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
dwij28: 2016-04-25 10:31:39

Finally did it in O(2 * n) space. Key is that we while building dp matrix in lcs problem, we only need the current and previous rows .. :)

maxeinstle: 2016-02-10 17:16:11

Do space optimization in c++ if getting TLE

Rishi Vikram: 2016-01-31 22:45:58

O(3*n) memory acceptable.

minhthai: 2016-01-18 05:02:52

even O(n) space in java cannot pass :(

sneh sajal: 2015-12-18 23:36:49

try to optimize space in linear :)

janina: 2015-12-18 18:42:37

O(n^2) space O(n^2) time and scanf,printf will give you AC.

rakhejabhai: 2015-12-09 19:46:28

linear space is the key to AC

LEMONICE: 2015-10-23 07:00:25

I am not able to submit! It says Error,Wrong problem code!

Shubham Garg: 2015-10-03 07:52:48

Use faster method for string input. No space optimization is required.But space optimization does give lower time.

Last edit: 2015-10-03 08:07:29
ashish: 2015-09-25 20:27:54

no space optimisation is required.
use faster Input output method.


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