Farmer John's N cows (1 <= N <= 2000) are all standing at various positions along the straight path from the barn to the pasture, which we can think of as a one-dimensional number line. Since his cows like to stay in email contact with each-other, FJ wants to install Wifi base stations at various positions so that all of the cows have wireless coverage.

After shopping around, FJ learns that the cost of a Wifi base station depends on distance it can transmit: a base station of power r costs A + B*r, where A is a fixed cost for installing the base station and B is a cost per unit of transmission distance. If FJ installs such a device at position x, then it can transmit data to any cow located in the range x-r ... x+r. A base station with transmission power of r=0 is allowed, but this only provides coverage to a cow located at the same position as the transmitter.

Given the values of A and B, as well as the locations of FJ's cows, please determine the least expensive way FJ can provide wireless coverage for all his cows. (The answer may be a half-integer such as 57.5.)

Line 1: Three space-separated integers: N A B (0 <= A, B <= 1000).

Lines 2..1+N: Each line contains an integer in the range 0..1,000,000 describing the location of one of FJ's cows.

The minimum cost of providing wireless coverage to all cows (an integer, or a half-integer printed with a single decimal place, e.g. 57.5).

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