2016.10.08--Intel Code Challenge Final Round--D. Dense Subsequence

time limit per test

2 seconds

memory limit per test

256 megabytes

input

standard input

output

standard output

You are given a string s, consisting of lowercase English letters, and the integer m.

One should choose some symbols from the given string so that any contiguous subsegment of length m has at least one selected symbol. Note that here we choose positions of symbols, not the symbols themselves.

Then one uses the chosen symbols to form a new string. All symbols from the chosen position should be used, but we are allowed to rearrange them in any order.

Formally, we choose a subsequence of indices 1 ≤ i₁ < i₂ < ... < i_t ≤ |s|. The selected sequence must meet the following condition: for every j such that 1 ≤ j ≤ |s| - m + 1, there must be at least one selected index that belongs to the segment [j,  j + m - 1], i.e. there should exist a k from 1 to t, such that j ≤ i_k ≤ j + m - 1.

Then we take any permutation p of the selected indices and form a new string s_ip1s_ip2... s_ipt.

Find the lexicographically smallest string, that can be obtained using this procedure.

Input

The first line of the input contains a single integer m (1 ≤ m ≤ 100 000).

The second line contains the string s consisting of lowercase English letters. It is guaranteed that this string is non-empty and its length doesn't exceed 100 000. It is also guaranteed that the number m doesn't exceed the length of the string s.

Output

Print the single line containing the lexicographically smallest string, that can be obtained using the procedure described above.

Examples

Input

3
cbabc

Output

a

Input

2
abcab

Output

aab

Input

3
bcabcbaccba

Output

aaabb

Note

In the first sample, one can choose the subsequence {3} and form a string "a".

In the second sample, one can choose the subsequence {1, 2, 4} (symbols on this positions are 'a', 'b' and 'a') and rearrange the chosen symbols to form a string "aab".

刚开始看题我认为是一道贪心题，可我想的简单的贪心无法证明是对的。直到看了某大神的代码。。。。。尼玛。。真是贪心。。。。下面是代码

#include <iostream>
#include <string>
#include <algorithm>
using namespace std;

int main()
{
	int n;
	cin >> n;
	string s;
	cin >> s;
	string news = "";
	int i = -1;
	int mx = -1;
	while (i + n < s.size())
	{
		int m = i + n;
		for (int j = m; j > i; j--)
			if (s[j] < s[m])
				m = j;
		i = m;
		news += s[i];
	}
	sort(news.begin(), news.end());

	string m = "";
	for (int i = news.size() - 1; news[i] == news[news.size() - 1]; i--)
		m += news[i];
	for (int i = 0; i < s.size(); i++)
		if (s[i] < m[0])
			m += s[i];
	sort(m.begin(), m.end());
	cout << m;
}