Creating a df based on total permutations deriving from user-input variables

I would like to pass 'n' amount of cities to travel to and corresponding days in each city to a function that would return a df with all possible permutations of the journey. The kayak_search_url column in the df should contain this string in the first row:

https://www.kayak.com/flights/AMS-WAW,nearby/2023-02-14/WAW-BOG,nearby/2023-02-17/BOG-MIL,nearby/2023-02-20/MIL-SDQ,nearby/2023-02-23/SDQ-AMS,nearby/2023-02-25/?sort=bestflight_a

...but instead contains this string:

https://www.kayak.com/flights/AMS-WAW,nearby/2023-02-14/AMS-BOG,nearby/2023-02-17/AMS-MIL,nearby/2023-02-20/AMS-SDQ,nearby/2023-02-23/AMS,nearby/2023-02-25/?sort=bestflight_a

I can't figure out why the origin code 'AMS' shows up instead of the chain of cities. Here's the code:

# List the cities you want to travel to and from, how long you'd like to stay in each, and the appropriate start/end dates
start_city = 'Amsterdam'
end_city = 'Amsterdam'
start_date = '2023-02-14'

cities = ['Warsaw', 'Bogota', 'Milan', 'Santo Domingo']
days = [3,3,3,2]

def generate_permutations(cities, days, start_city, end_city, start_date):
    city_to_days = dict(zip(cities, days))
    
    permutations = list(itertools.permutations(cities))
    df = pd.DataFrame(permutations, columns=['city' + str(i) for i in range(1, len(cities) + 1)])
    df['origin'] = start_city
    df['end'] = end_city
    first_column = df.pop('origin')
    df.insert(0, 'origin', first_column)
    
    st_dt = pd.to_datetime(start_date)
    df = df.assign(flight_dt_1=st_dt)
    
    for i in range(len(cities)):
        df['flight_dt_' + str(i + 2)] = df['flight_dt_' + str(i + 1)] + df['city' + str(i + 1)].map(city_to_days).map(lambda x: pd.Timedelta(days=x))
    
    # IATA city code dictionary from iata_code.csv file in repo and create Kayak 'url' column for each permutation
    iata = {'Amsterdam': 'AMS',
            'Warsaw': 'WAW',
            'Bogota': 'BOG',
            'Milan': 'MIL',
            'Santo Domingo': 'SDQ'}

    url = 'https://www.kayak.com/flights/'
    df['kayak_search_url'] = df.apply(lambda x: url + ''.join([iata[x['origin']] + '-' + iata[x['city' + str(i+1)]] + \
                                                               ',nearby/' + str(x['flight_dt_' + str(i+1)].strftime("%Y-%m-%d")) + '/' \
                                                               for i in range(len(cities))]) + iata[x['end']] + ',nearby/' + str(x['flight_dt_' + str(len(cities) + 1)].strftime("%Y-%m-%d")) + \
                                                               '/?sort=bestflight_a', axis=1)
    
    return df

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