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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crypt:
20130127 09:21:53
in case of P2's move, i.e, When employing the greedy strategy if there is a tie, remove the left end, why ??


Lai Manh Tuan:
20130121 16:40:37
interesting problem


sagar gandhi:
20120915 19:46:29
what will be the O/P for


npsabari:
20120613 18:18:11
Plain DP!


The Champ:
20101224 19:45:15
very nice problem. enjoyed solving it :) 

numerix:
20101004 13:10:35
You can disqualify it yourself. 

Daniel Ampuero:
20101004 05:21:18
Disqualify my solution in TEXT, I pasted the official output for checking if it was the same you used. 

amit kumar:
20100923 11:01:45
sry got it 

amit kumar:
20100923 11:00:09
why do the test cases have odd numbers of cards?


Sib:
20100718 13:33:08
why do the test cases have odd numbers of cards?

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 