The number of diagonals of an n-gon is not less than N. What is the minimum possible value of n? Input The input file contains less than 1001 lines of inputs. Each line contains a positive integer N (N ≤ 1015) that indicates the minimum possible number of diagonals. Input is terminated by a line containing a zero. This line should not be processed. Output For each line of input produce one line of output, which contains the output serial number, and also the minimum possible value for n (Number of sides). Sample Input 10 100 1000 0 Sample Output Case 1: 7 Case 2: 16 Case 3: 47