Problem H. Healthy run ≡

Statement

Young programmer Vasya decided to start running every morning to keep himself in a good shape.

Vasya googled how to run properly if you have lead a sedentary lifestyle for too long and found an article where the following technique was offered.

You need to run along a circular track divided into N segments. Length of i-th segment is a_i meters.

One should alternate slow and fast running: on the first, third and following odd segments — with the speed of V m/s, on the second, fourth and following even segments — with the speed of 2V m/s.

Vasya wondered how far he would run in T seconds, given the sequence of segment lengths and the starting speed.

Input file format

The first line of the input file contains integers N, V, T — the number of segments, the initial speed and the time that Vasya will run for.

The second line of the input file contains integers a_i — lengths of the segments along the track. The sum of the lengths of the segments is equal to the length of the track.

Output file format

Output file must contain a single number — the distance that Vasya will run in the specified time with an accuracy of at least 5 digits after the decimal point.

Constraints

1 ≤ N ≤ 10⁴

1 ≤ a_i ≤ 10⁴

1 ≤ V, T ≤ 10⁴

Sample tests

1 2 1
1

2.5

2 10 2
3 7

30.5