Not Too Hard

Showmik is very popular nowadays. Junior coders always seek help from him. He also wants them to improve their skills. So for them he has given a problem which is not too easy and again not too hard. He is generating a tree which has the following properties:

1. Each node takes 1 second to be created.
2. Each node will have $m$ child nodes. $m$ will be equal to (current level + 1).
3. Each node will be marked with a number starting from left. Number starts with 1.

He will give a random number $N$. They have to find the level number and mark number of the node being created at $N$-th second.

Input

First line of input contains a single number $T$ ($T \le 10000$). $T$ test cases follows. Each case has a single number $N$ ($1 \le N \le 10^{16}$) which indicates the $N$-th second.

Output

For each test case, print answer as the format “Case x: y z” without quotation. Here, $x$ indicates the case number and $y$, $z$ indicate the desired results.

Sample

4
5
21
63
1326509874132650

Case 1: 3 2
Case 2: 4 12
Case 3: 5 30
Case 4: 18 948498053512337

Tree is basically a graph which is connected and there is no cycle. There is only one root node and each node may have zero or more child nodes.