How can I use a string to be the end symbol in python?

How can I use a string to be the end symbol while I was prompting the user to input a specific integer '1' or specific string 'end' as the end symbol, just like the samples below? I now only can use '1' as the end symbol. I am a beginner, so please explain as simple as possible. Many thanks!

list = []
num = 0
stop = False

num = int(input('Enter a negative integer (1 or ‘end’ to end):'))
if num == 1:
    print('No input!')
else:
    list.append(num)
    print(list)
    while stop == False:
        num = int(input('Enter a negative integer (1 or ‘end’ to end):'))
        list.append(num)
        print(list)
        if num == 1:
            stop = True
            print('The smallest integer is', min(list))

sample1 output:

Enter a negative integer (1 or ‘end’ to end): -56

Enter a negative integer (1 or ‘end’ to end): -42

Enter a negative integer (1 or ‘end’ to end): -112

Enter a negative integer (1 or ‘end’ to end): -1

Enter a negative integer (1 or ‘end’ to end): -89

Enter a negative integer (1 or ‘end’ to end): -676

Enter a negative integer (1 or ‘end’ to end): -312

Enter a negative integer (1 or ‘end’ to end): 1

The smallest integer is -676

Sample2 output:

Enter a negative integer (1 or 'end' to end): -123

Enter a negative integer (1 or 'end' to end): -1

Enter a negative integer (1 or 'end' to end): -23

Enter a negative integer (1 or 'end' to end): -1144

Enter a negative integer (1 or 'end' to end): -222

Enter a negative integer (1 or 'end' to end): -23

Enter a negative integer (1 or 'end' to end): -33

Enter a negative integer (1 or 'end' to end): -33

Enter a negative integer (1 or 'end' to end): end

The smallest integer is -1144

Sample3 output:

Enter negative integers (1 to end): 1

No input!