# Implement these 4 utilities on iterables:
# - prefix and suffix list
# - prefix and suffix sum

from __future__ import annotations
import types
from typing import List, Generator

# Prefix / Postfix iterator
class Fix:

    def __init__( self, step: int, list_in: List[ int ] ) -> None:
        self.slice = 0
        self.step = step
        self.list = list_in
        self.lenlist = len( list_in )

    def __iter__( self ) -> Fix:
        return self

    def __next__( self ) -> List[ int ]:
        slice_ = self.slice
        self.slice += self.step
        if self.slice > 0:
            if slice_ > self.lenlist:
                raise StopIteration
            return self.list[ 0 : slice_ ]
        else:
            if slice_ < -self.lenlist:
                raise StopIteration
            return self.list[ self.lenlist + slice_ : self.lenlist ]

def prefixes_iter( list_in: List[ int ] ) -> Fix:
    return Fix( 1, list_in )

def prefixes_gen( list_in: List[ int ] ) \
        -> Generator[ List[ int ], None, None ]:
    for i in range( len( list_in ) + 1 ):
        yield list_in[ : i ]

def suffixes( list_in: List[ int ] ) -> Fix:
    return Fix( -1, list_in )

def prefix_sum( list_in: List[ int ] ) \
        -> Generator[ int, None, None ]:
    count = 0
    for item in list_in:
        count += item
        yield count

def suffix_sum( list_in: List[ int ] ) \
        -> Generator[ int, None, None ]:
    count = 0
    for item in reversed( list_in ):
        count += item
        yield count