Codeforces celebrates 10 years! We are pleased to announce the crowdfunding-campaign. Congratulate us by the link https://codeforces.com/10years.
×

Virtual contest is a way to take part in past contest, as close as possible to participation on time. It is supported only ICPC mode for virtual contests.
If you've seen these problems, a virtual contest is not for you - solve these problems in the archive.
If you just want to solve some problem from a contest, a virtual contest is not for you - solve this problem in the archive.
Never use someone else's code, read the tutorials or communicate with other person during a virtual contest.

No tag edit access

B1. Send Boxes to Alice (Easy Version)

time limit per test

1 secondmemory limit per test

256 megabytesinput

standard inputoutput

standard outputThis is the easier version of the problem. In this version, $$$1 \le n \le 10^5$$$ and $$$0 \le a_i \le 1$$$. You can hack this problem only if you solve and lock both problems.

Christmas is coming, and our protagonist, Bob, is preparing a spectacular present for his long-time best friend Alice. This year, he decides to prepare $$$n$$$ boxes of chocolate, numbered from $$$1$$$ to $$$n$$$. Initially, the $$$i$$$-th box contains $$$a_i$$$ chocolate pieces.

Since Bob is a typical nice guy, he will not send Alice $$$n$$$ empty boxes. In other words, at least one of $$$a_1, a_2, \ldots, a_n$$$ is positive. Since Alice dislikes coprime sets, she will be happy only if there exists some integer $$$k > 1$$$ such that the number of pieces in each box is divisible by $$$k$$$. Note that Alice won't mind if there exists some empty boxes.

Charlie, Alice's boyfriend, also is Bob's second best friend, so he decides to help Bob by rearranging the chocolate pieces. In one second, Charlie can pick up a piece in box $$$i$$$ and put it into either box $$$i-1$$$ or box $$$i+1$$$ (if such boxes exist). Of course, he wants to help his friend as quickly as possible. Therefore, he asks you to calculate the minimum number of seconds he would need to make Alice happy.

Input

The first line contains a single integer $$$n$$$ ($$$1 \le n \le 10^5$$$) — the number of chocolate boxes.

The second line contains $$$n$$$ integers $$$a_1, a_2, \ldots, a_n$$$ ($$$0 \le a_i \le 1$$$) — the number of chocolate pieces in the $$$i$$$-th box.

It is guaranteed that at least one of $$$a_1, a_2, \ldots, a_n$$$ is positive.

Output

If there is no way for Charlie to make Alice happy, print $$$-1$$$.

Otherwise, print a single integer $$$x$$$ — the minimum number of seconds for Charlie to help Bob make Alice happy.

Examples

Input

3 1 0 1

Output

2

Input

1 1

Output

-1

Codeforces (c) Copyright 2010-2020 Mike Mirzayanov

The only programming contests Web 2.0 platform

Server time: Feb/23/2020 02:30:46 (i2).

Desktop version, switch to mobile version.

Supported by

User lists

Name |
---|