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Problem 1546 Best Cow Line

Accept: 110    Submit: 573
Time Limit: 1000 mSec    Memory Limit : 32768 KB

Problem Description

FJ is about to take his N (1 <= N <= 2,000) cows to the annual "Farmer of the Year" competition. In this contest every farmer arranges his cows in a line and herds them past the judges.

The contest organizers adopted a new registration scheme this year: simply register the initial letter of every cow in the order they will appear (i.e., If FJ takes Bessie, Sylvia, and Dora in that order he just registers BSD). After the registration phase ends, every group is judged in increasing lexicographic order according to the string of the initials of the cows' names.

FJ is very busy this year and has to hurry back to his farm, so he wants to be judged as early as possible. He decides to rearrange his cows, who have already lined up, before registering them.

FJ marks a location for a new line of the competing cows. He then proceeds to marshal the cows from the old line to the new one by repeatedly sending either the first or last cow in the (remainder of the) original line to the end of the new line. When he's finished,FJ takes his cows for registration in this new order.

Given the initial order of his cows, determine the least lexicographic string of initials he can make this way.

Input

The input will consist of several datasets.
Each dataset contains two parts:
  *Line 1: A single integer: N.
  *Lines 2..N+1: Line i+1 contains a single initial ('A'..'Z') of the cow in the ith position in the original line

Output

For each dataset,you should output the least lexicographic string he can make. Every line (except perhaps the last one) contains the initials of 80 cows ('A'..'Z') in the new line.

Sample Input

6 A C D B C B

Sample Output

ABCBCD

Hint

Input Details:
FJ has 6 cows in this order: ACDBCB
Output Details:
 Step   Original     New
   #1     ACDBCB
   #2      CDBCB     A
   #3      CDBC      AB
   #4      CDB       ABC
   #5      CD        ABCB
   #6       D        ABCBC
   #7                ABCBCD

Source

USACO 2007 November

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