Extensions

Last school year Nodir participated in \(N\) olympiads and won one extension cord (power strip) in each of them. The \(i\)-th extension cord has \(a[i]\) sockets.

Nodir also has an unlimited number of phones. Charging each phone requires one socket, but Nodir's home has only a single power source (wall outlet).

Connect the extension cords to each other in such a way that the number of power sources is maximized and as many phones as possible can be charged.

Input

The first line contains the number \(N\) – the total number of extension cords.
The second line contains \(a[1], a[2], \dots, a[N]\) – the number of sockets on each extension cord.

Output

Print a single line – the maximum number of phones that can be charged.

Example

For example, let \(N = 3\) and \(a = [3, 3, 4]\).

If Nodir connects the extension cords in the order \([3, 4, 3]\), he can charge \(8\) phones.

3
3 3 4

8

Constraints

• \(1 \le N \le 10^5\)
• \(2 \le a[i] \le 100\), for all \(1 \le i \le N\)

Subtasks

1. (15 points) \(N = 1\)
2. (20 points) \(N \le 8\)
3. (20 points) \(a[1] = a[2] = \ldots = a[N]\).
4. (45 points) No additional constraints.