AT_abc474_f Increment All Divisors

You are given a length- $ N $ integer sequence $ A=(A_1,A_2,\dots,A_N) $ . You can perform the following operation on $ A $ any number of times. - Choose an integer $ i $ with $ 1 \leq i \leq N $ . For every integer $ j $ that is a positive divisor of $ i $ , add $ 1 $ to $ A_j $ . Determine whether it is possible to make all elements of $ A $ equal, and if it is possible, find the minimum number of operations required to do so.

The input is given from Standard Input in the following format: > $ N $ $ A_1 $ $ A_2 $ $ \ldots $ $ A_N $

If it is possible to make all elements of $ A $ equal, output, in one line, the minimum number of operations required to do so; otherwise, output $ -1 $ .

### Sample Explanation 1 If you choose $ i=3 $ for the first operation, you get $ A=(5,7,5) $ . If you choose $ i=3 $ for the second operation, you get $ A=(6,7,6) $ . If you choose $ i=3 $ for the third operation, you get $ A=(7,7,7) $ . It is impossible to make all elements of $ A $ equal with fewer than three operations, so the answer is $ 3 $ . ### Constraints - $ 1 \leq N \leq 2 \times 10^5 $ - $ 1 \leq A_i \leq 10^9 $ - All input values are integers.