Binary Search?

When Jojo was a little kid, his teacher asked him a question. What was the answer of 12+22+32+...+N2 ? Of course that problem was hard enough for a primary student. But since he is a university student, and he knows that the answer is 16 N ( N +1) (2 N +1), such problem is to easy for him. Now Jojo came up with a new problem. If he has an integer M, what is the smallest integer N such that 1 2 + 2 2 + 3 2 + ... + N 2 is greater than or equal to M. After thinking for some time, he came up with a solution, but his solution takes a lot of time. Since you are his nemesis, he challenges you to solve the problem quicker than him. Of course you accept his challenge!

Format Input

The first line is an integer T representing the number of test cases. For each test case there will be 1 line consisting of an integer M.

Format Output

For each test case output Case #X: N. X is the test case number (starting from 1) and N is the smallest integer such that 1 2 + 2 2 + 3 2 + ... + N 2 is greater than or equal to M.

Constraints

1 T 2000

1 M 10^18

Sample Input 1 (standard input)

1

2

Sample Output 1 (standard output)

Case #1: 2

Sample Input 2 (standard input)

1

10

Sample Output 2 (standard output)

Case #1: 3

PLEASE USE C PROGRAMMING AND USE HEADER INCLUDE STDIO.H

AND MAKE THE CODE SIMPLE AS YOU CAN

DON'T FORGET TO USE BINARY SEARCH FOR THE CODE