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        iMax = len(arr)\n        jMax = len(arr[0])\n        \n        # sortedIndex = [sorted([(arr[i][j], j) for j in range(jMax)]) for i in range(iMax)]\n        dp = {}\n        smallest2 = [None for _ in range(iMax)]\n        \n        def moveDown(preJ, iNow):\n            if iNow == iMax:\n                return 0\n\n            if (preJ, iNow) in dp:\n                return dp[(preJ, iNow)]\n            subAns = float('inf')\n            if smallest2[iNow] == None:\n                temp1 = float('inf')\n                temp1Index = None\n                temp2 = float('inf')\n                temp2Index = None\n                for j, val in enumerate(arr[iNow]):\n                    subAns = val + moveDown(j, iNow+1)\n                    if subAns <= temp1:\n                        temp1, temp2 = subAns, temp1\n                        temp1Index, temp2Index = j, temp1Index\n                    elif subAns <= temp2:\n                        temp2 = subAns\n                        temp2Index = j\n                smallest2[iNow] = [[temp1Index, temp1], [temp2Index, temp2]]\n                \n            if preJ == smallest2[iNow][0][0]:\n                subAns = smallest2[iNow][1][1]\n            else:\n                subAns = smallest2[iNow][0][1]\n            dp[(preJ, iNow)] = subAns\n            return subAns\n        return moveDown(-1, 0)\n    \n#         iMax = len(arr)\n#         jMax = len(arr[0])\n        \n#         # sortedIndex = [sorted([(arr[i][j], j) for j in range(jMax)]) for i in range(iMax)]\n#         # print(sortedIndex)\n#         dp = {}\n#         dp2 = {}\n#         ans = [float('inf')]\n        \n#         def moveDown(preJ, iNow, sumNow):\n#             if iNow == iMax:\n#                 ans[0] = min(ans[0], sumNow)\n#                 return 0\n\n#             if (preJ, iNow) in dp and dp[(preJ, iNow)] <= sumNow:\n#                 ans[0] = min(ans[0], sumNow +  dp2[(preJ, iNow)])\n#                 return dp2[(preJ, iNow)]\n#             # if (preJ, iNow) in dp2:\n#             #     ans[0] = min(ans[0], sumNow +  dp2[(preJ, iNow)])\n#             #     return dp2[(preJ, iNow)]\n#             dp[(preJ, iNow)] = sumNow\n#             # if sumNow >= ans[0]:\n#             #     return float('inf')\n#             subAns = float('inf')\n#             # for val,j in (sortedIndex[iNow]):\n#             for j, val in enumerate(arr[iNow]):\n#                 if j != preJ:\n#                     subAns = min(subAns, val + moveDown(j, iNow+1, val+sumNow))\n#                     # moveDown(j, iNow+1, val+sumNow)\n                    \n#             dp2[(preJ, iNow)] = subAns\n#             return subAns\n#         moveDown(-1, 0, 0)\n#         return ans[0]\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: 8670