Bessie the cow is a huge fan of card games, which is quite surprising, given her lack of opposable thumbs. Unfortunately, none of the other cows in the herd are good opponents. They are so bad, in fact, that they always play in a completely predictable fashion! Nonetheless, it can still be a challenge for Bessie to figure out how to win.

Bessie and her friend Elsie are currently playing a simple card game where they take a deck of 2N cards, conveniently numbered 1 \ldots 2N, and divide them into N cards for Bessie and N cards for Elsie. The two then play N rounds, where in each round Bessie and Elsie both play a single card. In the first N/2 rounds, the player with the highest card earns a point, and in the last N/2 rounds, the rules switch and the player who plays the lowest card wins a point.

Given that Bessie can predict the order in which Elsie will play her cards, please determine the maximum number of points Bessie can win.

Problem credits: Brian Dean

#3941 upload 3 done 2 how_to_reg 2

High Card Low Card (Gold) timer 2s memory 512MB

#3941

High Card Low Card (Gold) 2s 512MB