Problem:
Score : 300 points

Problem Statement

Sitting in a station waiting room, Joisino is gazing at her train ticket.

The ticket is numbered with four digits A, B, C and D in this order, each between 0 and 9 (inclusive).

In the formula A op1 B op2 C op3 D = 7, replace each of the symbols op1, op2 and op3 with + or - so that the formula holds.

The given input guarantees that there is a solution. If there are multiple solutions, any of them will be accepted.

Constraints

0≤A,B,C,D≤9

All input values are integers.

It is guaranteed that there is a solution.

Input

Input is given from Standard Input in the following format:

ABCD

Output

Print the formula you made, including the part =7.

Use the signs + and -.

Do not print a space between a digit and a sign.

Sample Input 1

1222

Sample Output 1

1+2+2+2=7

This is the only valid solution.

Sample Input 2

0290

Sample Output 2

0-2+9+0=7

0 - 2 + 9 - 0 = 7 is also a valid solution.

Sample Input 3

3242

Sample Output 3

3+2+4-2=7

Solution in OCaml (4.02.3) (judge verdict: Wrong Answer)

open Batteries
(* bitの数字の2真数の時の右からn番目の数字が0か1か *)
let is_bit_one bit n = if bit land (1 lsl n) = 0 then false else true

let int_to_list bit n =
  let rec get i =
    match i with 
    | i when i = n -> []
    | _ -> if is_bit_one bit i then i :: get (i+1) else get (i+1)
  in get 0

(* 文字列をcharのlistにする *)
let explode s = List.init (String.length s) (String.get s)

let abcd = read_line () |> explode |> List.map Char.escaped |> List.map int_of_string

let rec eval nums ops =
  match nums with
  | [] -> 0
  | first :: rest -> 
    match ops with
    | [] -> first
    | f :: r -> if f = "+" then first + eval rest r else first - eval rest r

let rec get_eval_text nums ops =
  match nums with
  | [] -> ""
  | first :: rest -> 
    match ops with
    | [] -> string_of_int first
    | f :: r -> if f = "+" then string_of_int first ^ "+" ^ get_eval_text rest r else string_of_int first ^ "-" ^ get_eval_text rest r

let get_ops bit n =
  let rec get i =
    match i with 
    | i when i = n -> []
    | _ -> if is_bit_one bit i then "+" :: get (i+1) else "-" :: get (i+1)
  in get 0

let rec ans bit =
  match bit with
  | bit when bit >= 3 * 3 -> ""
  | _ -> if eval abcd (get_ops bit 3) = 7 then get_eval_text abcd (get_ops bit 3) else ans (bit+1)

let _ = print_endline @@ (ans 0) ^ "=7"