```html LINQ: Data stream analysis with grouping and sliding window filtering ```

C# Hard LINQ

Task «```html LINQ: Data stream analysis with grouping and sliding window filtering ```»

Write a C# program that reads a sequence of integers (at least 10). Using LINQ, perform an analysis: group the numbers by value, keeping only those groups where the number of elements is greater than 1. Then, for each such group, calculate the arithmetic mean of all elements that are in a sliding window of size 3 (i.e., for each triple of consecutive elements in the original sequence where at least one element belongs to the group). If the window contains at least one element of the group, add its average to the result. Output the average values sorted in descending order with an accuracy of two decimal places. If there are no suitable windows, output "No data".

Input Format

In the first line, an integer N (10 ≤ N ≤ 1000). Then N lines, each containing one integer.

Output Format

A string of numbers separated by a space, each with two decimal places, sorted in descending order. Or "No data".

Examples

Example 1

INPUT
12 1 2 2 3 4 4 5 6 6 7 8 8
OUTPUT
7.67 7.00 6.33 5.67 5.00 4.33 3.67 3.00 2.33 1.67

Example 2

INPUT
3 1 2 3
OUTPUT
No data
main.cs