An average salary is pulled around by one very large one. Compensation wants the median instead.

Input

Output

One row per dept, with the columns:

• dept
• headcount — every employee in the department, salary recorded or not
• median_salary — the exact median of the recorded salaries, rounded to 2 decimal places, or null if none were recorded

For an even number of recorded salaries the median is the mean of the two middle ones.

Example

15.0 is the answer even though nobody earns it.

Constraints

• Exact, not approximate. An approximate median returns a value somebody actually earns, which for an even-sized department is the lower of the two middle salaries and not the median.
• An employee with no salary recorded is still in the headcount.
• Row order is not graded. Column names and their order are.