Score : 1500 points

Problem Statement

We have a sequence A of length N.

On this sequence, we can perform the following two kinds of operations:

  • Swap two adjacent elements.

  • Select one element, and increment it by 1.

We will repeatedly perform these operations so that A will be a non-decreasing sequence. Find the minimum required number of operations.

Constraints

  • 1 ≤ N ≤ 200000
  • 1 ≤ A_i ≤ 10^9
  • A_i is an integer.

Input

Input is given from Standard Input in the following format:

N
A_1
A_2
:
A_N

Output

Print the minimum number of operations required to turn A into a non-decreasing sequence.

Sample Input 1

5
4
1
8
8
7

Sample Output 1

2

We can turn A into a non-decreasing sequence in two operations:

  • Initially, A = \{4, 1, 8, 8, 7\}.
  • Swap the first two elements. Now, A = \{1, 4, 8, 8, 7\}.
  • Increment the last element by 1. Now, A = \{1, 4, 8, 8, 8\}.

Sample Input 2

20
8
2
9
7
4
6
7
9
7
4
7
4
4
3
6
2
3
4
4
9

Sample Output 2

62