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A tower is composed of \(2014\) vertically stacked bricks. The first brick from the top to the bottom weighs \(1\) mg, the second brick weighs \(2^3\) mg, the third brick weighs \(3^3\) mg and so on.

A demolition company wants to collapse the tower by only removing one of its bricks, such that the brick's weight is the smallest possible. The tower is granted to collapse if the weight of the bricks above the removed one is greater than the weight of the ones below.

Which brick from the bottom to the top must the company remove?


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