Arya and Bran are playing a game. Initially, two positive integers ~A~ and ~B~ are written on a blackboard. The players take turns, starting with Arya. On his or her turn, a player can replace ~A~ with ~A - k \cdot B~ for any positive integer ~k~, or replace ~B~ with ~B - k \cdot A~ for any positive integer ~k~. The first person to make one of the numbers drop to zero or below loses.

For example, if the numbers are initially ~(12, 51)~, the game might progress as follows:

• Arya replaces ~51~ with ~51 - 3*12 = 15~, leaving ~(12, 15)~ on the blackboard.
• Bran replaces ~15~ with ~15 - 1*12 = 3~, leaving ~(12, 3)~ on the blackboard.
• Arya replaces ~12~ with ~12 - 3*3 = 3~, leaving ~(3, 3)~ on the blackboard.
• Bran replaces one ~3~ with ~3 - 1*3 = 0~, and loses.

We will say ~(A, B)~ is a winning position if Arya can always win a game that starts with ~(A, B)~ on the blackboard, no matter what Bran does.

Given four integers ~A_{1}~, ~A_{2}~, ~B_{1}~, ~B_{2}~, count how many winning positions ~(A, B)~ there are with ~A_{1} \le A \le A_{2}~ and ~B_{1} \le B \le B_{2}~.

Input Specification

The first line of the input gives the number of test cases, ~T~. ~T~ test cases follow, one per line. Each line contains the four integers ~A_{1}~, ~A_{2}~, ~B_{1}~, ~B_{2}~, separated by spaces.

Output Specification

For each test case, output one line containing Case #x: y, where ~x~ is the case number (starting from 1), and ~y~ is the number of winning positions ~(A, B)~ with ~A_{1} \le A \le A_{2}~ and ~B_{1} \le B \le B_{2}~.

Limits

Memory limit: 1 GB.

~1 \le T \le 100~.

~1 \le A_{1} \le A_{2} \le 1\,000\,000~.

~1 \le B_{1} \le B_{2} \le 1\,000\,000~.

Small Dataset

Time limit: 30 seconds.

~A_{2} - A_{1} \le 30~.

~B_{2} - B_{1} \le 30~.

Large Dataset

Time limit: 90 seconds.

~A_{2} - A_{1} \le 999\,999~.

~B_{2} - B_{1} \le 999\,999~.

No additional constraints.

Sample Input

3
5 5 8 8
11 11 2 2
1 6 1 6

Sample Output

Case #1: 0
Case #2: 1
Case #3: 20

Note

This problem has different time limits for different batches. If you exceed the Time Limit for any batch, the judge will incorrectly display >90.000s regardless of the actual time taken. Refer to the Limits section for batch-specific time limits.