datatype rope = 
  N0 of string
  | N1 of rope
  | N2 of rope * int * int * rope
  | L2 of string * string
  | N3 of rope * rope * rope

val target_length = 1024
val empty = N0 ""
fun of_string string = N0 string

fun size rope = 
   case rope of
   N0 s => String.size s
   | N1 t => size t
   | N2(_, lm, rm, _) => lm + rm
   | N3(t1, t2, t3) => 
      let
        val t1_size = size t1
        val t2_size = size t2
        val t3_size = size t3
      in
        t1_size + t2_size + t3_size
      end
    | _ => raise Empty

fun root rope =
  case rope of
  L2(s1, s2) => N2(N0 s1, String.size s1, String.size s2, N0 s2)
  | N3(t1, t2, t3) =>
    let
      val t1_size = size t1
      val t2_size = size t2
      val left = N2(t1, t1_size, t2_size, t2)
      val left_size = t1_size + t2_size
      val t3_size = size t3
    in
      N2(left, left_size, t3_size, N1 t3)
    end
    | t => t

fun n1 rope = 
  case rope of
    L2(s1, s2) => 
      N2(N0 s1, String.size s1, String.size s2, N0 s2)
  | N3(t1, t2, t3) =>
      let
        val t1_size = size t1
        val t2_size = size t2
        val left = N2(t1, t1_size, t2_size, t2)
        val left_size = t1_size + t2_size
        val t3_size = size t3
      in
        N2(left, left_size, t3_size, t3)
      end
  | t => N1 t

fun ins_n2_left left right = 
  case (left, right) of
    (L2(s1, s2), t3) => N3(N0 s1, N0 s2, t3)
  | (N3(t1, t2, t3), N1 t4) =>
      let
        val t1_size = size t1
        val t2_size = size t2 
        val left = N2(t1, t1_size, t2_size, t2)
        val left_size = t1_size + t2_size
        val t3_size = size t3
        val t4_size = size t4
        val right = N2(t3, t3_size, t4_size, t4)
        val right_size = t3_size + t4_size
      in
        N2(left, left_size, right_size, right)
      end
  | (N3(t1, t2, t3), t4 as N2 _) =>
      let
        val left = N2(t1, size t1, size t2, t2)
      in
        N3(left, N1 t3, t4)
      end
  | (N3(t1, t2, t3), t4) =>
      let
        val t1_size = size t1
        val t2_size = size t2
        val left = N2(t1, t1_size, t2_size, t2)
        val t3_size = size t3
        val t4_size = size t4
        val right = N2(t3, t3_size, t4_size, t4)
        val left_size = t1_size + t2_size
        val right_size = t3_size + t4_size
      in
        N2(left, left_size, right_size, right)
      end
  | (l, r) =>
      N2(l, size l, size r, r)

fun ins_n2_right left right =
  case (left, right) of
    (t1, L2(s1, s2)) => N3(t1, N0 s1, N0 s2)
  | (N1 t1, N3(t2, t3, t4)) =>
      let
        val t1_size = size t1
        val t2_size = size t2
        val left = N2(t1, t1_size, t2_size, t2)
        val t3_size = size t3
        val t4_size = size t4
        val right = N2(t3, t3_size, t4_size, t4)
        val right_size = t3_size + t4_size
        val left_size = t1_size + t2_size
      in
        N2(left, left_size, right_size, right)
      end
  | (t1 as N2 _, N3(t2, t3, t4)) =>
      let
        val right = N2(t3, size t3, size t4, t4)
      in
        N3(t1, N1 t2, right)
      end
  | (l, r) =>
      N2(l, size l, size r, r)

fun ins cur_index string rope =
  case rope of
    N0 str =>
      let
        val old_str_size = String.size str 
        val ins_str_size = String.size string
        val total_str_size = old_str_size + ins_str_size
        val left_size = ins_str_size + cur_index
        val prefer_left = left_size <= target_length
        val right_size = ins_str_size - cur_index
        val prefer_right = right_size <= target_length
      in
        if cur_index <= 0 then
            if total_str_size <= target_length then
              N0(string ^ str)
            else L2(string, str)
        else if cur_index >= old_str_size then
            if total_str_size <= target_length then
              N0(str ^ string)
            else L2(str, string)
        else if total_str_size <= target_length then
            let
              val str1 = String.substring(str, 0, cur_index)
              val str3 = String.substring(str, cur_index, old_str_size - cur_index)
            in
              N0(String.concat [str1, string, str3])
            end
        else 
            let
              val str1 = String.substring(str, 0, cur_index)
              val str3 = String.substring(str, cur_index, old_str_size - cur_index)
            in
              if prefer_left then
                L2(str1 ^ string, str3)
              else if prefer_right then
                L2(str1, string ^ str3)
              else
                N3(N0 str1, N0 string, N0 str3)
            end
      end
    | N1 t =>
        let
          val t = ins cur_index string t
        in
          n1 t
        end
    | N2(l, lm, _, r) =>
        if cur_index < lm then
          let
            val l = ins cur_index string l
          in
            ins_n2_left l r
          end
        else
          let 
            val next_index = cur_index - lm
            val r = ins next_index string r
          in
            ins_n2_right l r
          end
    | _ => raise Empty