There is a brick wall in front of you. The wall is rectangular and has several rows of bricks. The bricks have the same height but different width. You want to draw a vertical line from the top to the bottom and cross the least bricks. 


The brick wall is represented by a list of rows. Each row is a list of integers representing the width of each brick in this row from left to right. 


If your line go through the edge of a brick, then the brick is not considered as crossed. You need to find out how to draw the line to cross the least bricks and return the number of crossed bricks. 

You cannot draw a line just along one of the two vertical edges of the wall, in which case the line will obviously cross no bricks. 

Example:

Input: 
[[1,2,2,1],
 [3,1,2],
 [1,3,2],
 [2,4],
 [3,1,2],
 [1,3,1,1]]
Output: 2
Explanation: 




Note:

The width sum of bricks in different rows are the same and won't exceed INT_MAX.
The number of bricks in each row is in range [1,10,000]. The height of wall is in range [1,10,000]. Total number of bricks of the wall won't exceed 20,000.

```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 leastBricks(self, wall):\n         """\n         :type wall: List[List[int]]\n         :rtype: int\n         """\n         """\n         Time O(r*c) because we iterate through the wall once and do O(1) work for each element\n         in the wall.\n         Space O(c) because in the worst case, our hashmap will have length c.\n         """\n         if not wall:\n             return 0\n         \n         """\n         The maximum number of bricks we have to intersect is the equal to the number of rows,\n         in the case that we have to intersect a brick at every row.\n         columns will be a map from a column to the number of bricks that would be intersected\n         if we drew a line through that column. For now, we assume that every column will intersect\n         the maximum number of bricks, which is the number of rows in the wall.\n         """\n         numRows = len(wall)\n         columns = collections.defaultdict(lambda: numRows)\n         \n         for r in range(len(wall)):\n             """\n             col will be the current column that we are considering drawing a line through.\n             If a brick in this row ends at column col, then we can avoid intersecting that\n             brick by drawing a line through column col.\n             """\n             col = 0\n             for c in range(len(wall[r])-1):\n                 """\n                 Add the length of the current brick to col to find the column where\n                 this brick ends.\n                 """\n                 col += wall[r][c]\n                 """\n                 Because this brick ends at col, it won\'t be intersected if we draw a line\n                 at column col. So we can decrement the number of bricks that will be intersected \n                 if we draw a line at column col.\n                 """\n                 columns[col] -= 1\n         \n         return numRows if len(columns) == 0 else min(columns.values())\n'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

_target = None
_fn_name = 'leastBricks'
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: 5906