TWENDS  Two Ends
In the twoplayer 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.
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Dhawal Harkawat:
20150327 05:57:37
For those getting WA, plz refer to Shashank Garg's HINT.. that may be the possible reason. 

Rishabh:
20150316 18:38:45
Which player would take 1st turn ? 

Lehar:
20150207 10:00:12
So happy to do this, without any help! :D 

Ashish Sareen:
20150205 18:54:38
DP Recursive with memoization and fast i/o worked without TLE!! surprised o.O 

Mahesh Mishra:
20150119 21:38:37
"If there is a tie, remove the left end." 

Shashank Garg:
20141230 13:05:22
Nice DP!


ALISHA:
20141229 19:35:04
Last edit: 20141229 19:51:09 

Hasil Sharma:
20141130 11:51:27
Nice for gaining confidence in DP :D 

Pritam Prakash:
20140816 10:14:07
easy DP but good one for beginners. 

Sachin Malhotra:
20140806 20:12:36
:D 
Added by:  Camilo Andrés Varela León 
Date:  20070726 
Time limit:  0.100s 
Source limit:  50000B 
Memory limit:  1536MB 
Cluster:  Cube (Intel G860) 
Languages:  All except: ERL JSRHINO NODEJS PERL6 VB.NET 
Resource:  East Central North America 2005 