can't find the mistake Itering through list of dates

I’m writing a program to find how many sundays on the first of a month there are between two dates.
I want to do it without using datatime.
The thing is, I obtain 173 when the expected answer is 171.

#How many Sundays fell on the first of the month during the twentieth century (1 Jan 1901 to 31 Dec 2000)?
days_of_week = ['Monday', 'Tuesday', 'Wednesday', 'Thursday', 'Friday', 'Saturday', 'Sunday']

dict_months = {"January": 31, "February": 28, "March": 31, "April": 30, "May": 31, "June": 30, "July": 31, "August": 31, "September": 30, "October": 31, "November": 30, "December": 31}

count = 0
weekday_index = -1

for year in range(1900,2001):    
    for month in dict_months:
        #handling february
        if month == "February":
            #handling gap year
            if year % 4 == 0:
                #if year is a century it is not a leap year unless it is also a multiple of 400
                if year % 100 == 0 and year % 400 != 0:
                    dict_months[month] = 28
                else:
                    dict_months["February"] = 29
            else:
                dict_months["February"] = 28
        for day in range(1, dict_months[month]+1):
            weekday_index += 1
            weekday = days_of_week[weekday_index]
            #handling sundays
            if weekday == 'Sunday':
                weekday_index = -1
                if day == 1:
                    # print(f"{month} {day} {year}")
                    count += 1

print(count)