Problem Statement

There is an $N \times M$ grid.

The cell $(i, j)$ in the $i$-th row from the top and the $j$-th column from the left has an integer $A_{i, j}$ written on it.

You are going to travel from the top-left cell $(1, 1)$ to the bottom-right cell $(N, M)$ by moving up, down, left, or right.

You may perform the following action up to $K$ times.

• Choose integers $i, j$ satisfying $1 \leq i \leq N, 1 \leq j \leq M$, and change the integer written on cell $(i, j)$ to any integer from $1$ to $10^{9}$.

The score is the minimum of the integers written on the cells you passed through during the move, including $(1, 1) と (N, M)$.

Find the maximum possible score.

Constraints

• $2 \leq N, M \leq 300$
• $0 \leq K \leq N \times M$
• $1 \leq A_{i, j} \leq 10^{9}$
• All input values are integers.

Input

The input is given from Standard Input in the following format.

$N$ $M$ $K$ 
$A_{1,1}$ $A_{1,2}$ ... $A_{1,M}$  
$A_{2,1}$ $A_{2,2}$ ... $A_{2,M}$  
$\vdots$

$A_{N,1}$ $A_{N,2}$ ... $A_{N,M}$  

Output

Print the answer to the problem on one line.

Sample

3 3 2
1 2 4
3 5 7
6 8 9

6

5 5 0
1 7 7 7 7
1 7 1 1 1
1 7 1 7 1
1 7 1 7 1
1 1 1 7 1

1

2 3 6
2 3 3
5 7 8

1000000000