You are given a multiset . Each element in the multiset is an integer between and (inclusive), where appears times in the multiset.

In each operation, you choose two different elements of the multiset, and , such that . Then, and will be deleted from the multiset, and will be added to the multiset twice.

Find the minimum number of operations such that every element of is equal to . The data guarantees that such a sequence of operations will exist.

#### Constraints

#### Input Specification

The first line contains an integer, .

The next line contains integers, .

#### Output Specification

Output the minimum number of operations to set all elements to modulo .

#### Sample Input

```
2
1 1 1 1 1
```

#### Sample Output

`5`

#### Explanation for Sample

Let's keep track of the elements in the multiset after each operation.

Initially, the multiset has the elements within it.

- Choose and
- Choose and
- Choose and
- Choose and
- Choose and

It can be proven that is the minimum number of operations required to set everything to .

## Comments