Competitions

# Simple Combinatorics

# Diagonal

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** ≤ **10 ^{15}**) 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).

Input example #1

10 100 1000 0

Output example #1

Case 1: 7 Case 2: 16 Case 3: 47