Given the following sum: \[ S = \sum_{i=1}^n a_i b_i \ \ \ where \ a_i \ ,\ b_i > 0 \] \( S \) is minimal when the two equences \([ a_1,a_2,\cdots,a_n] \) and \( [b_1,b_2,\cdots,b_n] \)

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