skipping Byte Order mark (BOM) when using Stream CopyTo

I am trying to merge files into an output file and my individual files have the BOM on them, how can I get rid of it while using Stream.CopyTo method..

My code looks like this:

using (var output = File.Open(outputFile,FileMode.Append,FileAccess.Write))
       {
          foreach (var inputFile in inputFiles)
          {
            using (var input = File.OpenRead(inputFile))
            {
               input.CopyTo(output);
            }
          }
       }
 

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