

import sys





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

      snake_case__					=   snake_case__					=   snake_case__					=   0
      snake_case__					=   sys.maxsize

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

      return 0 if min_len == sys.maxsize else min_len









class     SCREAMING_SNAKE_CASE__     :





       '''simple docstring'''




       def __init__(						self       :						Tuple							)			->    None:
             # numbermap keys are the number and its values are lists of indexes sorted
             # in ascending order
             snake_case__					=   {}
             # indexmap keys are an index and it's values are the number at that index
             snake_case__					=   {}

       def UpperCAmelCase_						(						self       :						Optional[int]    ,		lowerCAmelCase__       :						list | str | range    ,		lowerCAmelCase__       :						int							)			->    list[int]:
             if isinstance(lowerCAmelCase__    ,		(range, str)							):
                   snake_case__					=   list(lowerCAmelCase__							)
             elif not isinstance(lowerCAmelCase__    ,		lowerCAmelCase__							):
                   raise TypeError(
                       """binary_search_delete() only accepts either a list, range or str"""							)

             snake_case__					=   0
             snake_case__					=   len(lowerCAmelCase__							) - 1

             while low <= high:
                   snake_case__					=   (low + high) // 2
                   if array[mid] == item:
                         array.pop(lowerCAmelCase__							)
                         return array
                   elif array[mid] < item:
                         snake_case__					=   mid + 1
                   else:
                         snake_case__					=   mid - 1
             raise ValueError(
                 """Either the item is not in the array or the array was unsorted"""							)

       def UpperCAmelCase_						(						self       :						Optional[Any]    ,		lowerCAmelCase__       :						list | str | range    ,		lowerCAmelCase__       :						int							)			->    list[int]:
             if isinstance(lowerCAmelCase__    ,		(range, str)							):
                   snake_case__					=   list(lowerCAmelCase__							)
             elif not isinstance(lowerCAmelCase__    ,		lowerCAmelCase__							):
                   raise TypeError(
                       """binary_search_insert() only accepts either a list, range or str"""							)

             snake_case__					=   0
             snake_case__					=   len(lowerCAmelCase__							) - 1

             while low <= high:
                   snake_case__					=   (low + high) // 2
                   if array[mid] == index:
                         # If the item already exists in the array,
                         # insert it after the existing item
                         array.insert(mid + 1    ,		lowerCAmelCase__							)
                         return array
                   elif array[mid] < index:
                         snake_case__					=   mid + 1
                   else:
                         snake_case__					=   mid - 1

        # If the item doesn't exist in the array, insert it at the appropriate position
             array.insert(lowerCAmelCase__    ,		lowerCAmelCase__							)
             return array

       def UpperCAmelCase_						(						self       :						str    ,		lowerCAmelCase__       :						int    ,		lowerCAmelCase__       :						int							)			->    None:
             # Remove previous index
             if index in self.indexmap:
                   snake_case__					=   self.indexmap[index]
                   if len(self.numbermap[n]							) == 1:
                         del self.numbermap[n]
                   else:
                         snake_case__					=   self.binary_search_delete(self.numbermap[n]    ,		lowerCAmelCase__							)

        # Set new index
             snake_case__					=   number

             # Number not seen before or empty so insert number value
             if number not in self.numbermap:
                   snake_case__					=   [index]

             # Here we need to perform a binary search insertion in order to insert
             # The item in the correct place
             else:
                   snake_case__					=   self.binary_search_insert(
                       self.numbermap[number]    ,		lowerCAmelCase__							)

       def UpperCAmelCase_						(						self       :						Any    ,		lowerCAmelCase__       :						int							)			->    int:
             return self.numbermap.get(lowerCAmelCase__    ,		[-1]							)[0]


if __name__ == "__main__":
       import doctest

       doctest.testmod()






