CF1525D.Armchairs

There 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?

有 $n$ 张扶手椅，从左到右依次编号为 $1$ 到 $n$。其中一些扶手椅上坐着人（每张椅子上至多坐一人），其余为空。初始时被占据的扶手椅数量不超过 $\frac{n}{2}$。

出于某种原因，你希望让人们从当前所坐的扶手椅移动到其他扶手椅上。若第 $i$ 张扶手椅上有人，而第 $j$ 张扶手椅为空，则你可以让坐在第 $i$ 张扶手椅上的人移动到第 $j$ 张扶手椅上。此人从第 $i$ 张扶手椅移动到第 $j$ 张扶手椅所需时间为 $|i - j|$ 分钟。你可以执行该操作任意多次，但这些操作必须顺序进行，即：在上一次操作中被要求移动的人尚未到达目标扶手椅之前，你不能发出下一次移动指令。

你的目标是达成如下状态：所有最初被占据的扶手椅最终都必须为空。实现该目标所需的最短总时间是多少？

The 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 $\frac{n}{2}$.

第一行包含一个整数 $n$（$2 \le n \le 5000$）—— 表示扶手椅的数量。

第二行包含 $n$ 个整数 $a_1, a_2, \dots, a_n$（$0 \le a_i \le 1$）。若 $a_i = 1$，表示第 $i$ 个扶手椅初始时被占用；若 $a_i = 0$，表示它初始时为空闲。被占用的扶手椅数量至多为 $\frac{n}{2}$。

Print 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.

输出一个整数——为达成以下情形所需的最少分钟数：所有最初被占用的座位都必须变为空闲。

In the first test, you can perform the following sequence:

1. ask a person to move from armchair $1$ to armchair $2$, it takes $1$ minute;
2. ask a person to move from armchair $7$ to armchair $6$, it takes $1$ minute;
3. 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:

1. ask a person to move from armchair $1$ to armchair $4$, it takes $3$ minutes;
2. ask a person to move from armchair $2$ to armchair $6$, it takes $4$ minutes;
3. ask a person to move from armchair $4$ to armchair $5$, it takes $1$ minute;
4. 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.

在第一次测试中，你可以执行以下操作序列：

1. 让一个人从扶手椅 $1$ 移动到扶手椅 $2$，耗时 $1$ 分钟；
2. 让一个人从扶手椅 $7$ 移动到扶手椅 $6$，耗时 $1$ 分钟；
3. 让一个人从扶手椅 $4$ 移动到扶手椅 $5$，耗时 $1$ 分钟。

在第二次测试中，你可以执行以下操作序列：

1. 让一个人从扶手椅 $1$ 移动到扶手椅 $4$，耗时 $3$ 分钟；
2. 让一个人从扶手椅 $2$ 移动到扶手椅 $6$，耗时 $4$ 分钟；
3. 让一个人从扶手椅 $4$ 移动到扶手椅 $5$，耗时 $1$ 分钟；
4. 让一个人从扶手椅 $3$ 移动到扶手椅 $4$，耗时 $1$ 分钟。

在第三次测试中，没有扶手椅被占用，因此你的目标立即达成。