Cool Numbers

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Consider a positive integer N. Denote its decimal digits by X1, X2,..., XK. N is called a Cool Number if you can select at most three (but at least one) of its digits such that the following number is divisible by N: (X1 + X2 + ... + XK – S)S where S is the sum of the selected digits. Let LC(N) be the largest Cool Number which is not greater than N, and UC(N) be the smallest Cool Number which

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