Problem D
Voronoi Diagrams?

"Well, and? Details! I mean, not details,
I don't need a diagram. But, you know, like
maybe a blurry watercolor."
Willow Rosenberg

Given a sorted set of n+1 even numbers S = (s0, s1, ..., sn), it is easy to construct the corresponding set of n midpoints, M = (m1, m2, ..., mn), where each mi is the average of the i'th and (i-1)'th elements of S. Your task is, given a set of integers, M, to determine whether it is possible for M to be a set of midpoints for some set of even integers S. No two elements of S can be the same.

The first line of input gives the number of cases, N. N test cases follow. Each one starts with a line containing n (0<=n<=10000). The next line will contain the integers m1 through mn in sorted order, each one between -100000000 and 100000000.

For each test case, output one line containing "Case #x:" followed by either "YES" or "NO".

Sample Input Sample Output

7 13
1 3 5 7 9 11 13 15 17 19
1 10 11 20 21 30
Case #1: YES
Case #2: YES
Case #3: YES
Case #4: NO

Problemsetter: Igor Naverniouk