Map

In Byteland, a new institution has been founded to study how similar the country's various regions are to one another. The map of the country is an $n \times m$ rectangle made up of $n \cdot m$ unit squares. Each square is a province, and every province is assigned exactly one natural number describing a characteristic feature (for example, 1 for coal deposits, 2 for lakes, and so on).

Two regions are called $k$-similar if, among all pairs of corresponding provinces, at most $k$ pairs have differing features (all the others are identical). Given the map, you must answer queries asking whether two given regions are $k$-similar.

For example, consider the following two $3 \times 3$ regions:

The two regions above are 2-similar and 3-similar, but they are neither 1-similar nor 0-similar.

The first line contains three integers $n$, $m$, $q$ ($1 \le n, m \le 200$, $1 \le q \le 20000$): the number of rows and columns of the map and the number of queries. Each of the next $n$ lines describes the map; line $i+1$ contains $m$ integers $a_{i,1}, \dots, a_{i,m}$ ($1 \le a_{i,j} \le 100$), where $a_{i,j}$ is the feature of the province in row $i$, column $j$ (rows and columns are numbered from 1).

Each of the next $q$ lines contains one query as seven integers $x_1\ y_1\ x_2\ y_2\ w\ h\ k$ ($0 \le k \le 1000$, $1 \le w \le m$, $1 \le h \le n$). The two regions are rectangles whose top-left province lies at (column $x_1$, row $y_1$) and (column $x_2$, row $y_2$) respectively, each spanning $w$ columns across and $h$ rows down; their bottom-right provinces are therefore at (column $x_1+w-1$, row $y_1+h-1$) and (column $x_2+w-1$, row $y_2+h-1$). Both regions lie entirely inside the map. Decide whether the two regions are $k$-similar.

Print $q$ lines, one per query: TAK if the two regions are $k$-similar, or NIE otherwise.