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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ram:
20150802 15:04:32
Easy DP!!


PRIBAN91:
20150722 06:26:54
Very nice problem! 

mayank:
20150630 13:56:15
Height of stupidity, thinking that I memoized, but did not, and then clueless about TLEs :P _ 

ASHU:
20150622 21:23:45
Is removing left end means


Nitesh Tiwari:
20150610 14:01:24
Isn't the result for the first test case should be 9, 16 (2316) =9 ,Hows's it 7.


:.Mohib.::
20150608 07:47:14
Learned a lot.... nice que!! 

Rushikesh Potdar:
20150530 16:42:58
is complexity is less than ( queries*O(N^2)) Last edit: 20150530 16:44:27 

forma:
20150414 05:22:44
Could anyone explain why in a case of tie we should always remove the left end ?


Aadil Ahmad:
20150407 14:31:20
"If there is a tie, remove the left end." :P :P Last edit: 20150407 14:31:40 

kunaal:
20150402 19:43:50
AC in one go!! :) 
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 