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

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".

分析：贪心，在选取当前字符后最多隔m个取一个最小的（坐标尽量靠后）；

　　　这样选完后扫一遍字符串，那些没有被选取且不是当前答案里最大的字符也能加入答案；

　　　最后排序即可；

代码：

#include <iostream>

#include <cstdio>

#include <cstdlib>

#include <cmath>

#include <algorithm>

#include <climits>

#include <cstring>

#include <string>

#include <set>

#include <map>

#include <queue>

#include <stack>

#include <vector>

#include <list>

#define rep(i,m,n) for(i=m;i<=n;i++)

#define rsp(it,s) for(set<int>::iterator it=s.begin();it!=s.end();it++)

#define mod 1000000007

#define inf 0x3f3f3f3f

#define vi vector<int>

#define pb push_back

#define mp make_pair

#define fi first

#define se second

#define ll long long

#define pi acos(-1.0)

#define pii pair<int,int>

#define Lson L, mid, ls[rt]

#define Rson mid+1, R, rs[rt]

const int maxn=2e5+;

using namespace std;

ll gcd(ll p,ll q){return q==?p:gcd(q,p%q);}

ll qpow(ll p,ll q){ll f=;while(q){if(q&)f=f*p;p=p*p;q>>=;}return f;}

inline ll read()

{

    ll x=;int f=;char ch=getchar();

    while(ch<''||ch>''){if(ch=='-')f=-;ch=getchar();}

    while(ch>=''&&ch<=''){x=x*+ch-'';ch=getchar();}

    return x*f;

}

int n,m,k,t,vis[maxn];

struct node

{

    char x;

    int pos;

    node(char _x,int _pos):x(_x),pos(_pos){}

    bool operator<(const node&p)const

    {

        return x==p.x?pos>p.pos:x<p.x;

    }

};

char a[maxn],ma;

string ans;

set<node>pq;

int main()

{

    int i,j;

    scanf("%d%s",&n,a);

    int len=strlen(a),pre=;

    for(i=;i<n;i++)pq.insert(node(a[i],i));

    i=n;

    while()

    {

        node now=*pq.begin();

        ans+=now.x;

        ma=max(ma,now.x);

        vis[now.pos]=;

        for(j=pre;j<=now.pos;j++)pq.erase(node(a[j],j));

        pre=now.pos+;

        int cnt=;

        for(j=i;j<len&&j-now.pos<=n;j++)

        {

            i=j;

            cnt=j-now.pos;

            pq.insert(node(a[j],j));

        }

        i++;

        if(cnt<n)break;

    }

    for(i=;a[i];i++)if(!vis[i]&&a[i]<ma)ans+=a[i];

    sort(ans.begin(),ans.end());

    cout<<ans<<endl;

    //system("Pause");

    return ;

}

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Dense Subsequence

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