201293: [AtCoder]ARC129 D - -1+2-1

Memory Limit：1024 MB Time Limit：2 S
Judge Style：Text Compare Creator：
Submit：0 Solved：0

Description

Score : $600$ points

Problem Statement

Given is an integer sequence of length $N$: $A=(A_1,A_2,\cdots,A_N)$.

You can repeat the operation below any number of times.

  • Choose an integer $i$ ($1 \leq i \leq N$) and add $-1, 2, -1$ to $A_{i-1},A_i,A_{i+1}$, respectively. Here, $A_0$ stands for $A_N$, and $A_{N+1}$ stands for $A_1$.

Determine whether it is possible to make every element of $A$ $0$. If it is possible, find the minimum number of operations needed.

Constraints

  • $3 \leq N \leq 200000$
  • $-100 \leq A_i \leq 100$
  • All values in input are integers.

Input

Input is given from Standard Input in the following format:

$N$
$A_1$ $A_2$ $\cdots$ $A_N$

Output

If it is impossible to make every element of $A$ $0$, print -1. If it is possible to do so, print the minimum number of operations needed.

Sample Input 1

4
3 0 -1 -2

Sample Output 1

5

We can achieve the objective in five operations, as follows.

  • Do the operation with $i=2$. Now we have $A=(2,2,-2,-2)$.
  • Do the operation with $i=3$. Now we have $A=(2,1,0,-3)$.
  • Do the operation with $i=3$. Now we have $A=(2,0,2,-4)$.
  • Do the operation with $i=4$. Now we have $A=(1,0,1,-2)$.
  • Do the operation with $i=4$. Now we have $A=(0,0,0,0)$.

Sample Input 2

3
1 0 -2

Sample Output 2

-1

Sample Input 3

4
1 -1 1 -1

Sample Output 3

-1

Sample Input 4

10
-28 -3 90 -90 77 49 -31 48 -28 -84

Sample Output 4

962

Input

题意翻译

给定一个环$a_1,a_2,\dots,a_n(3\leq n\leq200000，-100\leq a_i\leq100)$，其中$a_n$的后一个数为$a_1$. 你可以执行任意次如下操作： 选择一个位置$i(1\leq i \leq n)$，将$a_i$加$2$，将与$a_i$在环上相邻的两个数减$1$. 你需要将$a$数组中所有元素变为$0$.求最少操作次数，如果无解输出`-1`.

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