Ivan has n different boxes. The first of them contains some balls of n different colors.
Ivan wants to play a strange game. He wants to distribute the balls into boxes in such a way that for every i (1 ≤ i ≤ n) i-th box will contain all balls with color i.
In order to do this, Ivan will make some turns. Each turn he does the following:
The penalty of the turn is the number of balls Ivan takes from the box during the first step of the turn. And penalty of the game is the total penalty of turns made by Ivan until he distributes all balls to corresponding boxes.
Help Ivan to determine the minimum possible penalty of the game!
The first line contains one integer number n (1 ≤ n ≤ 200000) — the number of boxes and colors.
The second line contains n integer numbers a1, a2, ..., an (1 ≤ ai ≤ 109), where ai is the number of balls with color i.
Print one number — the minimum possible penalty of the game.
1 2 3
2 3 4 5
In the first example you take all the balls from the first box, choose k = 3 and sort all colors to corresponding boxes. Penalty is 6.
In the second example you make two turns:
Total penalty is 19.
AC Rate 31.82%
Date 03/04/2019 16:09:20