A *palindrome* is a string that reads the same from left to right as it does from right to left.

Given a string, , of lowercase English letters, we define a *-length rotation* as cutting the first characters from the beginning of and appending them to the end of . For each , there are possible -length rotations (where ). See the *Explanation* section for examples.

Given and , find all -length rotations of ; for each rotated string, , print the maximum possible length of any palindromic substring of on a new line.

**Input Format**

The first line contains an integer, (the length of ).

The second line contains a single string, .

**Constraints**

**Output Format**

There should be lines of output, where each line contains an integer denoting the maximum length of any palindromic substring of rotation .

**Sample Input 0**

```
13
aaaaabbbbaaaa
```

**Sample Output 0**

```
12
12
10
8
8
9
11
13
11
9
8
8
10
```

**Sample Input 1**

```
7
cacbbba
```

**Sample Output 1**

```
3
3
3
3
3
3
3
```

**Sample Input 2**

```
12
eededdeedede
```

**Sample Output 2**

```
5
7
7
7
7
9
9
9
9
7
5
4
```

**Explanation**

Consider *Sample Case 1*, where .

The possible rotations, , for string are:

.

The longest palindromic substrings for each are:

and , so we print their length () on a new line.

, so we print its length () on a new line.

and , so we print their length () on a new line.

and , so we print their length () on a new line.

and , so we print their length () on a new line.

and , so we print their length () on a new line.

and , so we print their length () on a new line.