You are going to hold an international programming contest in a rectangular hall, which has seats arranged in rows and columns. The rows are numbered from through and the columns are numbered from through . The seat in row and column is denoted by . You invited contestants, numbered from through . You also made a seating chart, which assigns the contestant to the seat . The chart assigns exactly one contestant to each seat.
A set of seats in the hall is said to be rectangular if there are integers , , , and satisfying the following conditions:
- is exactly the set of all seats such that and .
A rectangular set consisting of seats , is beautiful if the contestants whose assigned seats are in the set have numbers from through . The beauty of a seating chart is the number of beautiful rectangular sets of seats in the chart.
After preparing your seating chart, you receive several requests to swap two seats assigned to two contestants. More precisely, there are such requests numbered from through in chronological order. The request is to swap the seats assigned to contestants and . You accept each request immediately and update the chart. After each update, your goal is to compute the beauty of the current seating chart.
Implementation Details
You should implement the following procedure and function:
void give_initial_chart(int H, int W, std::vector<int> R, std::vector<int> C)
- : the number of rows and the number of columns.
- : arrays of length representing the initial seating chart.
- This procedure is called exactly once, and before any call to
swap_seats
.
int swap_seats(int a, int b)
- This function describes a request to swap two seats.
- : contestants whose seats are to be swapped.
- This function is called times.
- This function should return the beauty of the seating chart after the swap.
Example
Let , , , , and .
The grader first calls give_initial_chart(2, 3, [0, 1, 1, 0, 0, 1], [0, 0, 1, 1, 2, 2])
.
At first, the seating chart is as follows.
Let's say the grader calls swap_seats(0, 5)
.
After the request , the seating chart is as follows.
The sets of seats corresponding to the contestants , , and are rectangular and beautiful.
Thus, the beauty of this seating chart is , and swap_seats
should return .
Let's say the grader calls swap_seats(0, 5)
again.
After the request , the seating chart goes back to the initial state.
The sets of seats corresponding to the contestants
, , , and are rectangular and beautiful.
Hence, the beauty of this seating chart is , and swap_seats
should return .
The files sample-01-in
and sample-01-out
in the zipped attachment package correspond to this example.
Other sample inputs/outputs are also available in the package.
Constraints
- for any call to
swap_seats
- for any call to
swap_seats
- for any call to
swap_seats
Subtasks
- ( points) ,
- ( points) ,
- ( points) , ,
- ( points) , for any call to
swap_seats
- ( points)
- ( points) No additional constraints
Sample Grader
The sample grader reads the input in the following format:
- line :
- line :
- line :
Here, and are parameters for the call to swap_seats
for the request .
The sample grader prints your answers in the following format:
- line : the return value of
swap_seats
for the request .
Attachment Package
The sample grader along with sample test cases are available here.
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