A1050. Cow Hopscotch Gold

Just like humans enjoy playing the game of Hopscotch, Farmer John's cows have
invented a variant of the game for themselves to play. Being played by clumsy
animals weighing nearly a ton, Cow Hopscotch almost always ends in disaster,
but this has surprisingly not deterred the cows from attempting to play nearly
every afternoon.
The game is played on an R by C grid (2 <= R <= 750, 2 <= C <= 750), where
each square is labeled with an integer in the range 1..K (1 <= K <= R*C). Cows
start in the top-left square and move to the bottom-right square by a sequence
of jumps, where a jump is valid if and only if
1) You are jumping to a square labeled with a different integer than your
current square,
2) The square that you are jumping to is at least one row below the current
square that you are on, and
3) The square that you are jumping to is at least one column to the right of
the current square that you are on.
Please help the cows compute the number of different possible sequences of
valid jumps that will take them from the top-left square to the bottom-right
square.

The first line contains the integers R, C, and K. The next R lines will each
contain C integers, each in the range 1..K.

Output the number of different ways one can jump from the top-left square to
the bottom-right square, mod 1000000007.