Fishermen

There are $$$n$$$ fishermen who have just returned from a fishing trip. The $$$i$$$-th fisherman has caught a fish of size $$$a_i$$$.

The fishermen will choose some order in which they are going to tell the size of the fish they caught (the order is just a permutation of size $$$n$$$). However, they are not entirely honest, and they may "increase" the size of the fish they have caught.

Formally, suppose the chosen order of the fishermen is $$$[p_1, p_2, p_3, \dots, p_n]$$$. Let $$$b_i$$$ be the value which the $$$i$$$-th fisherman in the order will tell to the other fishermen. The values $$$b_i$$$ are chosen as follows:

• the first fisherman in the order just honestly tells the actual size of the fish he has caught, so $$$b_1 = a_{p_1}$$$;
• every other fisherman wants to tell a value that is strictly greater than the value told by the previous fisherman, and is divisible by the size of the fish that the fisherman has caught. So, for $$$i > 1$$$, $$$b_i$$$ is the smallest integer that is both strictly greater than $$$b_{i-1}$$$ and divisible by $$$a_{p_i}$$$.

For example, let $$$n = 7$$$, $$$a = [1, 8, 2, 3, 2, 2, 3]$$$. If the chosen order is $$$p = [1, 6, 7, 5, 3, 2, 4]$$$, then:

• $$$b_1 = a_{p_1} = 1$$$;
• $$$b_2$$$ is the smallest integer divisible by $$$2$$$ and greater than $$$1$$$, which is $$$2$$$;
• $$$b_3$$$ is the smallest integer divisible by $$$3$$$ and greater than $$$2$$$, which is $$$3$$$;
• $$$b_4$$$ is the smallest integer divisible by $$$2$$$ and greater than $$$3$$$, which is $$$4$$$;
• $$$b_5$$$ is the smallest integer divisible by $$$2$$$ and greater than $$$4$$$, which is $$$6$$$;
• $$$b_6$$$ is the smallest integer divisible by $$$8$$$ and greater than $$$6$$$, which is $$$8$$$;
• $$$b_7$$$ is the smallest integer divisible by $$$3$$$ and greater than $$$8$$$, which is $$$9$$$.

You have to choose the order of fishermen in a way that yields the minimum possible $$$\sum\limits_{i=1}^{n} b_i$$$.