Problem:
Score : 500 points

Problem Statement

We have N locked treasure boxes, numbered 1 to N.

A shop sells M keys. The i-th key is sold for a_i yen (the currency of Japan), and it can unlock b_i of the boxes: Box c_{i1}, c_{i2}, ..., c_{i{b_i}}. Each key purchased can be used any number of times.

Find the minimum cost required to unlock all the treasure boxes. If it is impossible to unlock all of them, print -1.

Constraints

All values in input are integers.

1 \leq N \leq 12

1 \leq M \leq 10^3

1 \leq a_i \leq 10^5

1 \leq b_i \leq N

1 \leq c_{i1} < c_{i2} < ... < c_{i{b_i}} \leq N

Input

Input is given from Standard Input in the following format:

N M
a_1 b_1
c_{11} c_{12} ... c_{1{b_1}}
:
a_M b_M
c_{M1} c_{M2} ... c_{M{b_M}}

Output

Print the minimum cost required to unlock all the treasure boxes.
If it is impossible to unlock all of them, print -1.

Sample Input 1

2 3
10 1
1
15 1
2
30 2
1 2

Sample Output 1

25

We can unlock all the boxes by purchasing the first and second keys, at the cost of 25 yen, which is the minimum cost required.

Sample Input 2

12 1
100000 1
2

Sample Output 2

-1

We cannot unlock all the boxes.

Sample Input 3

4 6
67786 3
1 3 4
3497 1
2
44908 3
2 3 4
2156 3
2 3 4
26230 1
2
86918 1
3

Sample Output 3

69942

Solution in OCaml (4.02.3) (judge verdict: Accepted)

let scan_int () = Scanf.scanf " %d" (fun x -> x)
let scan_array len read_func = Array.init len (fun _ -> read_func())
let print_int n = Printf.printf "%d\n" n

let rec calc_bit i n ret =
  if i = n then ret
  else
    let c = scan_int() in
    calc_bit (i+1) n (ret lor (1 lsl (c-1)))

let rec input i n arr =
  if i = n then arr
  else
    let a = scan_int() and b = scan_int() in
    let c = calc_bit 0 b 0 in
    let _ = arr.(i) <- (a, c) in
    input (i+1) n arr

let rec dp table i n m arr =
  if i = m then table.((1 lsl n) - 1)
  else
    let a, c = arr.(i) in
    let rec update_dp_table j n a c =
      if j = n then ()
      else
        let _ = table.(j lor c) <- min table.(j lor c) (table.(j) + a) in
        update_dp_table (j+1) n a c in
    let _ = update_dp_table 0 (1 lsl n) a c in
    dp table (i+1) n m arr


let max_cost = int_of_float 1e15

let () = 
  let n = scan_int() and m = scan_int() in
  let arr = Array.make m (0, 0) and dp_table = Array.make (1 lsl n) max_cost in
  let _ = dp_table.(0) <- 0 in
  let _ = input 0 m arr in
  let ret = dp dp_table 0 n m arr in
  if ret = max_cost then print_int (-1)
  else print_int ret