How to get the computers' name in a workgroup

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C#

C#4.0

active-directory

Hi I need to get names of all the computers in a workgroup. Computers which are shut down must be omitted.
The following code gives the computers which are shut down in the immediate past, too.

using (DirectoryEntry workgroup = new DirectoryEntry("WinNT://Workgroup"))
                {
                   
                    foreach (DirectoryEntry childEntry in workgroup.Children)
                        currentSystems.Add(childEntry.Name);
                }

Please, help me to get all the computers in a workgroup , except the shut down ones.