Mr. M is an undergraduate student of FDU, Shanghai. He finds an intern position in Beijing, so that he cannot attend all the college activities. But in some conditions, he must come back to Shanghai on certain dates. We can assume the important activities that Mr. M must attend occupy a whole day. Mr. M must take a flight to Shanghai before that day and leave after that day. On the other hand, when Mr. M is absent in Beijing and he will lose his salary for his absence.

Sometimes the cost of a flight is much higher than the loss of salary, so to save the cost on the travel, Mr. M can stay in Shanghai to wait for another important date before he returns to Beijing.

Now, Mr. M knows all of the important dates in the next year. Help him schedule his travel to optimize the cost.

Input

The input contains several test cases. The first line of single integer indicates the number of test cases.

For each test case, the first line contains three integers: n, a and b, denoting the number of important events, the cost of a single flight from Beijing to Shanghai or Shanghai to Beijing and the salary for a single day stay in Beijing. (1 ≤ n ≤ 100000, 1 ≤ a ≤ 1000000000, 1 ≤ b ≤100)

Next line contains n integers t_i, denoting the dates of the important events. You can assume the t_i are in increasing order and they are different from each other. (0 ≤ t_i ≤ 10000000)

Output

For each test case, output a single integer indicating the minimum cost for this year.

Example

Input:
2
1 10 10
5
5 10 2
5 10 15 65 70

Output:
Case #1: 30
Case #2: 74

Warning: large input/output data, be careful with certain languages.