
'''simple docstring'''

from __future__ import annotations

from collections.abc import Iterable, Iterator
from typing import Any, Generic, TypeVar

UpperCamelCase_            =    TypeVar("""T""", bound=bool)


class 					a_					(Generic[T]      ):




       def __init__(       self				,				snake_case_					):
         _lowerCAmelCase    :					T							=   value
         _lowerCAmelCase    :					SkewNode[T] | None							=   None
         _lowerCAmelCase    :					SkewNode[T] | None							=   None




       @property
       def 							__UpperCamelCase    (       self					):
         return self._value







       @staticmethod
       def 							__UpperCamelCase    (       snake_case_				,				snake_case_					):
         if not roota:
           return roota

         if not roota:
           return roota

         if roota.value > roota.value:
           _lowerCAmelCase			,   _lowerCAmelCase    :					int							=   roota, roota

         _lowerCAmelCase    :					str							=   roota
         _lowerCAmelCase    :					Any							=   roota.right
         _lowerCAmelCase    :					Union[str, Any]							=   roota.left
         _lowerCAmelCase    :					Optional[Any]							=   SkewNode.merge(snake_case_				,				snake_case_					)

         return result



class 					a_					(Generic[T]      ):




       def __init__(       self				,				snake_case_ = ()					):
         _lowerCAmelCase    :					SkewNode[T] | None							=   None
         if data:
           for item in data:
             self.insert(snake_case_					)




       def __bool__(       self					):
         return self._root is not None




       def __iter__(       self					):
         _lowerCAmelCase    :					list[Any]							=   []
         while self:
           result.append(self.pop()					)

         # Pushing items back to the heap not to clear it.
         for item in result:
           self.insert(snake_case_					)

         return iter(snake_case_					)




       def 							__UpperCamelCase    (       self				,				snake_case_					):
         _lowerCAmelCase    :					str							=   SkewNode.merge(self._root				,				SkewNode(snake_case_					)					)




       def 							__UpperCamelCase    (       self					):
         _lowerCAmelCase    :					Tuple							=   self.top()
         _lowerCAmelCase    :					int							=   (
             SkewNode.merge(self._root.left				,				self._root.right					) if self._root else None
         )

         return result




       def 							__UpperCamelCase    (       self					):
         if not self._root:
           raise IndexError("""Can't get top element for the empty heap."""					)
         return self._root.value







       def 							__UpperCamelCase    (       self					):
         _lowerCAmelCase    :					str							=   None


if __name__ == "__main__":
     import doctest

     doctest.testmod()




'''simple docstring'''

def 		_UpperCAmelCase			(					_lowerCamelCase  :    list[list[int]]					, _lowerCamelCase  :    list[list[int]]						)      ->  list[list[int]]:
  _lowerCAmelCase    :					int							=   []
  _lowerCAmelCase    :					Union[str, Any]							=   len(_lowerCamelCase						)
  for i in range(_lowerCamelCase						):
    _lowerCAmelCase    :					List[str]							=   []
    for j in range(_lowerCamelCase						):
      _lowerCAmelCase    :					Union[str, Any]							=   0
      for k in range(_lowerCamelCase						):
        _lowerCAmelCase    :					Any							=   val + matrix_a[i][k] * matrix_b[k][j]
      list_a.append(_lowerCamelCase						)
    matrix_c.append(_lowerCamelCase						)
  return matrix_c


def 		_UpperCAmelCase			(					_lowerCamelCase  :    int						)      ->  list[list[int]]:
  return [[int(row == column						) for column in range(_lowerCamelCase						)] for row in range(_lowerCamelCase						)]


def 		_UpperCAmelCase			(					_lowerCamelCase  :    int						)      ->  int:
  if n <= 1:
    return n
  _lowerCAmelCase    :					Tuple							=   identity(2						)
  _lowerCAmelCase    :					Union[str, Any]							=   [[1, 1], [1, 0]]
  _lowerCAmelCase    :					Optional[int]							=   n - 1
  while n > 0:
    if n % 2 == 1:
      _lowerCAmelCase    :					str							=   multiply(_lowerCamelCase					, _lowerCamelCase						)
    _lowerCAmelCase    :					Tuple							=   multiply(_lowerCamelCase					, _lowerCamelCase						)
    _lowerCAmelCase    :					Dict							=   int(n / 2						)
  return res_matrix[0][0]


def 		_UpperCAmelCase			(					_lowerCamelCase  :    int						)      ->  int:
  if n <= 1:
    return n
  _lowerCAmelCase    :					Any							=   0
  _lowerCAmelCase    :					Dict							=   1
  for _ in range(2					, n + 1						):
    _lowerCAmelCase			,   _lowerCAmelCase    :					int							=   fiba, fiba + fiba
  return fiba


def 		_UpperCAmelCase			(					)      ->  None:
  for ordinal in "0th 1st 2nd 3rd 10th 100th 1000th".split():
    _lowerCAmelCase    :					Union[str, Any]							=   int("""""".join(c for c in ordinal if c in """0123456789"""						)						)  # 1000th --> 1000
    print(
        f'{ordinal} fibonacci number using matrix exponentiation is '
        f'{nth_fibonacci_matrix(_lowerCamelCase						)} and using bruteforce is '
        f'{nth_fibonacci_bruteforce(_lowerCamelCase						)}\n'						)
  # from timeit import timeit
  # print(timeit("nth_fibonacci_matrix(1000000)",
  #              "from main import nth_fibonacci_matrix", number=5))
  # print(timeit("nth_fibonacci_bruteforce(1000000)",
  #              "from main import nth_fibonacci_bruteforce", number=5))
  # 2.3342058970001744
  # 57.256506615000035


if __name__ == "__main__":
     import doctest

     doctest.testmod()
     main()


