






"""simple docstring"""







from __future__ import annotations

from typing import Any

def _a (		*_snake_case							):







      """simple docstring"""






      if all(_check_not_integer(_snake_case							) for m in matrix_s							):
            for i in matrix_s[1:]:
                  _verify_matrix_sizes(matrix_s[0]      ,       _snake_case							)
            return [[sum(_snake_case							) for t in zip(*_snake_case							)] for m in zip(*_snake_case							)]
      raise TypeError("""Expected a matrix, got int/list instead"""							)

def _a (		_snake_case      ,       _snake_case							):







      """simple docstring"""






      if (
          _check_not_integer(_snake_case							)
          and _check_not_integer(_snake_case							)
          and _verify_matrix_sizes(_snake_case      ,       _snake_case							)
      ):
            return [[i - j for i, j in zip(*_snake_case							)] for m in zip(_snake_case      ,       _snake_case							)]
      raise TypeError("""Expected a matrix, got int/list instead"""							)

def _a (		_snake_case      ,       _snake_case							):







      """simple docstring"""






      return [[x * n for x in row] for row in matrix]

def _a (		_snake_case      ,       _snake_case							):







      """simple docstring"""






      if _check_not_integer(_snake_case							) and _check_not_integer(_snake_case							):
            UpperCAmelCase			,					UpperCAmelCase							=       _verify_matrix_sizes(_snake_case      ,       _snake_case							)

      if cols[0] != rows[1]:
            UpperCAmelCase							=       (
                """Cannot multiply matrix of dimensions """
                F'''({rows[0]},{cols[0]}) and ({rows[1]},{cols[1]})'''
            )
            raise ValueError(_snake_case							)
      return [
          [sum(m * n for m, n in zip(_snake_case      ,       _snake_case							)							) for j in zip(*_snake_case							)] for i in matrix_a
      ]

def _a (		_snake_case							):







      """simple docstring"""






      UpperCAmelCase							=       int(_snake_case							)
      return [[int(row == column							) for column in range(_snake_case							)] for row in range(_snake_case							)]

def _a (		_snake_case      ,       _snake_case = True							):







      """simple docstring"""






      if _check_not_integer(_snake_case							):
            if return_map:
                  return map(_snake_case      ,       zip(*_snake_case							)							)
            else:
                  return list(map(_snake_case      ,       zip(*_snake_case							)							)							)
      raise TypeError("""Expected a matrix, got int/list instead"""							)

def _a (		_snake_case      ,       _snake_case      ,       _snake_case							):







      """simple docstring"""






      UpperCAmelCase							=       matrix[:row] + matrix[row + 1 :]
      return [row[:column] + row[column + 1 :] for row in minor]

def _a (		_snake_case							):







      """simple docstring"""






      if len(_snake_case							) == 1:
            return matrix[0][0]

      return sum(
          x * determinant(minor(_snake_case      ,       0      ,       _snake_case							)							) * (-1) ** i
          for i, x in enumerate(matrix[0]							)							)

def _a (		_snake_case							):







      """simple docstring"""






      UpperCAmelCase							=       determinant(_snake_case							)
      if det == 0:
            return None

      UpperCAmelCase							=       [
          [determinant(minor(_snake_case      ,       _snake_case      ,       _snake_case							)							) for j in range(len(_snake_case							)							)]
          for i in range(len(_snake_case							)							)
      ]

      UpperCAmelCase							=       [
          [x * (-1) ** (row + col) for col, x in enumerate(matrix_minor[row]							)]
          for row in range(len(_snake_case							)							)
      ]
      UpperCAmelCase							=       list(transpose(_snake_case							)							)
      return scalar_multiply(_snake_case      ,       1 / det							)

def _a (		_snake_case							):







      """simple docstring"""






      return not isinstance(_snake_case      ,       _snake_case							) and not isinstance(matrix[0]      ,       _snake_case							)

def _a (		_snake_case							):







      """simple docstring"""






      return len(_snake_case							), len(matrix[0]							)

def _a (		_snake_case      ,       _snake_case							):







      """simple docstring"""






      UpperCAmelCase							=       _shape(_snake_case							) + _shape(_snake_case							)
      if shape[0] != shape[3] or shape[1] != shape[2]:
            UpperCAmelCase							=       (
                """operands could not be broadcast together with shape """
                F'''({shape[0], shape[1]}), ({shape[2], shape[3]})'''
            )
            raise ValueError(_snake_case							)
      return (shape[0], shape[2]), (shape[1], shape[3])

def _a (		):







      """simple docstring"""






      UpperCAmelCase							=       [[12, 10], [3, 9]]
      UpperCAmelCase							=       [[3, 4], [7, 4]]
      UpperCAmelCase							=       [[11, 12, 13, 14], [21, 22, 23, 24], [31, 32, 33, 34], [41, 42, 43, 44]]
      UpperCAmelCase							=       [[3, 0, 2], [2, 0, -2], [0, 1, 1]]
      print(F'''Add Operation, {add(_snake_case      ,       _snake_case							) = } \n'''							)
      print(
          F'''Multiply Operation, {multiply(_snake_case      ,       _snake_case							) = } \n'''      ,       )
      print(F'''Identity: {identity(5							)}\n'''							)
      print(F'''Minor of {matrix_c} = {minor(_snake_case      ,       1      ,       2							)} \n'''							)
      print(F'''Determinant of {matrix_b} = {determinant(_snake_case							)} \n'''							)
      print(F'''Inverse of {matrix_d} = {inverse(_snake_case							)}\n'''							)


if __name__ == "__main__":
  import doctest

  doctest.testmod()
  main()











"""simple docstring"""







import sys

def _a (		_snake_case      ,       _snake_case							):







      """simple docstring"""






      if not numbers:
            return 0
      if target == 0 and target in numbers:
            return 0
      if not isinstance(_snake_case      ,       (list, tuple)							) or not all(
          isinstance(_snake_case      ,       _snake_case							) for number in numbers							):
            raise ValueError("""numbers must be an iterable of integers"""							)

      UpperCAmelCase							=       UpperCAmelCase							=       UpperCAmelCase							=       0
      UpperCAmelCase							=       sys.maxsize

      while right < len(_snake_case							):
            curr_sum += numbers[right]
            while curr_sum >= target and left <= right:
                  UpperCAmelCase							=       min(_snake_case      ,       right - left + 1							)
                  curr_sum -= numbers[left]
                  left += 1
            right += 1

      return 0 if min_len == sys.maxsize else min_len



