# Permutation and inequality

Algebra Level 4

Let $$a_1 , a_2 , a_3, \ldots ,a_n$$ be positive real numbers. If $$b_1 , b_2 , b_3 \dots b_n$$ is a permutation of $$a_1 , a_2 , a_3 \dots a_n$$ then find the minimum value of the expression below:

$\large \displaystyle \sum_{r=1}^{1234567890} \dfrac{a_r}{b_r}$

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