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 C (GCC 5.4.1) (judge verdict: Time Limit Exceeded)

#include <limits.h>
#include <stdbool.h>
#include <stdio.h>

#define N 12
#define M 1000

#define CS_OPEN 1
#define CS_CLOSE 0

static int n, m;
static int prices[M];
static unsigned short cs[M][N]; // what boxes a key can open. 1 means open, 0 means not.
static int keymap[N];
static char included_keys[M];

int solve(int key, int price, int key_num) {
    int price_1, price_2;

    bool all_opened = true;
    for (int i = 0; i < n; i++) {
        if (keymap[i] == 0) {
            all_opened = false;
            break;
        }
    }
    if (all_opened) {
        return price;
    }

    if (key_num >= n || key >= m) {
        return -1;
    }

    for (int i = 0; i < n; i++) {
        if (cs[key][i] == CS_OPEN) {
            keymap[i]++;
        }
    }
    price_1 = price + prices[key];
    price_1 = solve(key+1, price_1, key_num+1);

    for (int i = 0; i < n; i++) {
        if (cs[key][i] == CS_OPEN) {
            keymap[i]--;
        }
    }
    price_2 = price;
    price_2 = solve(key+1, price_2, key_num);

    if (price_1 < 0 && price_2 < 0) {
        return -1;
    } else if (price_1 < 0) {
        return price_2;
    } else if (price_2 < 0) {
        return price_1;
    } else {
        if (price_1 < price_2) {
            return price_1;
        } else {
            return price_2;
        }
    }
}

int main(void) {
    scanf("%d %d", &n, &m);

    // setup prices and cs
    for (int i = 0; i < m; i++) {
        int l;
        scanf("%d %d", &prices[i], &l);
        for (int j = 0; j < n; j++) {
            cs[i][j] = CS_CLOSE;
        }
        for (int j = 0; j < l; j++) {
            int x;
            scanf("%d", &x);
            cs[i][x-1] = CS_OPEN;
        }
    }

    // setup keymap and included_keys
    for (int i = 0; i < m; i++) {
        included_keys[i] = 0;
    }
    for (int i = 0; i < n; i++) {
        keymap[i] = 0;
    }

    printf("%d\n", solve(0, 0, 0));

    return 0;
}