Mirko has recently installed a new screensaver. If he is away from the keyboard for five minutes, the screen shows a picture of an aquarium with animated fish. The screensaver has settings for customizing the shape of the (virtual, sandy) aquarium bottom, as well as the water level.
The aquarium can be represented in a 2D Cartesian coordinate system as a shape
If the water level is set to
For different shapes of the aquarium bottom, Mirko would like to know the total area of his screen covered by water. Help Mirko find answers to his questions (other than
Input Specification
The first line of input contains two positive integers,
The second line of input contains
Each of the following
Q h
– if the water level is set to , assuming the current bottom shape, what is the total screen area covered by water?U i h
– Mirko has decided to change the bottom height at x-coordinate to ; in other words, set .
Output Specification
For each query with type
Sample Input 1
3 2
20 20 20
Q 20
Q 30
Sample Output 1
0.000
20.000
Sample Input 2
3 5
0 2 0
Q 2
U 1 1
Q 1
U 1 10
Q 5
Sample Output 2
2.000
1.000
2.500
Sample Input 3
7 7
0 2 1 3 2 1 0
Q 1
Q 2
Q 3
U 3 0
Q 1
Q 2
Q 3
Sample Output 3
0.750
3.750
9.000
1.500
6.000
12.000
Explanation for Sample Output 3
The left image below shows the situation before, and the right one after the U-type query, for water level Q 2
). In the first image, the submerged area equals

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