Bessie and her friend Elsie are currently playing a simple card game where they take a deck of 2N2N cards, conveniently numbered 1…2N1…2N, and divide them into NN cards for Bessie and NN cards for Elsie. The two then play NN rounds, where in each round Bessie and Elsie both play a single card. Initially, the player who plays the highest card earns a point. However, at one point during the game, Bessie can decide to switch the rules so that for the rest of the game, the player who plays the lowest card wins a point. Bessie can choose not to use this option, leaving the entire game in "high card wins" mode, or she can even invoke the option right away, making the entire game follow the "low card wins" rule.
Given that Bessie can predict the order in which Elsie will play her cards, please determine the maximum number of points Bessie can win.
The first line of input contains the value of N (2≤N≤50,0002≤N≤50,000).
The next N lines contain the cards that Elsie will play in each of the successive rounds of the game. Note that it is easy to determine Bessie's cards from this information.
Output a single line giving the maximum number of points Bessie can score.