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 Rust (1.42.0) (judge verdict: Accepted)

#[allow(unused_imports)]
use proconio::input;
#[allow(unused_imports)]
use proconio::marker::{Chars, Usize1};
#[allow(unused_imports)]
use std::cmp::{max, min};
#[allow(unused)]
const ALPHA_SMALL: [char; 26] = [
    'a', 'b', 'c', 'd', 'e', 'f', 'g', 'h', 'i', 'j', 'k', 'l', 'm', 'n', 'o', 'p', 'q', 'r', 's',
    't', 'u', 'v', 'w', 'x', 'y', 'z',
];
#[allow(unused)]
const ALPHA: [char; 26] = [
    'A', 'B', 'C', 'D', 'E', 'F', 'G', 'H', 'I', 'J', 'K', 'L', 'M', 'N', 'O', 'P', 'Q', 'R', 'S',
    'T', 'U', 'V', 'W', 'X', 'Y', 'Z',
];
#[allow(unused)]
fn read<T: std::str::FromStr>() -> T {
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).ok();
    s.trim().parse().ok().unwrap()
}
#[allow(unused)]
fn read_vec<T: std::str::FromStr>() -> Vec<T> {
    read::<String>()
        .split_whitespace()
        .map(|e| e.parse().ok().unwrap())
        .collect()
}
#[allow(unused)]
fn read_touple<T: std::str::FromStr + Copy>() -> (T, T) {
    let v: Vec<T> = read_vec();
    assert_eq!(v.len(), 2);
    (v[0], v[1])
}

const INF: usize = 1_000_000_000 + 1000;
fn main() {
    input!(N: usize, M: usize);
    let mut keys = vec![(0usize, 0usize); M];
    for _ in 0..M {
        input!(a: usize, b: usize);
        input!(c: [Usize1; b]);
        let t = c.into_iter().fold(0, |acc, x| acc | (1 << x));
        keys.push((t, a));
    }
    let mut dp = vec![INF; (1 << N)];
    let bits = BitSet::empty(N);

    // init
    dp[0] = 0;
    for set in bits {
        let s = set.unwrap();
        for &(now, a) in &keys {
            let t = s | now;
            let cost = dp[s] + a;
            dp[t] = min(dp[t], cost);
        }
    }

    let mut ans = dp[(1 << N) - 1] as i64;
    if ans == INF as i64 {
        ans = -1;
    }

    println!("{}", ans);
}

#[derive(Clone, Copy, Eq, PartialEq, Ord, PartialOrd)]
struct BitSet {
    bits: usize,
    size: usize,
}

impl std::fmt::Debug for BitSet {
    fn fmt(&self, f: &mut std::fmt::Formatter) -> std::fmt::Result {
        write!(f, "BitSet {{ bits: {:b}, size: {} }}", self.bits, self.size)
    }
}

impl BitSet {
    //
    fn empty(size: usize) -> BitSet {
        if size > 64 {
            panic!("large set size")
        }
        BitSet {
            bits: 0,
            size: size,
        }
    }
    // コンンストラクター
    fn new(n: usize, size: usize) -> BitSet {
        BitSet {
            bits: n,
            size: size,
        }
    }

    // 和集合を求める
    fn union(&self, other: BitSet) -> BitSet {
        BitSet {
            bits: self.bits | other.bits,
            size: self.size, // debug
        }
    }

    // 共通部分を求める
    fn intersect(&self, other: BitSet) -> BitSet {
        BitSet {
            bits: self.bits & other.bits,
            size: self.size, // debug
        }
    }

    // n を含むかどうか
    // n = 0, bits = 0b0001 => true
    // n = 1, bits = 0b0001 => false
    fn include(&self, n: usize) -> bool {
        if self.size < n {
            return false;
        }
        self.bits & (1 << n) != 0
    }

    // bitsをvectorに変換
    // 反転することに注意！
    // 0b0001 => vec![1, 0, 0, 0]
    // 0b1010 => vec![0, 1, 0, 1]
    fn to_vec(&self) -> std::vec::Vec<usize> {
        let mut res = std::vec::Vec::new();
        let mut bits = self.bits;

        for _ in 0..self.size {
            res.push(bits % 2);
            bits /= 2;
        }
        res
    }

    // 集合を表すusizeの値を返す
    fn unwrap(&self) -> usize {
        self.bits
    }
}

impl Iterator for BitSet {
    type Item = BitSet;

    fn next(&mut self) -> Option<Self::Item> {
        if (1 << self.size) <= self.bits {
            return None;
        }
        self.bits += 1;
        Some(BitSet {
            bits: self.bits - 1,
            size: self.size,
        })
    }
}