# Task

John won the championship of a TV show. He can get some bonuses.

He needs to play a game to determine the amount of his bonus.

Here are `n` rows and `m` columns of cards were placed on the ground. A non-negative number is written on each card.

The rules of the game are:

- Player starts from the top-left coner, walk to the bottom-right coner. 

- Players can only walk downward or right. 

- The sum of the numbers collected by the players will be used as the bonus.

John has two chances to play this game on a game map. Specifically, when John finishes the game, the card on his path will be removed, and then he can walk again.

Your task is to help John calculate the maximum amount of bonuses he can get.

# Input

- `gameMap/gamemap`: A `n` x `m` integer array. Each element represents the number on the card.
  - `4 <= n,m <= 40(Pyhon)/100(JS)`


- All inputs are valid.

# Output

An integer. the maximum amount of bonuses John can get.

# Eaxmple

For 
```
gameMap=
[
[1, 3, 9],
[2, 8, 5],
[5, 7, 4]
]
```
The output should be `39`.

One of the possible solution is:
```
1st game:
[
[>, >, v],
[2, 8, v],
[5, 7, v]
]
1+3+9+5+4=22

2nd game:
[
[v, 0, 0],
[>, v, 0],
[5, >, >]
]
0+2+8+7+0=17

Final bonus = 22 + 17 = 39
```

```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 = 'from itertools import combinations\n\ndef calc(game_map):\n    """ A state is denoted a NE-SW diagonal of :game_map: and two different cells contained in it.        \n        Its key is a triplet (diagonal, row_cell_1, row_cell_2), where holds the invariant\n        diagonal == row_cell_1 + column_cell_1 == row_cell_2 + column_cell_2\n        Its value is the sum of the points scored by respective paths from the top left to the cells.\n    """\n    rows = len(game_map)\n    cols = len(game_map[0])\n    \n    states = {\n        (1, 0, 1): game_map[0][0] + game_map[0][1] + game_map[1][0]\n        }\n    \n    state_keys = []\n    for diagonal in range(2, rows + cols - 1):\n        min_row = max(0, diagonal - cols + 1)\n        max_row = min(rows - 1, diagonal)\n        row_codes = range(min_row, max_row + 1)\n        for (row_cell_1, row_cell_2) in combinations(row_codes, 2):\n            state_keys.append((diagonal, row_cell_1, row_cell_2))\n\n    for (diagonal, row_cell_1, row_cell_2) in state_keys:       \n        prev_values = []\n        \n        # Both paths downwards\n        if row_cell_1 > 0:\n            prev_values.append(states[(diagonal - 1, row_cell_1 - 1, row_cell_2 - 1)])\n            \n        # Cell 1 downwards and cell 2 rightwards\n        if row_cell_1 > 0 and row_cell_2 < diagonal:\n            prev_values.append(states[(diagonal - 1, row_cell_1 - 1, row_cell_2)])\n            \n        # Cell 1 rightwards and cell 2 downwards. Excluded the case\n        # where both paths come from a common cell for efficiency.\n        if row_cell_2 > row_cell_1 + 1:\n            prev_values.append(states[(diagonal - 1, row_cell_1, row_cell_2 - 1)])\n            \n        # Both paths rightwards\n        if row_cell_2 < diagonal:\n            prev_values.append(states[(diagonal - 1, row_cell_1, row_cell_2)])\n            \n        prev_value = max(prev_values)\n        col_cell_1 = diagonal - row_cell_1\n        col_cell_2 = diagonal - row_cell_2\n        new_value = prev_value + game_map[row_cell_1][col_cell_1] + game_map[row_cell_2][col_cell_2]\n        states[(diagonal, row_cell_1, row_cell_2)] = new_value\n    \n    final_diagonal = (rows + cols - 3, rows - 2, rows - 1)\n    return states[final_diagonal] + game_map[rows - 1][cols - 1]'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

_target = None
_fn_name = 'calc'
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: 7098