Problem 3. (3 pts) 2n cards, each with different value vi, are placed in a row from left to right, and form the basis for a 2 player game. Each player, in her turn, picks of the two extreme cards (either the left-most card or the right-most card), removes it off the board and puts it to her pile. Once all cards have been collected, the score of each player is computed as the sum of all card-values in her pile. Here is an example of a play with 4 card: 1. Out of the two most extreme cards, Player one picks the -1 card. 2. Out of the two most extreme cards left (i.e. I and 2), Player two picks the 2 card. 3. Out of the two most extreme cards left (i.e. 1 and 5, Player one picks the 5 card. 4. As there is a single card left, Player two picks the 1 card and the game ends. Player one ends 5 2-1 with (-1) + 5-4 points, and Player two has 2+1 3 points. (i) (3 pts) Give a O(n2)-time algorithm that finds the max-score of each player and a strategy that obtains that score