D. Armchairstime limit per test2 secondsmemory limit per test512 megabytesinputstandard inputoutputstandard outputThere are n armchairs, numbered from 1 to n from left to right. Some armchairs are occupied by people (at most one person per armchair), others are not. The number of occupied armchairs is not greater than \frac{n}{2}.For some reason, you would like to tell people to move from their armchairs to some other ones. If the i-th armchair is occupied by someone and the j-th armchair is not, you can tell the person sitting in the i-th armchair to move to the j-th armchair. The time it takes a person to move from the i-th armchair to the j-th one is |i - j| minutes. You may perform this operation any number of times, but these operations must be done sequentially, i. e. you cannot tell a person to move until the person you asked to move in the last operation has finished moving to their destination armchair.You want to achieve the following situation: every seat that was initially occupied must be free. What is the minimum time you need to do it?InputThe first line contains one integer n (2 \le n \le 5000) — the number of armchairs.The second line contains n integers a_1, a_2, \dots, a_n (0 \le a_i \le 1). a_i = 1 means that the i-th armchair is initially occupied, a_i = 0 means that it is initially free. The number of occupied armchairs is at most \frac{n}{2}.OutputPrint one integer — the minimum number of minutes you have to spend to achieve the following situation: every seat that was initially occupied must be free.ExamplesInput
7
1 0 0 1 0 0 1
Output
3
Input
6
1 1 1 0 0 0
Output
9
Input
5
0 0 0 0 0
Output
0
NoteIn the first test, you can perform the following sequence:  ask a person to move from armchair 1 to armchair 2, it takes 1 minute;  ask a person to move from armchair 7 to armchair 6, it takes 1 minute;  ask a person to move from armchair 4 to armchair 5, it takes 1 minute. In the second test, you can perform the following sequence:  ask a person to move from armchair 1 to armchair 4, it takes 3 minutes;  ask a person to move from armchair 2 to armchair 6, it takes 4 minutes;  ask a person to move from armchair 4 to armchair 5, it takes 1 minute;  ask a person to move from armchair 3 to armchair 4, it takes 1 minute. In the third test, no seat is occupied so your goal is achieved instantly.
7
1 0 0 1 0 0 1

3 
['dp', 'flows', 'graph matchings', 'greedy', '*1800']