IOIPALIN - Palindrome 2000


A palindrome is a symmetrical string, that is, a string read identically from left to right as well as from right to left. You are to write a program which, given a string, determines the minimal number of characters to be inserted into the string in order to obtain a palindrome. As an example, by inserting 2 characters, the string "Ab3bd" can be transformed into a palindrome ("dAb3bAd" or "Adb3bdA"). However, inserting fewer than 2 characters does not produce a palindrome.

Input

The first line contains one integer: the length of the input string N, 3≤N≤5000. The second line contains one string with length N. The string is formed from uppercase letters from ‘A’ to ‘Z’, lowercase letters from ‘a’ to ‘z’ and digits from ‘0’ to ‘9’. Uppercase and lowercase letters are to be considered distinct.

Output

The first line contains one integer, which is the desired minimal number.

Example

Input:
5
Ab3bd

Output:
2

hide comments
the_root: 2018-12-03 20:40:49

pass in o(n^2)
hhhhhhhh but i have some WA because i forget start dp

elliot1: 2018-08-25 10:18:59

top down leads to TLE and bottom up works!! this is really weird -_-

one_piece_: 2018-07-10 05:22:27

@boris_dishov
min insertion required = n - (longest palindromic subsequence i.e. lcs of string 's' and reverse of string 's')
Here 'n' is length of string 's'

Last edit: 2018-07-10 05:22:55
tanmayak99: 2018-06-03 11:08:43

Similar to Aibohphobia problem

boris_dishov: 2018-05-23 01:24:37

Hello, I see in the comments (and in the description as well) the LCS. I solved this with something I don't concider LCS (and it was bottom - up), and I am interested to know how it works with LCS if someone can tell me :)

flyingduchman_: 2018-04-03 18:11:32

No Country For Java Man. Only 6 Java Soln passed :-D

pratyush_lzy: 2018-01-25 18:37:23

I don't know why using macros gives TLE :( Removed macros got AC :)

rohit9934: 2017-11-05 13:18:07


problema clásico de DP

shikhars387: 2017-10-11 19:09:24

Easy DP :)
Spoiler comments.

Last edit: 2017-10-11 19:10:05
raghav_chawla7: 2017-09-26 11:51:39

O(N*N) time and O(N*N) space accepted in 1 go


Added by:Gareev
Date:2010-08-16
Time limit:0.158s
Source limit:50000B
Memory limit:1536MB
Cluster: Cube (Intel G860)
Languages:All except: NODEJS OBJC PERL6 VB.NET
Resource:IOI 2000, Day 1