There are
n boxes with colored balls on the table. Colors are numbered from
1 to
n.
i-th box contains
ai balls, all of which have color
i. You have to write a program that will divide all balls into sets such that:
- each ball belongs to exactly one of the sets,
- there are no empty sets,
- there is no set containing two (or more) balls of different colors (each set contains only balls of one color),
- there are no two sets such that the difference between their sizes is greater than 1.
Print the minimum possible number of sets.
Output
Print one integer number − the minimum possible number of sets.
Note
In the first example the balls can be divided into sets like that: one set with
4 balls of the first color, two sets with
3 and
4 balls, respectively, of the second color, and two sets with
4 balls of the third color.