Problem:
Largest Square

Given a matrix (H × W) which contains only 1 and 0, find the area of the largest square matrix which only contains 0s.

Input

H W
c1,1 c1,2 ... c1,W
c2,1 c2,2 ... c2,W
:
cH,1 cH,2 ... cH,W

In the first line, two integers H and W separated by a space character are given. In the following H lines, ci,j, elements of the H × W matrix, are given.

Output

Print the area (the number of 0s) of the largest square.

Constraints

1 ≤ H, W ≤ 1,400

Sample Input

4 5
0 0 1 0 0
1 0 0 0 0
0 0 0 1 0
0 0 0 1 0

Sample Output

4

Solution in OCaml (judge verdict: Accepted)

let solve h w c =
  let v0 = Array.make w 0 in
  let v1 = Array.make w 0 in
  let r = ref 0 in
  for i = 0 to h - 1 do if c.(i).(0) = 0 then r := 1 done;
  for j = 0 to w - 1 do if c.(0).(j) = 0 then begin v0.(j) <- 1; r := 1 end done;
  for i = 1 to h - 1 do
    if c.(i).(0) = 0 then v1.(0) <- 1;
    for j = 1 to w - 1 do
      if c.(i).(j) = 1 then v1.(j) <- 0
      else begin
        let t = if v0.(j) < v1.(j-1) then v0.(j) else v1.(j-1) in
        v1.(j) <- if v0.(j-1) < t then v0.(j-1) + 1 else t + 1;
        r := if v1.(j) > !r then v1.(j) else !r;
      end
    done;
    Array.iteri (fun i e -> v0.(i) <- e) v1
  done;
  !r * !r

let split_on_char sep s =
  let open String in
  let r = ref [] in
  let j = ref (length s) in
  for i = length s - 1 downto 0 do
    if get s i = sep then begin
      r := sub s (i + 1) (!j - i - 1) :: !r;
      j := i
    end
  done;
  sub s 0 !j :: !r

let read () = List.map int_of_string (split_on_char ' ' (read_line ()))

let () =
  match read () with
  | [h; w] ->
    let c = Array.make_matrix h w 0 in
    for i = 0 to h - 1 do
      let rec doit j = function
        | [] -> ()
        | x::xs ->
          c.(i).(j) <- x;
          doit (j + 1) xs in
      doit 0 (read ())
    done;
    Printf.printf "%d\n" (solve h w c)
  | _ -> ()