#215817. [JAG 2025 Summer Camp #1] Path Flipping

For a grid with each cell colored either white or black, let us define the beauty of the grid as follows:

• Consider performing the following operation any number of times:
  • Choose a path from the upper-left corner to the lower-right corner, consisting only of downward and rightward moves. Invert the colors of all cells on the chosen path.
• The beauty of the grid is defined as the maximum possible number of cells colored black.

You have a grid with rows and columns. Initially, all cells are colored white.

You need to process queries in order. The -th query is given in the following format:

• You are given two integers and .
  • If , invert the colors of all cells in the -th row from the top.
  • If , invert the colors of all cells in the -th column from the left.
• Then, find the beauty of the current grid.

The input is given in the following format:

• ()
• ()
• ()
• All input values are integers.

Output lines. On the -th line (), output the answer for the -th query.

样例输入 1

3 4 5
2 2
2 3
1 1
1 2
2 3

样例输出 1

9
12
10
10
9