Question 87
Two intelligent players play a game on a $1403 \times 1403$ grid consists of $1403^2$ unit squares, taking turns. On their turn, the first player chooses one of the unchosen cells and draws a unit line segment from the midpoint of its top side to the midpoint of its bottom side. In their turn, the second player chooses one of the free cells and draws a unit line segment from the midpoint of its right side to the midpoint of its left side. After $1403^2$ steps, the game ends. The first player scores points equal to the length of the longest *connected* vertical line segment they have formed. The second player also scores points equal to the length of the longest *connected* horizontal line segment they have formed. At the end of the game, the player with the higher score wins; if scores are equal, there would be a draw. What will be the outcome of the game? Justify your answer.