Grid Operations

You are given a (N \times M) grid (with rows numbered from 1 to (N) and columns from 1 to (M)), initially filled with zeros. You need to process (Q) operations sequentially. The operations are one of the following three types:

• row i x: Add the integer \(x\) to every cell in the \(i\)-th row.
• col j x: Add the integer \(x\) to every cell in the \(j\)-th column.
• max: Query and output the current maximum value present in the grid.

Note that the row and column indices are 1-indexed. Your task is to simulate these operations and, whenever a max command is encountered, print the maximum value in the grid at that moment.

inputFormat

The input is given via standard input in the following format:

• The first line contains three integers \(N\), \(M\), and \(Q\) separated by spaces — representing the number of rows, the number of columns, and the number of operations respectively.
• The next \(Q\) lines describe an operation. Each operation is in one of the following formats:
  • row i x — add the integer \(x\) to each cell of the \(i\)-th row.
  • col j x — add the integer \(x\) to each cell of the \(j\)-th column.
  • max — output the current maximum value in the grid.

outputFormat

For each max operation in the input, output a single line to standard output containing the maximum value in the grid after applying all preceding operations.## sample

2 3 5
row 1 4
col 2 2
max
row 2 3
max

6
6

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