TWENDS - Two Ends


In the two-player game “Two Ends”, an even number of cards is laid out in a row. On each card, face up, is written a positive integer. Players take turns removing a card from either end of the row and placing the card in their pile. The player whose cards add up to the highest number wins the game. Now one strategy is to simply pick the card at the end that is the largest — we’ll call this the greedy strategy. However, this is not always optimal, as the following example shows: (The first player would win if she would first pick the 3 instead of the 4.)

3 2 10 4

You are to determine exactly how bad the greedy strategy is for different games when the second player uses it but the first player is free to use any strategy she wishes.

Input

There will be multiple test cases. Each test case will be contained on one line. Each line will start with an even integer n followed by n positive integers. A value of n = 0 indicates end of input. You may assume that n is no more than 1000. Furthermore, you may assume that the sum of the numbers in the list does not exceed 1,000,000.

Output

For each test case you should print one line of output of the form:

In game m, the greedy strategy might lose by as many as p points.

where m is the number of the game (starting at game 1) and p is the maximum possible difference between the first player’s score and second player’s score when the second player uses the greedy strategy. When employing the greedy strategy, always take the larger end. If there is a tie, remove the left end.

Example

Input:
4 3 2 10 4
8 1 2 3 4 5 6 7 8
8 2 2 1 5 3 8 7 3
0

Output:
In game 1, the greedy strategy might lose by as many as 7 points.
In game 2, the greedy strategy might lose by as many as 4 points.
In game 3, the greedy strategy might lose by as many as 5 points.

hide comments
Hasil Sharma: 2014-11-30 11:51:27

Nice for gaining confidence in DP :D

Pritam Prakash: 2014-08-16 10:14:07

easy DP but good one for beginners.

Sachin Malhotra: 2014-08-06 20:12:36

:D

Julian Waldby: 2014-06-29 16:44:33

Got AC, my 250th.

HUNG-SI-QUAN: 2014-06-19 17:47:10

i got NZEC runtime error
what it means
any one help

Aman Verma: 2014-06-17 08:57:21

My first question DP :)

Divyank Duvedi: 2014-05-21 14:14:53

@Vijay Jain,@New_Bullet,@sagar gandhi
Read the problem statement carefully.
Your test case is an invalid test case as the problem clearly states that you can have only even number of cards....so test case 5 1 2 1 2 1 is AN INVALID TEST CASE
however if it is 6 5 1 2 1 2 1 then its answer is 6

paras meena: 2014-05-20 20:58:48

maja aa gaya.. :D

Sanjeev Kumar: 2014-05-15 16:39:55

Easy DP!!!

Pratik kumar: 2014-04-23 13:09:57

The period '.' at the end is necessary.


Added by:Camilo Andrés Varela León
Date:2007-07-26
Time limit:0.100s
Source limit:50000B
Memory limit:1536MB
Cluster: Cube (Intel G860)
Languages:All except: ERL JS-RHINO NODEJS PERL6 VB.NET
Resource:East Central North America 2005