Problem Statement

You are given a two-dimensional array $A$ with $H$ rows and $W$ columns. For this two-dimensional array, define the intersection value $C_{i,j}$ as $(i行目の和)\times(j列目の和)$, that is, as follows.

$$ C_{i,j} = \left(\sum_{k=1}^WA_{i,k}\right)\ \times\ \left(\sum_{l=1}^HA_{l,j}\right) $$

Also, define the score $S$ of this two-dimensional array $A$ as the maximum value of $C_{i,j}$, that is, as follows.

$$ S = \max_{1 \le i \le H, 1 \le j \le W} C_{i,j} $$

Consider performing the following operation on $A$ $0$ or more times.

• Choose any $i,j$ $(1 \le i \le H, 1 \le j \le W)$. Spend a cost of $2^{B_{i,j}}$ and add $+1$ to $A_{i,j}$.

Given that you can spend a cost of up to $K$, find the maximum value of the score $S$ of the two-dimensional array $A$ after the operations.

Constraints

• $2 \le H,W \le 600$
• $1 \le K \le 2^{30}$
• $1 \le A_{i,j} \le 10^6$
• $0 \le B_{i,j} \le 30$
• All input values are integers.

Input

The input is given from standard input in the following format.

$H\ W\ K$
$A_{1,1}\ A_{1,2}\ \ldots\ A_{1,W} $
$A_{2,1}\ A_{2,2}\ \ldots\ A_{2,W} $
$\vdots$
$A_{H,1}\ A_{H,2}\ \ldots\ A_{H,W} $
$B_{1,1}\ B_{1,2}\ \ldots\ B_{1,W} $
$B_{2,1}\ B_{2,2}\ \ldots\ B_{2,W} $
$\vdots$
$B_{H,1}\ B_{H,2}\ \ldots\ B_{H,W} $

Output

Output the maximum score of $A$ after the operations. End the output with a newline.

Sample

2 2 6
1 2
3 4
1 1
2 2

64

1 3
3 5

5 6 67
6 5 46 35 48 5
34 1 20 46 45 5
41 19 38 49 30 22
32 48 41 12 38 24
30 4 8 37 15 37
1 0 4 1 2 2
2 3 4 4 0 2
3 3 1 4 0 2
0 4 0 3 0 1
4 3 3 1 3 4

64638