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.

Examples

Input

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

Output

120

Input

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

Output

-1

Input

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

Output

1067

见题面

见题面