int[] smoothed(int[] input)
{
   int[] output = new int[input.length];
   if (input.length == 0)
       return output;
   if (input.length == 1)
   {
       // we could just return input, but this maintains that a new array will be created with each function call
       output[0] = input[0];
       return output;
   }
   //handle the inside
   for (int i = 1; i < input.length - 1; ++i)
       output[i] = (input[i-1] + input[i] + input[i+1]) / 3;
   //handle the ends
   output[0] = (input[0] + input[1]) / 2;
   output[output.length-1] = (input[input.length-1] + input[input.length-2]) / 2;
   return output;
}