While the most typical type of dice have ~6~ sides, each of which shows a different integer ~1~ through ~6~, there are many games that use other types. In particular, a ~dk~ is a die with ~k~ sides, each of which shows a different integer ~1~ through ~k~. A ~d6~ is a typical die, a ~d4~ has four sides, and a ~d1000000~ has one million sides.

In this problem, we start with a collection of ~N~ dice. The ~i^\text{th}~ die is a ~dS_i~, that is, it has ~S_i~ sides showing integers ~1~ through ~S_i~. A straight of length ~\ell~ starting at ~x~ is the list of integers ~x, x+1, \dots, x+(\ell-1)~. We want to choose some of the dice (possibly all) and pick one number from each to form a straight. What is the longest straight we can form in this way?

Input Specification

The first line of the input gives the number of test cases, ~T~. ~T~ test cases follow. Each test case is described in two lines. The first line of a test case contains a single integer ~N~, the number of dice in the game. The second line contains ~N~ integers ~S_1, S_2, \dots, S_N~, each representing the number of sides of a different die.

Output Specification

For each test case, output one line containing Case #x: y, where ~x~ is the test case number (starting from ~1~) and ~y~ is the maximum number of input dice that can be put in a straight.

Limits

~1 \le T \le 100~

Test Set 1

Time Limit: 5 seconds

~1 \le N \le 10~

~4 \le S_i \le 20~

Test Set 2

Time Limit: 15 seconds

~1 \le N \le 10^5~

~4 \le S_i \le 10^6~

Sample Input

4
4
6 10 12 8
6
5 4 5 4 4 4
10
10 10 7 6 7 4 4 5 7 4
1
10

Sample Output

Case #1: 4
Case #2: 5
Case #3: 9
Case #4: 1

Explanation for Sample

In Sample Case #1, there are multiple ways to form a straight using all ~4~ dice. One possible way is shown in the image above.

In Sample Case #2, since none of the dice can show an integer greater than ~5~, there is no way to have a straight with more than ~5~ dice. There are multiple ways to form a straight with exactly ~5~ dice. For example, pick the integers ~4~ and ~5~ for both ~d5~'s and then integers ~1~, ~2~, and ~3~ for three of the ~d4~'s to form ~1, 2, 3, 4, 5~.

In Sample Case #3, it is possible to form the straight ~1,2,3,4,5,6,7,8,9~ by discarding one ~d4~ and using the ~d4~'s, ~d5~, and ~d6~ to get ~1~ through ~4~; the ~d7~'s to get ~5~ through ~7~; and the ~d10~'s to get ~8~ and ~9~. There is no way to form a straight of length ~10~, so this is the best that can be done.

In Sample Case #4, we can only form a straight of length ~1~, but we can do so by picking any integer for the ~d10~ we are given.

Note

This problem has different time limits for different batches. If you exceed the Time Limit for any batch, the judge will incorrectly display >15.000s regardless of the actual time taken. Refer to the Limits section for batch-specific time limits.