As the earth slows in rotation, we can add leap seconds more frequently until we are adding one to every minute: a minute becomes 61 seconds. (It will be very confusing before that, a complicated pattern of 60 and 61 second minutes, reminiscent of the number of days in a month or the number of months in a Jewish year.)
The day will have become 1440 seconds longer, or 24 (old style, 60-second) minutes.
After that, we can start adding 2 leap seconds to some minutes, so some minutes will be 62 seconds long. What remains constant is that there will always be 1440 minutes in a day.
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