Problem Statement

You have one black-and-white image.
Although it is called black-and-white, it is expressed as a gradation of grays of different darkness, and it contains $N$ kinds of colors. These colors are represented by a value called "gray darkness", and $2$ grays are considered the same color only when these values are equal.
The image consists of cells in $H$ rows and $W$ columns, each painted in a color, and the "gray darkness" of cell $(i,j)$, in the $i$-th row from the top and the $j$-th column from the left, is $C_{ij}$. You want to convert this image into an image with as few colors as possible.
Here, a conversion of the original image means generating an image with $H$ rows and $W$ columns, where the "gray darkness" of cell $(i,j)$, in the $i$-th row from the top and the $j$-th column from the left, is $D_{ij}$, that satisfies the following conditions.

■Conditions
1. For any $2$ colors, the order of their "gray darkness" is not reversed between the image before the conversion and the image after the conversion.
　Strictly, for any $2$ cells $(i,j)$, $(k,l)$, if $C_{ij}≤C_{kl}$ then $D_{ij}≤D_{kl}$.
2. The "color boundaries" do not change through the conversion.
　That is, for any $2$ cells adjacent by sharing an edge, if their "gray darkness" differs before the conversion, then it also differs after the conversion.

Find the minimum number of kinds of colors appearing in the converted image, over all conversions satisfying the conditions.

Input

$H$ $W$ $N$
$C_{11}$ $C_{12}$ ... $C_{1W}$
$C_{21}$ $C_{22}$ ... $C_{2W}$
... 
$C_{H1}$ $C_{H2}$ ... $C_{HW}$

$H$ is the number of rows of cells forming the image, $W$ is the number of columns, and $N$ is the number of kinds of colors appearing in the image before the conversion.
$C_{ij}$ represents the "gray darkness" of cell $(i,j)$, in the $i$-th row from the top and the $j$-th column from the left.

■Constraints
$1≤H,W≤1000$
$1≤N≤HW$
$1≤C_{ij}≤N$
For any $k$ satisfying $1≤k≤N$, there exists a cell $(i,j)$ such that $C_{ij}=k$.
All inputs are integers.

Output

Output the minimum number of kinds of colors of an output image satisfying the conditions of the problem.
Print a newline at the end.

Sample

2 2 4
1 2
3 4

3

3 3 7
1 4 5
7 7 7
2 3 6

4