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)

n,m,x = map(int,input().split())
c_ = [list(map(int,input().split())) for i in range(n)]

cc_ = []
for i in range(n):
    cc_.append(c_[i][0])
# print(cc_)

import numpy as np
import itertools
l = np.arange(n)

res1_ = []
res2_ = []
res3_ = []
res4_ = []
res5_ = []
res6_ = []
res7_ = []
res8_ = []
res9_ = []
res10_ = []
res11_ = []
res12_ = []
cc_r_ = []
resList = []
flag = False
for i in range(2,n+1):
    c = list(itertools.combinations(l, i))
    for j in c:
        # print(j)
        res1_ = []
        res2_ = []
        res3_ = []
        res4_ = []
        res5_ = []
        res6_ = []
        res7_ = []
        res8_ = []
        res9_ = []
        res10_ = []
        res11_ = []
        res12_ = []
        cc_r_ = []
        for k in range(len(j)):
            res1_.append(c_[j[k]][1])
            if m >= 2:
                res2_.append(c_[j[k]][2])
            if m >= 3:
                res3_.append(c_[j[k]][3])
            if m >= 4:
                res4_.append(c_[j[k]][4])
            if m >= 5:
                res5_.append(c_[j[k]][5])
            if m >= 6:
                res6_.append(c_[j[k]][6])
            if m >= 7:
                res7_.append(c_[j[k]][7])
            if m >= 8:
                res8_.append(c_[j[k]][8])
            if m >= 9:
                res9_.append(c_[j[k]][9])
            if m >= 10:
                res10_.append(c_[j[k]][10])
            if m >= 11:
                res11_.append(c_[j[k]][11])
            if m >= 12:
                res12_.append(c_[j[k]][12])
            cc_r_.append(cc_[j[k]])
        res1 = sum(res1_)
        if m >= 2:
            res2 = sum(res2_)
        if m >= 3:
            res3 = sum(res3_)
        if m >= 4:
            res4 = sum(res4_)
        if m >= 5:
            res5 = sum(res5_)
        if m >= 6:
            res6 = sum(res6_)
        if m >= 7:
            res7 = sum(res7_)
        if m >= 8:
            res8 = sum(res8_)
        if m >= 9:
            res9 = sum(res9_)
        if m >= 10:
            res10 = sum(res10_)
        if m >= 11:
            res11 = sum(res11_)
        if m >= 12:
            res12 = sum(res12_)
        cc_r = sum(cc_r_)
        if res1 >= x :
            if m >= 2 and res2 >= x:
                resList.append(cc_r)
                flag = True
                if m >= 3 and res3 >= x:
                    resList.append(cc_r)
                    flag = True
                    if m >= 4 and res4 >= x:
                        resList.append(cc_r)
                        flag = True
                        if m >= 5 and res5 >= x:
                            resList.append(cc_r)
                            flag = True
                            if m >= 6 and res6 >= x:
                                resList.append(cc_r)
                                flag = True
                                if m >= 7 and res7 >= x:
                                    resList.append(cc_r)
                                    flag = True
                                    if m >= 8 and res8 >= x:
                                        resList.append(cc_r)
                                        flag = True
                                        if m >= 9 and res9 >= x:
                                            resList.append(cc_r)
                                            flag = True
                                            if m >= 10 and res10 >= x:
                                                resList.append(cc_r)
                                                flag = True
                                                if m >= 11 and res11 >= x:
                                                    resList.append(cc_r)
                                                    flag = True
                                                    if m >= 12 and res12 >= x:
                                                        resList.append(cc_r)
                                                        flag = True
print(min(resList) if flag else -1)