You're the railways minister of a state. You intend to connect the four major cities in the state, located at four corners of a square with side length 100 miles. You're on tight budget. What's the shortest length, in miles, of railway tracks do you need so that all cities are connected? (Round your answer to the nearest integer)
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PS: There's an elegant solution to this problem from physics: https://youtu.be/dAyDi1aa40E