




from __future__ import annotations

from typing import Any



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



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



def      UpperCAmelCase_   (     __UpperCamelCase,    __UpperCamelCase     ):
    return [[x * n for x in row] for row in matrix]



def      UpperCAmelCase_   (     __UpperCamelCase,    __UpperCamelCase     ):
    if _check_not_integer(__UpperCamelCase     ) and _check_not_integer(__UpperCamelCase     ):
        SCREAMING_SNAKE_CASE__      ,		SCREAMING_SNAKE_CASE__       =_verify_matrix_sizes(__UpperCamelCase,    __UpperCamelCase     )

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



def      UpperCAmelCase_   (     __UpperCamelCase     ):
    SCREAMING_SNAKE_CASE__       =int(__UpperCamelCase     )
    return [[int(row == column     ) for column in range(__UpperCamelCase     )] for row in range(__UpperCamelCase     )]



def      UpperCAmelCase_   (     __UpperCamelCase,    __UpperCamelCase = True     ):
    if _check_not_integer(__UpperCamelCase     ):
        if return_map:
            return map(__UpperCamelCase,    zip(*__UpperCamelCase     )     )
        else:
            return list(map(__UpperCamelCase,    zip(*__UpperCamelCase     )     )     )
    raise TypeError("""Expected a matrix, got int/list instead"""     )



def      UpperCAmelCase_   (     __UpperCamelCase,    __UpperCamelCase,    __UpperCamelCase     ):
    SCREAMING_SNAKE_CASE__       =matrix[:row] + matrix[row + 1 :]
    return [row[:column] + row[column + 1 :] for row in minor]



def      UpperCAmelCase_   (     __UpperCamelCase     ):
    if len(__UpperCamelCase     ) == 1:
        return matrix[0][0]

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



def      UpperCAmelCase_   (     __UpperCamelCase     ):
    SCREAMING_SNAKE_CASE__       =determinant(__UpperCamelCase     )
    if det == 0:
        return None

    SCREAMING_SNAKE_CASE__       =[
        [determinant(minor(__UpperCamelCase,    __UpperCamelCase,    __UpperCamelCase     )     ) for j in range(len(__UpperCamelCase     )     )]
        for i in range(len(__UpperCamelCase     )     )
    ]

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



def      UpperCAmelCase_   (     __UpperCamelCase     ):
    return not isinstance(__UpperCamelCase,    __UpperCamelCase     ) and not isinstance(matrix[0],    __UpperCamelCase     )



def      UpperCAmelCase_   (     __UpperCamelCase     ):
    return len(__UpperCamelCase     ), len(matrix[0]     )



def      UpperCAmelCase_   (     __UpperCamelCase,    __UpperCamelCase     ):
    SCREAMING_SNAKE_CASE__       =_shape(__UpperCamelCase     ) + _shape(__UpperCamelCase     )
    if shape[0] != shape[3] or shape[1] != shape[2]:
        SCREAMING_SNAKE_CASE__       =(
            """operands could not be broadcast together with shape """
            f"""({shape[0], shape[1]}), ({shape[2], shape[3]})"""
        )
        raise ValueError(__UpperCamelCase     )
    return (shape[0], shape[2]), (shape[1], shape[3])



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


if __name__ == "__main__":
    import doctest

    doctest.testmod()
    main()












def      UpperCAmelCase_   (     __UpperCamelCase,    __UpperCamelCase     ):
    SCREAMING_SNAKE_CASE__       =len(__UpperCamelCase     )
    # Create a stack and push index of fist element to it
    SCREAMING_SNAKE_CASE__       =[]
    st.append(0     )

    # Span value of first element is always 1
    SCREAMING_SNAKE_CASE__       =1

    # Calculate span values for rest of the elements
    for i in range(1,    __UpperCamelCase     ):
        # Pop elements from stack while stack is not
        # empty and top of stack is smaller than price[i]
        while len(__UpperCamelCase     ) > 0 and price[st[0]] <= price[i]:
            st.pop()

        # If stack becomes empty, then price[i] is greater
        # than all elements on left of it, i.e. price[0],
        # price[1], ..price[i-1]. Else the price[i]  is
        # greater than elements after top of stack
        SCREAMING_SNAKE_CASE__       =i + 1 if len(__UpperCamelCase     ) <= 0 else (i - st[0])

        # Push this element to stack
        st.append(__UpperCamelCase     )



def      UpperCAmelCase_   (     __UpperCamelCase,    __UpperCamelCase     ):
    for i in range(0,    __UpperCamelCase     ):
        print(arr[i],    end=""" """     )


# Driver program to test above function
lowerCamelCase_  						=       [10, 4, 5, 90, 120, 80]
lowerCamelCase_  						=       [0 for i in range(len(price) + 1)]

# Fill the span values in array S[]
calculation_span(price, S)




print_array(S, len(price))






