chartFix

As an economist, you are interested in Pingland PING to Pongland PONG currency chart. In a conference that will take place really soon, you want to show everyone that PING/PONG rate has been increasing lately. In order to do this you decided to remove from the chart some points so that the remaining points form a strictly increasing sequence. Find the smallest number of points you have to remove.

Example

• For chart = [3, 2, 6, 4, 5, 1, 7], the output should be
  chartFix(chart) = 3.
  
  After you remove points 2, 6, and 1 the remaining points will form a sequence [3, 4, 5, 7], which is strictly increasing. Check out the image below for better understanding:

Input/Output

• [execution time limit] 0.5 seconds

• [input] array.integer chart

  PING/PONG rates on the chart. In accordance with the current trade agreements, PING/PONG rate is always an integer value.

  Guaranteed constraints:
  3 ≤ chart.length ≤ 10000,
  0 ≤ chart[i] ≤ 2000.

• [output] integer

  • The number of points to be removed.