Maryam, a famous mathematician, recently has bought an old vintage car. This car uses a combustion engine to generate the power needed to move the car. Inside the engine, there are $$$n$$$ cylinders of length $$$m$$$ and inside each cylinder, there is a piston constantly moving up and down. All pistons move independently and at the same speed. At any given time, the position of a piston inside a cylinder can be shown with an integer from $$$0$$$ to $$$m$$$, which also describes the area of the cylinder occupied by the piston. A piston instantly changes its direction when it reaches the top (position $$$m$$$) or bottom (position $$$0$$$) of its cylinder.
Maryam managed to determine the position and direction of all the pistons at a specific time. Now she is curious about the maximum total area occupied by all the pistons. Help Maryam find out this value.
The first line of input contains two integers $$$n$$$ and $$$m$$$ ($$$1 \le n \le 10^5, 1 \le m \le 10^6$$$), describing the number of pistons and the length of cylinders, respectively. Each of the next $$$n$$$ lines describe the position and direction of a single piston. The $$$(i+1)^\mathrm{th}$$$ line of the input contains an integer $$$p_i$$$ ($$$0 \le p_i \le m$$$), and a character $$$d_i$$$ ($$$d_i \in \{\mathtt{U}, \mathtt{D}\}$$$), the initial position of the $$$i^\mathrm{th}$$$ piston and its direction (Up or Down), respectively.
Print a single integer, the maximum total area occupied by all the pistons.
2 5 2 U 5 D
7
4 6 0 U 0 D 6 U 3 U
15
