Rainfall Summary

Story

A weather station logs the rainfall (in millimetres) of every day of the season, in the order the readings arrived. Before the data goes into a dashboard, the analyst wants a one-glance summary.

Task

Read the readings and print four statistics, one per line, in this order:

1. mean: the sum divided by the count
2. median: the middle value of the sorted readings; for an even count, the average of the two middle values
3. mode: the most frequent value; if several values share the highest frequency, print the smallest of them
4. standard deviation: the population standard deviation, sqrt( Σ(x − mean)² / n ) (divide by n, not n − 1)

Input

• Line 1: n (1 ≤ n ≤ 5000)
• Line 2: n numbers, each with at most 2 decimal places and |x| ≤ 100000, in no particular order

Output

Four lines with the four numbers. Print at least 4 decimals; any answer within 0.0001 of the exact value is accepted.

Example

8
2 4 4 4 5 5 7 9

Output:

5
4.5
4
2

(The mean is 40 / 8 = 5, the two middle values 4 and 5 give 4.5, the value 4 appears three times, and the squared distances from 5 add up to 32, so σ = √(32 / 8) = 2.)

8
2 4 4 4 5 5 7 9