Grass

Edo takes care of the grass in his garden. The garden is represented as a one-dimensional row of exactly N grass plants, ordered from left to right. Initially every plant has height 0 millimeters. No plant can grow higher than H millimeters.

Process M operations in order and output the sum of all plant heights whenever it is requested.

Each operation is one of the following five types.

• N X: every plant grows by X millimeters. If a plant would become taller than H, its height becomes exactly H.
• L X: the leftmost X plants are completely mowed, so their heights become 0.
• D X: the rightmost X plants are completely mowed, so their heights become 0.
• S X: the lawnmower is set to height X and used on the whole garden. Every plant taller than X is cut down to X; all other plants keep their height.
• Z: output the current sum of all plant heights.

The first line contains three positive integers N, H, and M: the number of grass plants, the maximum height of a plant, and the number of operations.

1 <= N <= 10^9, 1 <= H <= 10^6, and 1 <= M <= 10^6.

Each of the next M lines describes one operation. The operation is one of the five types described above. Operations N, L, D, and S consist of one uppercase letter and an integer X, separated by one space. Operation Z has no integer after it.

For operations L and D, 1 <= X <= N. For operations N and S, 1 <= X <= H.

For every Z operation, output one line containing one integer: the current sum of all grass heights. The answers must be printed in the same order as the corresponding Z operations in the input.

The sum of heights can be larger than 2^32.