高精度乘法

Description

Think about a plane: 

● One straight line can divide a plane into two regions. 
● Two lines can divide a plane into at most four regions. 
● Three lines can divide a plane into at most seven regions. 
● And so on... 

Now we have some figure constructed with two parallel rays in the same direction, joined by two straight segments. It looks like a character “M”. You are given N such “M”s. What is the maximum number of regions that these “M”s can divide a plane ? 

 

Input

The first line of the input is T (1 ≤ T ≤ 100000), which stands for the number of test cases you need to solve. 

Each case contains one single non-negative integer, indicating number of “M”s. (0 ≤ N ≤ 10 ¹²)

 

Output

For each test case, print a line “Case #t: ”(without quotes, t means the index of the test case) at the beginning. Then an integer that is the maximum number of regions N the “M” figures can divide.

 

Sample Input

2 1 2

 

Sample Output

Case #1: 2

Case #2: 19

 

 

解题思路：在直线划分平面中f(n)=f(n-1)+(n-1)+1;

推测"M"划分平面中，一次是4条线划分，故f(n)=f(n-1)+4*(n-1)+1;

整理得f(n)=8*n*n-7*n+1;

n取值范围为10^12次方，故使用高精度乘法。