Min Elevator Trips

You are at the bottom of the elevator shaft of a 100 story building.
You see 21 wires labelled 1 2 3 ... 21.
The wires go up to the 100th floor where the ends are labelled A B C ... U, but you don’t know how they correspond to the ends at the bottom.
You have a battery, a light bulb, and many small wires.
What is the minimum number of trips required to find out the pairing between the letters and the numbers?
Note that connecting the small wires to form a wire 21 floor long is not an option.

• Case 1 : Answer is a integer. Just put the number without any decimal places if its an integer. If the answer is Infinity, output Infinity.
• Case 2 : Floating point number. Round it off to 2 decimal places and output it as I.xx where I is the integer part of the answer, and xx are 2 decimal digits after rounding off.

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