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NSUBSTR - Substrings

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You are given a string S which consists of 250000 lowercase latin letters at most. We define F(x) as the maximal number of times that some string with length x appears in S. For example for string 'ababa' F(3) will be 2 because there is a string 'aba' that occurs twice. Your task is to output F(i) for every i so that 1<=i<=|S|.

Input

String S consists of at most 250000 lowercase latin letters.

Output

Output |S| lines. On the i-th line output F(i).

Example

Input:
ababa

Output:
3
2
2
1
1

思路：

　　先求出每个状态的endpos集合大小，用cnt记录，用cnt[s]去更新f[len[s]],再用f[i+1]去更新f[i].

 #include <bits/stdc++.h>

 using namespace std;

 char ss[];

 int ans,f[<<];

 struct SAM

 {

     static const int MAXN = <<;//大小为字符串长度两倍

     static const int LetterSize = ;

     int tot, last, ch[MAXN][LetterSize], fa[MAXN], len[MAXN];

     int sum[MAXN], tp[MAXN], cnt[MAXN]; //sum,tp用于拓扑排序，tp为排序后的数组

     void init( void)

     {

         last = tot = ;

         len[] = ;

         memset(ch,,sizeof ch);

         memset(fa,,sizeof fa);

         memset(cnt,,sizeof cnt);

     }

     void add( int x)

     {

         int p = last, np = last = ++tot;

         len[np] = len[p] + , cnt[last] = ;

         while( p && !ch[p][x]) ch[p][x] = np, p = fa[p];

         if( p == )

             fa[np] = ;

         else

         {

             int q = ch[p][x];

             if( len[q] == len[p] + )

                 fa[np] = q;

             else

             {

                 int nq = ++tot;

                 memcpy( ch[nq], ch[q], sizeof ch[q]);

                 len[nq] = len[p] + , fa[nq] = fa[q], fa[q] = fa[np] = nq;

                 while( p && ch[p][x] == q)  ch[p][x] = nq, p = fa[p];

             }

         }

     }

     void toposort( void)

     {

         for(int i = ; i <= len[last]; i++)   sum[i] = ;

         for(int i = ; i <= tot; i++)   sum[len[i]]++;

         for(int i = ; i <= len[last]; i++)   sum[i] += sum[i-];

         for(int i = ; i <= tot; i++)   tp[sum[len[i]]--] = i;

         for(int i = tot; i; i--)   cnt[fa[tp[i]]] += cnt[tp[i]];

     }

 } sam;

 int main(void)

 {

     //freopen("in.acm","r",stdin);

     sam.init();

     scanf("%s",ss);

     for(int i=,len=strlen(ss);i<len;i++)  sam.add(ss[i]-'a');

     sam.toposort();

     for(int i=;i<=sam.tot;i++)    f[sam.len[i]]=max(f[sam.len[i]],sam.cnt[i]);

     for(int i=sam.len[sam.last];i;i--) f[i]=max(f[i],f[i+]);

     for(int i=;i<=sam.len[sam.last];i++)   printf("%d\n",f[i]);

     return ;

 }

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spoj8222

NSUBSTR - Substrings

Input

Output

Example

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