CodeForces 666A Reberland Linguistics（DP）

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本文探讨了Reberland语言中单词构造规则及其应用，特别关注于如何识别长度为2或3的可能后缀。通过实例解析，详细介绍了后缀的构造过程和识别方法。

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First-rate specialists graduate from Berland State Institute of Peace and Friendship. You are one of the most talented students in this university. The education is not easy because you need to have fundamental knowledge in different areas, which sometimes are not related to each other.

For example, you should know linguistics very well. You learn a structure of Reberland language as foreign language. In this language words are constructed according to the following rules. First you need to choose the "root" of the word — some string which has more than 4 letters. Then several strings with the length 2 or 3 symbols are appended to this word. The only restriction — it is not allowed to append the same string twice in a row. All these strings are considered to be suffixes of the word (this time we use word "suffix" to describe a morpheme but not the few last characters of the string as you may used to).

Here is one exercise that you have found in your task list. You are given the word s. Find all distinct strings with the length 2 or 3, which can be suffixes of this word according to the word constructing rules in Reberland language.

Two strings are considered distinct if they have different length or there is a position in which corresponding characters do not match.

Let's look at the example: the word abacabaca is given. This word can be obtained in the following ways: $\text{[math]}$ , where the root of the word is overlined, and suffixes are marked by "corners". Thus, the set of possible suffixes for this word is {aca, ba, ca}.

Input

The only line contains a string s (5 ≤ |s| ≤ 104) consisting of lowercase English letters.

Output

On the first line print integer k — a number of distinct possible suffixes. On the next k lines print suffixes.

Print suffixes in lexicographical (alphabetical) order.

Examples

input
abacabaca

output
3
aca
ba
ca

input
abaca

output

0




动态规划，一开始看错了题目，题目的意思是不能有连续相邻的两个后缀是相同的




#include <iostream>
#include <string.h>
#include <stdlib.h>
#include <math.h>
#include <algorithm>
#include <stdio.h>
#include <map>
#include <string>

using namespace std;
#define MAX 10000
struct Node
{
  string a;
}a[MAX*10];
int cmp(Node a,Node b)
{
    return a.a<b.a;
}
int dp[MAX+5];
string s;
map<string,int> m;
int main()
{
    cin>>s;
    int len=s.length();
    memset(dp,0,sizeof(dp));
    dp[len]=1;dp[len-1]=0;dp[len+1]=0;
    m.clear();
    int cnt=0;
    for(int i=len-2;i>=5;i--)
    {
        if(dp[i+2]!=0)
        {
           string  b=s.substr(i,2);
            if(dp[i+2]!=2||b!=s.substr(i+2,2))
            {
                if(!m.count(b))
                {
                     m[b]=1;
                     a[cnt++].a=b;
                }
                dp[i]+=2;
            }
        }
         if(dp[i+3]!=0)
        {
            string b=s.substr(i,3);
            if(dp[i+3]!=3||b!=s.substr(i+3,3))
            {
                if(!m.count(b))
                {
                     m[b]=1;
                     a[cnt++].a=b;
                }
                dp[i]+=3;
            }
        }
    }
    sort(a,a+cnt,cmp);
    printf("%d\n",cnt);
    for(int i=0;i<cnt;i++)
        cout<<a[i].a<<endl;
    return 0;

}