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22/11/2024 11:02:59

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1633. Matrix

Ограничения: время – 1s/2s, память – 128MiB Ввод: input.txt или стандартный ввод Вывод: output.txt или стандартный вывод copy
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A `N\ times\ N` matrix is filled with numbers 1 to `N*N`, diagonally in a zig-zag fashion. The illustration below shows numbers in the matrix for `N\ =\ 6`.

 1   2   6   7  15  16
 3   5   8  14  17  26
 4   9  13  18  25  27
10  12  19  24  28  33
11  20  23  29  32  34
21  22  30  31  35  36

There is a rabbit in the cell containing number 1. A rabbit can jump to a neighboring cell (up, down, left or right) if that cell exists.

Given `K` valid rabbit jumps, write a program that will calculate the sum of numbers of all cells that rabbit visited (add the number to the sum each time rabbit visits the same cell).

Input

The first line contains two integers `N` and `K` (`1\ ≤\ N\ ≤\ 100000`, `1\ ≤\ K\ ≤\ 300000`), the size of the matrix and the number of rabbit jumps.

The second line contains a sequence of `K` characters 'U', 'D', 'L' and 'R', describing the direction of each jump. The sequence of jumps will not leave the matrix at any moment.

Output

Output one integer, the sum of numbers on visited cells. Note: This number doesn't always fit in 32-bit integer type.

Sample Input 1

6 8
DDRRUULL

Sample Output 1

Sample Input 2

3 8
DDRRUULL

Sample Output 2

Sample Input 3

6 10
RRRRRDDDDD

Sample Output 3

Clarification for the first sample: The rabbit visits cells 1, 3, 4, 9, 13, 8, 6, 2 and 1.
Clarification for the second sample: The rabbit visits cells 1, 3, 4, 8, 9, 7, 6, 2 and 1.
Clarification for the third sample: The rabbit visits cells 1, 2, 6, 7, 15, 16, 26, 27, 33, 34 and 36.
Source: School competition, February 2010

04/07/2011	Лето 2011 - дорешивание (10H)
15/07/2011	Лето 2011 - 10 (H)

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1633. Matrix

Matrix