Word Folding

You will receive 5 points for solving this problem.

Manao has invented a new operation on strings that is called folding. Each fold happens between a pair of consecutive letters and places the second part of the string above first part, running in the opposite direction and aligned to the position of the fold. Using this operation, Manao converts the string into a structure that has one more level than there were fold operations performed. See the following examples for clarity.

We will denote the positions of folds with '|' characters. For example, the word "ABRACADABRA" written as "AB|RACA|DAB|RA" indicates that it has been folded three times: first, between the leftmost pair of 'B' and 'R' letters; second, between 'A' and 'D'; and third, between the rightmost pair of 'B' and 'R' letters. Here are several examples of folded strings:

"ABCDEF|GHIJK" |  "A|BCDEFGHIJK" |  "AB|RACA|DAB|RA" |  "X|XXXXX|X|X|XXXXXX"               |                 |                   |       XXXXXX    KJIHG      |   KJIHGFEDCB    |      AR           |       X   ABCDEF      |            A    |     DAB           |       X               |                 |     ACAR          |       XXXXX               |                 |       AB          |           X

One last example for "ABCD|EFGH|IJ|K":

 KIJHGFEABCD

Manao noticed that each folded string can be viewed as several piles of letters. For instance, in the previous example, there are four piles, which can be read as "AHI", "BGJK", "CF", and "DE" from bottom to top. Manao wonders what is the highest pile of identical letters he can build using fold operations on a given word. Note that the pile should not contain gaps and should start at the bottom level. For example, in the rightmost of the four examples above, none of the piles would be considered valid since each of them has gaps, starts above the bottom level, or both.

Input

The input will consist of one line containing a single string of n characters with 1 ≤ n ≤ 1000 and no spaces. All characters of the string will be uppercase letters.

This problem doesn't have subproblems. You will get 5 points for the correct submission.

Output

Print a single integer — the size of the largest pile composed of identical characters that can be seen in a valid result of folding operations on the given string.

Example

Input

ABRACADABRA

Output

3

Input

ABBBCBDB

Output

3

Input

AB

Output

1

Note

Consider the first example. Manao can create a pile of three 'A's using the folding "AB|RACAD|ABRA", which results in the following structure:

ABRADACAR   AB

In the second example, Manao can create a pile of three 'B's using the following folding: "AB|BB|CBDB".

CBDBBBAB

Another way for Manao to create a pile of three 'B's with "ABBBCBDB" is the following folding: "AB|B|BCBDB".

 BCBDB BAB

In the third example, there are no folds performed and the string is just written in one line.

题意：给一串字符，求经过若干次折叠后， 最多能有多少个相同字符在同一列。

思路：这题主要是题意的理解问题，由折叠可知下标之差为奇数的元素才有可能被排到一列，然后就是很简单的dp了。

#include <cstdio>#include <cstring>#include <algorithm>#include <iostream>#include <string>using namespace std;int dp[1005];string s;      //这里不知道为什么用char就TLE了int main(){    while(cin>>s)    {        int sum=0;        int len=s.size();        for(int i=0; i<len-1; i++)             //从前开始往后判断            for(int j=i+1; j<len; j+=2)      //下标之差为2            {                if(s[i]==s[j])                      //如果s[i]与s[j]相同就折叠                    dp[j]=dp[i]+1;                sum=max(sum, dp[j]);            }        printf("%d\n", sum+1);    }    return 0;}