Problem:
Score : 300 points

Problem

Takahashi, who is a novice in competitive programming, wants to learn M algorithms.
Initially, his understanding level of each of the M algorithms is 0.

Takahashi is visiting a bookstore, where he finds N books on algorithms.
The i-th book (1\leq i\leq N) is sold for C_i yen (the currency of Japan). If he buys and reads it, his understanding level of the j-th algorithm will increase by A_{i,j} for each j (1\leq j\leq M).
There is no other way to increase the understanding levels of the algorithms.

Takahashi's objective is to make his understanding levels of all the M algorithms X or higher. Determine whether this objective is achievable. If it is achievable, find the minimum amount of money needed to achieve it.

Constraints

All values in input are integers.

1\leq N, M\leq 12

1\leq X\leq 10^5

1\leq C_i \leq 10^5

0\leq A_{i, j} \leq 10^5

Input

Input is given from Standard Input in the following format:

N M X
C_1 A_{1,1} A_{1,2} \cdots A_{1,M}
C_2 A_{2,1} A_{2,2} \cdots A_{2,M}
\vdots
C_N A_{N,1} A_{N,2} \cdots A_{N,M}

Output

If the objective is not achievable, print -1; otherwise, print the minimum amount of money needed to achieve it.

Sample Input 1

3 3 10
60 2 2 4
70 8 7 9
50 2 3 9

Sample Output 1

120

Buying the second and third books makes his understanding levels of all the algorithms 10 or higher, at the minimum cost possible.

Sample Input 2

3 3 10
100 3 1 4
100 1 5 9
100 2 6 5

Sample Output 2

-1

Buying all the books is still not enough to make his understanding levels of all the algorithms 10 or higher.

Sample Input 3

8 5 22
100 3 7 5 3 1
164 4 5 2 7 8
334 7 2 7 2 9
234 4 7 2 8 2
541 5 4 3 3 6
235 4 8 6 9 7
394 3 6 1 6 2
872 8 4 3 7 2

Sample Output 3

1067

Solution in Python (3.8.2) (judge verdict: Wrong Answer)

import sys
import numpy as np
from itertools import combinations
sys.setrecursionlimit(10 ** 6)  # 再帰関数の再帰の深さを設定
to_index = lambda x: int(x) - 1  # 入力した数字に1を引いたものを返す
print_list_in_2D = lambda x: print(*x, sep="\n")  # リストの要素を改行を挟んで表示する関数

# 入力を整数に変換して受け取る
def input_int():
    return int(input())

def map_int_input():
    return map(int, input())

MII = map_int_input

def MII_split():
    return map(int, input().split())

def MII_to_index():
    return map(to_index, input())

def MII_split_to_index():
    return map(to_index, input().split())

# 入力全てを整数に変換したものの配列を受け取る
def list_int_inputs():
    return list(map(int, input()))

LII = list_int_inputs

def LII_split():
    return list(map(int, input().split()))

# 2次元リスト化
def LII_2D(rows_number):
    return [LII() for _ in range(rows_number)]

def LII_split_2D(rows_number):
    return [LII_split() for _ in range(rows_number)]

N, M, X = MII_split()

books = []
# prices = []
for i in range(N):
    book = LII_split()
    # prices.append(book[0])
    books.append(book)

# books = sorted(books.items(), key=lambda x: sum(x[1]), reverse=True)
# chosen_books = []
# is_chosen = [False for _ in range(N)]
price = 0
min_price = -1
for i in range(N):  # i = 選ぶ本の個数-1

    for tmp_books in combinations(books, i + 1):
        algo_skills = np.array([0 for _ in range(M)])
        price = 0
        for skills in tmp_books:
            algo_skills += np.array(skills[1:])
            price += skills[0]
        if np.all(algo_skills >= X):
            if min_price == -1 or price < min_price:
                min_price = price

print(price)