Let Xi, Yi be integers, i = 1, 2, ..., n, and
 0 <= Xi <= Yi, 0 < Yi;
 Let X1 + X2 + ... Xn = SX, Y1 + Y2 + ... + Yn = SY;
 Let Pi = Xi / Yi

 Then

 What is the maximum value of

 P1 * log(1 / P1) + P2 * log(1 / P2) + ... + Pn * log(1 / Pn).

 Note: I've tested with some data, the maximum value is not n * (SX /
SY) * log(SY / SX).

 Thanks a lot.



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