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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saurabh_38:
20210126 14:28:17
good question


the_sage:
20201113 14:29:42
memoization using map will give TLE, use 2d array


kumar_anubhav:
20200814 05:08:33
is this problem require 2D dp or 1D ?? 

robosapien:
20200712 21:04:09
good dp :)


deerawat:
20200625 21:02:37
A nice DP question!! 

ujjwal_jain10:
20200623 13:22:51
A.C in 69th go.


harry_shit:
20200521 11:04:50
nice dp,try to keep simple as much as you can. Last edit: 20200521 13:21:39 

manish_thakur:
20200520 08:36:04
2 WAs coz didn't read the last line 

bhavesh007:
20200515 19:20:35
Last edit: 20200515 19:27:45 

abhishek_2002:
20200514 14:59:26
Read the last line carefully. :( 
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 