Перекодировка ANSI в utf-8 - C#

using System;
using System.IO;
using System.Text;
 
class Program
{
    public static void Main(string[] args)
    {
        StreamReader reader = new StreamReader("E:\\Temp\\1.txt", Encoding.GetEncoding(1251));
        string str = reader.ReadToEnd();
        StreamWriter writer = new StreamWriter("E:\\Temp\\utf.txt", false,  Encoding.UTF8);
        writer.Write(str);
        reader.Dispose();
        writer.Dispose();
    }
}