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 JavaScript (Node.js 12.16.1) (judge verdict: Wrong Answer)

//Don't have to see. start------------------------------------------
var read = require('readline').createInterface({
  input: process.stdin, output: process.stdout
});
var obj; var inLine = [];
read.on('line', function(input){inLine.push(input);});
read.on('close', function(){
  obj = init(inLine);
  console.error("\n");
  var start = Date.now();
  Main();
  var end = Date.now() - start;
  myerr("time : " + end + "ms");
  myerr("memory : " + Math.round(process.memoryUsage().heapTotal / 1024) + "KB");
});
function makeClone(obj){return JSON.parse(JSON.stringify(obj));}
function nextInt(){return myconv(next(),1);} function nextStrArray(){return myconv(next(),2);}
function nextIntArray(){return myconv(next(),4);} function nextCharArray(){return myconv(next(),6);}
function next(){return obj.next();} function hasNext(){return obj.hasNext();}
function init(input){  
  return {
    list : input, index : 0, max : input.length,
    hasNext : function(){return (this.index < this.max);},
    next : function(){if(this.hasNext()){return this.list[this.index++];}else{throw "ArrayIndexOutOfBoundsException ‚There is no more input";}}
  };
}
function myout(s){console.log(s);}
function myerr(s){console.error("debug:" + require("util").inspect(s,false,null));}
//param "no" is
//unknown or outlier : return i. 1: parseInt.
//2: split space. 4: split space and parseInt.
//6: split 1 character. 7: split 1 character and parseInt.
//8: join space. 9: join nextline. 0: join no character.
function myconv(i,no){try{switch(no){case 1:return parseInt(i);case 2:return i.split(" ");case 4:return i.split(" ").map(Number);case 6:return i.split("");case 7:return i.split("").map(Number);case 8:return i.join(" ");case 9:return i.join("\n");case 0:return i.join("");default:return i;}}catch(e){return i;}}

//Don't have to see. end------------------------------------------
function Main(){
  var one = nextIntArray();
  var N = one[0];
  var M = one[1];
  var list = new Array(M + 1);
  var unlockList = {};
  for(var i = 0; i < M; i++){
    var one = nextIntArray();
    var a = one[0];
    var b = one[1];
    var clist = nextIntArray();
    list[i + 1] = {
      cost : a,
      success : clist
    };
    for(var j = 0; j < b; j++){
      if(unlockList[clist[j]] == null){
        unlockList[clist[j]] = [];
      }
      unlockList[clist[j]].push(i + 1);
    }
  }
  //myerr(list);
  //myerr(unlockList);
  var output = 0;
  var used = new Set();
  for(var i = 1; i <= N; i++){
    if(!used.has(i)){
      var min = 100000000000;
      var index = -1;
      unlock = unlockList[i];
      if(unlock == null){
        myout(-1);
        return;
      }
      for(var j = 0; j < unlock.length; j++){
        if(min > list[unlock[j]].cost){
          min = list[unlock[j]].cost;
          index = unlock[j];
        }
      }
      output += min;
      for(var j = 0; j < list[index].success.length; j++){
        used.add(list[index].success[j]);
      }
    }
  }
  //myerr(used);
  myout(output);
}