Cow Hopscotch

People enjoy playing hopscotch, and Farmer John's cows have invented a variant for themselves. Clumsy animals weighing nearly a ton play it, so cow hopscotch almost always ends in disaster. The cows still set the board up nearly every afternoon.

The board is an $R \times C$ grid ($2 \le R \le 100$, $2 \le C \le 100$). Each square holds one integer between $1$ and $K$ ($1 \le K \le R \times C$). A cow starts on the top-left square and reaches the bottom-right square with a sequence of jumps. A jump is valid only when all three of these conditions hold.

1. The integer on the destination square differs from the integer on the current square.
2. The destination square is at least one row below the current square.
3. The destination square is at least one column to the right of the current square.

Count the different sequences of valid jumps that take a cow from the top-left square to the bottom-right square.

The first line contains the integers $R$, $C$, and $K$.

Each of the next $R$ lines contains $C$ integers. All of them are between $1$ and $K$.

Print on one line the number of different ways to get from the top-left square to the bottom-right square, modulo $1000000007$.