G. Broken boards
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

Vadim's brother attends the karate section and practices breaking planks in halves. Vadim decided not to lose an opportunity and make money on it. He wants to fill the broken edges with epoxy and cut down all remaining splinters.

Merchant said to Vadim that he would buy each plank for $$$m * S$$$, $$$S$$$– plank area. It is originally a rectangle, three sides are flat, and the fourth is broken. Vadim placed the plank in the coordinate plane, broken side upwards so that its lower side coincides with the abscissa axis. Vadim can describe slivers on the drawing as a polyline that consists of $$$n$$$ vertices (img.1).

After that, in a hardware store, Vadim discovered that one epoxy drop costs $$$k$$$ coins. In the store, the merchant told him that one drop of epoxy would occupy precisely one unit of area in his drawing. Also, to help Vadim, the merchant promised to sell even a noninteger amount of drops of epoxy. After Vadim pours the epoxy and its polymerize (img. 2), he will cut down all remaining splitters and sell the plank (on img. 3, you can see the line by which the plank will be cut down). Help Vadim: write a program, which according to the description and prices of $$$m$$$ and $$$k$$$, will calculate the maximum amount of money that Vadim can get from this plank.

It is guaranteed that answer will be fit double. The answer should be displayed with an accuracy of $$$10^{-6}$$$

Input

The first row contains single integer $$$n$$$ ($$$1 \leq n \leq 10^5$$$) - the number of vertices in the polynomial. The following row contains 2 values $$$m$$$ and $$$k$$$ ($$$0 \lt m, k \leq 10^9$$$) ($$$m$$$ and $$$k$$$ may be float) - price per unit of area and price per drop of epoxy appropriately. $$$i$$$-th of following $$$n$$$ rows contain two integers $$$x$$$ and $$$y$$$ ($$$0 \leq x, y \leq 10^{9}$$$, $$$x_i \gt x_{i-1}$$$) - coordinates of $$$i$$$-th polygonal line vertex.

Output

Print single value — answer. The answer should be displayed with an accuracy of $$$10^{-6}$$$

Example
Input
8
1.5 10.2
1 4
3 5
4 2
5 6
6 5
8 6
9 2
11 6
Output
38.272059