You are given n coins, at least one of which is bad. All the good coins weigh the same, and all the bad coins weigh the same. The bad coins are lighter than the good coins. Find the exact number of bad coins by making O(logn)^2 weighings on a balance. Each weighing tells you whether the total weight of the coins you put on the left side of the balance is smaller than, equal to, or larger than the total weight of the coins you put on the right side.
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