Window

The Jewelry Art Gallery (JAG) building has a long corridor running east to west. A window sits on the north side of the corridor, and $N$ windowpanes are mounted in it. Each pane is $W$ wide and $H$ tall. Measured from the west edge of the window, the $i$-th pane from the west covers the horizontal range from $W \times (i - 1)$ to $W \times i$.

Figure A1. Structure of the window

The manager of JAG told you how to slide the panes. The instructions are $N$ integers $x_1, x_2, \dots, x_N$, and $x_i \le W$ holds for every $i$. If $i$ is odd, slide the $i$-th pane east by $x_i$. If $i$ is even, slide it west by $x_i$.

The panes never collide, even after you follow the instructions, because the $N$ panes hang on two rails in alternation. A pane with odd $i$ is attached to the inner rail of the building, and a pane with even $i$ is attached to the outer rail.

Before carrying out the instructions, you want to know the area of the window that is open once they are done.

The input is a single test case in the format below.

N H W
x1 ... xN

The first line has three integers $N$, $H$, and $W$ ($1 \le N \le 100$, $1 \le H, W \le 100$). $N$ is even. The second line has the $N$ integers $x_1, \dots, x_N$ that represent the manager's instructions. $x_i$ is the distance the $i$-th pane slides ($0 \le x_i \le W$).

Print the area of the window that is open after the instructions, on one line.

Figure A2. Illustration of the first example