Codeforces 803D Magazine Ad【二分+贪心】

D. Magazine Ad

time limit per test

1 second

memory limit per test

256 megabytes

input

standard input

output

standard output

The main city magazine offers its readers an opportunity to publish their ads. The format of the ad should be like this:

There are space-separated non-empty words of lowercase and uppercase Latin letters.

There are hyphen characters '-' in some words, their positions set word wrapping points. Word can include more than one hyphen.

It is guaranteed that there are no adjacent spaces and no adjacent hyphens. No hyphen is adjacent to space. There are no spaces and no hyphens before the first word and after the last word.

When the word is wrapped, the part of the word before hyphen and the hyphen itself stay on current line and the next part of the word is put on the next line. You can also put line break between two words, in that case the space stays on current line. Check notes for better understanding.

The ad can occupy no more that k lines and should have minimal width. The width of the ad is the maximal length of string (letters, spaces and hyphens are counted) in it.

You should write a program that will find minimal width of the ad.

Input

The first line contains number k (1 ≤ k ≤ 10⁵).

The second line contains the text of the ad — non-empty space-separated words of lowercase and uppercase Latin letters and hyphens. Total length of the ad don't exceed 10⁶ characters.

Output

Output minimal width of the ad.

Examples

Input

4
garage for sa-le

Output

7

Input

4
Edu-ca-tion-al Ro-unds are so fun

Output

10

Note

Here all spaces are replaced with dots.

In the first example one of possible results after all word wraps looks like this:

garage.
for.
sa-
le

The second example:

Edu-ca-
tion-al.
Ro-unds.
are.so.fun

题目大意：

给你一个字符串，其中两两单词之间用‘-’或者是空格分开，问你分组的最小长度，使得每个单词只能处于一个分组中并且分组数小于等于k.

思路：

很显然有单调性，如果长度len可以满足条件，那么长度len+1也一定满足条件，同理len+2更满足条件。

所以我们二分答案，然后贪心check一下即可。

尽可能将一个单词分到一组中。

注意一些细节，因为上界是1e6.而分组数最大可以到1e5.如果我们判定mid*kk和n的大小的时候，我们如果两个int相乘会爆int.

所以不妨将所有数据都设定为LL.稳妥更多。