1,10],[5,1]], m = 5, n = 2, target = 3
Output: 9
Explanation: Paint houses of this way [1,2,2,1,1]
This array contains target = 3 neighborhoods, [{1}, {2,2}, {1,1}].
Cost of paint all houses (1 + 1 + 1 + 1 + 5) = 9.

Example 2:
Input: houses = [0,2,1,2,0], cost = [[1,10],[10,1],[10,1],[1,10],[5,1]], m = 5, n = 2, target = 3
Output: 11
Explanation: Some houses are already painted, Paint the houses of this way [2,2,1,2,2]
This array contains target = 3 neighborhoods, [{2,2}, {1}, {2,2}]. 
Cost of paint the first and last house (10 + 1) = 11.

Example 3:
Input: houses = [0,0,0,0,0], cost = [[1,10],[10,1],[1,10],[10,1],[1,10]], m = 5, n = 2, target = 5
Output: 5

Example 4:
Input: houses = [3,1,2,3], cost = [[1,1,1],[1,1,1],[1,1,1],[1,1,1]], m = 4, n = 3, target = 3
Output: -1
Explanation: Houses are already painted with a total of 4 neighborhoods [{3},{1},{2},{3}] different of target = 3.

 
Constraints:

m == houses.length == cost.length
n == cost[i].length
1 <= m <= 100
1 <= n <= 20
1 <= target <= m
0 <= houses[i] <= n
1 <= cost[i][j] <= 10^4

```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

def _disabled_input(*args, **kwargs):
    raise RuntimeError("input() is disabled in callable mode")
builtins.input = _disabled_input

ns = {"__name__": "__judge__"}  # prevent if __name__ == "__main__" blocks
for _k, _v in list(globals().items()):
    if not _k.startswith("_"):
        ns[_k] = _v
_CODE = 'import numpy as np\nfrom collections import defaultdict\n\nclass Solution:\n    def minCost(self, houses: List[int], cost: List[List[int]], m: int, n: int, target: int) -> int:\n        \n        # DP(number of painted houses from left, last house color, number of groups in painted houses)\n        # DP(i, color, groups)\n        #       = min(DP(i - 1, x != color, groups - 1), DP(i - 1, color, groups)) + cost[i][x]\n\n        # m houses <= 100\n        # n colors <= 20\n        # number of states = m * n * target = 100 * 20 * 100 = 2e5\n        \n        INF = int(1e9)\n        DP = defaultdict(lambda: INF)  # (groups, last_color) -> min cost\n\n        if houses[0] == 0:\n            for col in range(1, n + 1):\n                DP[(1, col)] = cost[0][col - 1]\n        else:\n            DP[(1, houses[0])] = 0\n        \n        for i in range(1, m):\n            NDP = defaultdict(lambda: INF)\n            \n            ByGroups = defaultdict(list)  # (groups) -> [(cost, prev color)]\n            for key, min_cost in DP.items():\n                groups_prev, col_prev = key\n                ByGroups[groups_prev].append((min_cost, col_prev))\n\n            curr_colors = range(1, n + 1) if houses[i] == 0 else [houses[i]]\n                \n            for groups_prev, prev_colors_array in ByGroups.items():\n                prev_colors_array.sort()\n                prev_colors = [col_prev for min_cost, col_prev in prev_colors_array[:2]]\n                \n                for col_curr in curr_colors:\n                    paint_cost = cost[i][col_curr - 1] if houses[i] == 0 else 0\n\n                    for col_prev in [col_curr] + prev_colors:\n                        groups_curr = groups_prev + (col_prev != col_curr)\n                        curr_cost = DP[(groups_prev, col_prev)] + paint_cost\n                        if groups_curr <= target and curr_cost < INF:\n                            key = (groups_curr, col_curr)\n                            NDP[key] = min(NDP[key], curr_cost)\n                            \n            DP = NDP\n        \n        ans = -1\n        for key, min_cost in DP.items():\n            if key[0] == target and (ans < 0 or ans > min_cost):\n                ans = min_cost\n        return ans'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

_target = None
_fn_name = 'minCost'
if _fn_name:
    if "Solution" in ns:
        try:
            _obj = ns["Solution"]()
            if hasattr(_obj, _fn_name):
                _target = getattr(_obj, _fn_name)
        except Exception:
            _target = None
    if _target is None and _fn_name in ns and callable(ns[_fn_name]):
        _target = ns[_fn_name]
# Fallback: if there's exactly one user-defined function, use it
if _target is None:
    _cands = [v for k, v in ns.items() if callable(v) and getattr(v, "__module__", "") in ("__judge__", "__main__")]
    _user_funcs = [c for c in _cands if getattr(c, "__name__", "").startswith("_") is False]
    if len(_user_funcs) == 1:
        _target = _user_funcs[0]
if _target is None:
    raise RuntimeError(f"Could not resolve callable '{_fn_name}'")

_raw = sys.stdin.read().strip()
if _raw:
    _parsed = json.loads(_raw)
    if isinstance(_parsed, dict):
        _kwargs = _parsed.get("kwargs", {})
        _args = _parsed.get("args", [])
    else:
        _args, _kwargs = _parsed, {}
else:
    _args, _kwargs = [], {}
if not isinstance(_args, (list, tuple)):
    _args = [_args]
_res = _target(*_args, **_kwargs)
try:
    sys.stdout.write(repr(_res) + "\n")
except Exception:
    pass

```

Measured memory_bytes: 9956