CF724D. Dense Subsequence[贪心 字典序！]

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 < ... < it ≤ |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 ≤ ik ≤ j + m - 1.

Then we take any permutation p of the selected indices and form a new string sip1sip2... sipt.

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".

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题意：至少每m个选一个字符使得选择的字符字典序最小的排列的字典序最小

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和那个经典问题很想，就是多了选择的字符可以任意排列

要深入理解字典序

考虑只选a，可行就只选a，否则就要选b，此时a一定全选(字典序最小)，b尽量少的选

枚举选到哪个字符就行了

PS：貌似可以二分，然而才26个字符并不需要

#include <iostream>
#include <cstdio>
#include <algorithm>
#include <cstring>
using namespace std;
const int N=1e5+5,INF=1e9+5;

int n,m,a[300];
char s[N];
bool sol(char c){
    int last=0,cnt=0,lc=0;
    for(int i=1;i<=n;i++){
        if(s[i]==c) lc=i;
        if(s[i]<c) last=i;
        if(i-last>=m){
            if(i-lc<m) last=lc,cnt++;
            else return false;
        }
    }
    
    for(int i=1;i<=n;i++) a[s[i]]++;
    for(char now='a';now<c;now++){
        while(a[now]--) putchar(now);
    }
    while(cnt--) putchar(c);
    return true;
}
int main(){
    scanf("%d%s",&m,s+1);
    n=strlen(s+1);
    for(char c='a';c<='z';c++) 
        if(sol(c)) break;
}