Farmer John has a big square field split up into an (N+1)×(N+1) (1≤N≤1500) grid of cells. Let cell (i,j)

denote the cell in the ith row from the top and jth column from the left. There is one cow living in every cell (i,j) such that 1≤i,j≤N, and each such cell also contains a signpost pointing either to the right or downward. Also, every cell (i,j) such that either i=N+1 or j=N+1, except for (N+1,N+1), contains a vat of cow feed. Each vat contains cow feed of varying price; the vat at (i,j) costs c_i,j (1≤c_i,j≤500) to feed each cow.

Every day at dinner time, Farmer John rings the dinner bell, and each cow keeps following the directions of the signposts until it reaches a vat, and is then fed from that vat. Then the cows all return to their original positions for the next day.

To maintain his budget, Farmer John wants to know the total cost to feed all the cows each day. However, during every day, before dinner, the cow in in some cell (i,j) flips the direction of its signpost (from right to down or vice versa). The signpost remains in this direction for the following days as well, unless it is flipped back later.

Given the coordinates of the signpost that is flipped on each day, output the cost for every day (with Q days in total, 1≤Q≤1500).

SCORING:

Inputs 2-4: 1≤N,Q≤501≤N, Q≤50
Inputs 5-7: 1≤N,Q≤2501≤N, Q≤250
Inputs 2-10: The initial direction in each cell, as well as the queries, are uniformly randomly generated.
Inputs 11-15: No additional constraints.

#5470 upload 8 done 1 how_to_reg 1

Following Directions timer 8s memory 64MB

#5470

Following Directions 8s 64MB