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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kejriwal:
20150916 12:03:56
sweet easy dp !! :)


Liquid_Science:
20150913 21:16:41
This was in our term1 of algorithms course ,around 6 months back , Solved it at that time too :D 

elita lobo:
20150912 00:04:40
mayank, same here :P forgot to return dp[i][j] when it is not 1 and got so many tles. 

Surendra :
20150821 22:41:59
what's the ans for


anuveshkothari:
20150817 22:12:15
similar to TRT..


sarvagya:
20150816 19:16:52
0.01 with top down dp ! sweet :) 

kartikay singh:
20150813 11:58:33
EASY DP :)


Sarthak Taneja:
20150813 06:08:52
ac in 1 go :D.... 

Surendra :
20150810 21:14:03
give any other test cases please .. All the test cases shows correct output . but in it shows wrong output


anshal dwivedi:
20150807 18:21:26
AC in one go.. !..Nice DP for beginners like me..! 
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 