Given a square grid of integers arr, a falling path with non-zero shifts is a choice of exactly one element from each row of arr, such that no two elements chosen in adjacent rows are in the same column.
Return the minimum sum of a falling path with non-zero shifts.
 
Example 1:
Input: arr = [[1,2,3],[4,5,6],[7,8,9]]
Output: 13
Explanation: 
The possible falling paths are:
[1,5,9], [1,5,7], [1,6,7], [1,6,8],
[2,4,8], [2,4,9], [2,6,7], [2,6,8],
[3,4,8], [3,4,9], [3,5,7], [3,5,9]
The falling path with the smallest sum is [1,5,7], so the answer is 13.

 
Constraints:

1 <= arr.length == arr[i].length <= 200
-99 <= arr[i][j] <= 99

```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 = 'class Solution:\n    def minFallingPathSum(self, arr: List[List[int]]) -> int:\n        \\"\\"\\"\n        for each column, we can either choose or not choose\n        if we choose one, then the adjacent rows cannot choose the same column\n                                    []\n                             1       2       3 \n                        \n                          5   6    4   6    4   5\n                       \n                       7   9 7  8 \n        \\"\\"\\"\n        # brute force recursive solution\n        # answer = float(\\"inf\\")\n        # def helper(rowIdx, prevIdx, curr): \n        #     nonlocal answer\n        #     if rowIdx == len(arr):\n        #         answer = min(answer, sum(curr))\n        #         return\n        #     row = arr[rowIdx]\n        #     for i in range(len(row)):\n        #         if rowIdx != 0 and i != prevIdx:\n        #             curr.append(row[i])\n        #             helper(rowIdx+1, i, curr)\n        #             curr.pop()\n        #         elif rowIdx == 0: \n        #             curr.append(row[i])\n        #             helper(rowIdx+1, i, curr)\n        #             curr.pop()        \n        # helper(0, 0, [])\n        # return answer\n        \n        dp = [[0 for _ in range(len(arr))] for _ in range(len(arr[0]))]\n        for i in range(len(dp)):\n            dp[0][i] = arr[0][i]\n        \n        for i in range(1, len(dp)):\n            for j in range(len(dp[i])):\n                if j == 0: # left edge\n                    dp[i][j] = min(arr[i][j] + dp[i-1][k] for k in range(1, len(dp[i])))\n                elif j == len(dp[i])-1: # right edge\n                    dp[i][j] = min(arr[i][j] + dp[i-1][k] for k in range(len(dp[i])-1))\n                else: # in between \n                    left_max = min(arr[i][j] + dp[i-1][k] for k in range(j))\n                    right_max = min(arr[i][j] + dp[i-1][k] for k in range(j+1, len(dp[i])))\n                    dp[i][j] = min(left_max, right_max)\n    \n        return min(dp[-1])\n\n\n        \n                \n                \n                \n                \n        \n        '
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

_target = None
_fn_name = 'minFallingPathSum'
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: