Ryuju has developed his own video game. The game has N levels and each successfully completed level is worth a certain number of points, which add up to the player`s total score on an online rank list of all players. Ryuju has ordered his levels by difficulty from the easiest to the most difficult, but he has made a mistake and made some difficult levels worth less points than some of the easier ones.
To overcome this problem, Ryuju has decided to reduce the number of points for certain levels with the goal of making the point sequence strictly increasing (so in the end easier levels are worth less points than the difficult ones).
Help Ryuju fix his video game in such a way that the total number of points reduced is minimal.
Final points have to be positive. You can assume that a solution exists for each test case.