Practice Coding with the exercise "Minimal number of swaps"

Statement

Goal

Given a list of 1 and 0, you must regroup all the 1 at the begin of the list in a minimum number of steps. A step is the interchange of two elements located at different positions.

The expected result is the minimum number of steps required to obtain a sorted list.

Input

Line 1: an integer N.
Line 2: a list of N numbers that can take the values 0 or 1.

Output

Line 1 : The minimum number of steps to regroup all the 1 at the beginning of the list.

Constraints

1 ≤ N < 500

Example

Input

5
1 0 1 0 1

Output

Solve it

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