#SDNU1723. Zero Sum Game
Zero Sum Game
Description
There are people labeled to , who have played several one-on-one games without draws. Initially, each person started with points. In each game, the winner's score increased by and the loser's score decreased by (scores can become negative). Determine the final score of person if the final score of person is . It can be shown that the final score of person is uniquely determined regardless of the sequence of games.
Constraints
All input values are integers.
Format
Input
The input is given from Standard Input in the following format:
...
Output
One integer, the answer
Samples
4
1 -2 -1
2
Here is one possible sequence of games where the final scores of persons 1,2,3 are 1,−2,−1, respectively.
Initially, persons 1,2,3,4 have 0,0,0,0 points, respectively. Persons 1 and 2 play, and person 1 wins. The players now have 1,−1,0,0 point(s).
Persons 1 and 4 play, and person 4 wins. The players now have 0,−1,0,1 point(s).
Persons 1 and 2 play, and person 1 wins. The players now have 1,−2,0,1 point(s).
Persons 2 and 3 play, and person 2 wins. The players now have 1,−1,−1,1 point(s).
Persons 2 and 4 play, and person 4 wins. The players now have 1,−2,−1,2 point(s).
In this case, the final score of person 4 is 2. Other possible sequences of games exist, but the score of person 4 will always be 2 regardless of the progression.
3
0 0
0
6
10 20 30 40 50
-150
Limitation
1s, 1024KiB for each test case.