Problem: corporate_gifting (2015 round1)

The fine people of Corpro Corp. are a festive bunch. Every holiday season,
everybody buys a gift for their manager. A cynic might say that the employees
are just trying to bribe their way to a better performance review, but if you
asked them yourself, they'd say they just wanted to spread cheer.

The fine people of Corpro Corp. are a frugal bunch. When they buy gifts, they
cooperate to collectively buy the least expensive gifts that they can. A cynic
might say that the employees are cheap, but if you asked them yourself, they'd
say it's the thought that counts.

There are **N** employees working at Corpro Corp., and each of them has a
manager, except for the CEO who has no manager (the CEO also buys a gift every
year, but she donates it to charity). The employees each have a unique
employee ID which is an integer from 1 to **N**. As you might expect, the CEO
has the ID 1.

If there exists a set of two or more employees {**p1**, ..., **pk**} such
that, for all **i** < **k**, **pi** is the manager of **pi+1**, then we say
that **p1** is "responsible for" **pk**. There are never two employees who are
responsible for each other. That would be a silly hierarchy indeed.

There are **N** kinds of gifts available for purchase, and the **i**th kind of
gift costs **i** dollars. That is, the prices of the different kinds of gifts
are {$1, $2, $3, ... $**N**}. There are **N** copies of each gift available
for purchase.

The only thing that stops all employees from purchasing gifts that cost $1 is
the awkwardness of buying a gift for their manager that's the same as the one
their manager is giving away. No employee would ever do such a thing!

For example, in a company with just 2 employees, at least $3 must be spent in
total. If employee #1 (the CEO) buys a $1 gift to donate to charity, then
employee #2 cannot buy a $1 gift for employee #1 (their manager), but they can
buy a $2 gift instead. Note that it would be equally optimal for the CEO to
buy a $2 gift, while receiving a $1 gift from her subordinate.

What's the minimum possible total expenditure across the whole company during
the gift exchange?

### Input

Input begins with an integer **T**, the number of corporate hierarchies to
consider. Each hierarchy is made up of two lines. The first line contains the
integer **N**. The second line contains **N** space-separated integers. The
**i**th integer is the employee ID of the manager of employee **i**, with the
exception that the first integer is always 0, denoting that the CEO has no
manager.

### Output

For the **i**th hierarchy, print a line containing "Case #**i**: " followed by
the smallest amount of money the entire company would need to spend.

### Constraints

1 ≤ **T** ≤ 100  
1 ≤ **N** ≤ 200,000  

**NOTE:** The input file is about 10-20MB. 

### Explanation of Sample

In the first test case, the CEO will spend $2, and the other employees will
spend $1.

In the second test case, employees #2 and #3 will spend $2, and the other
employees will spend $1.



Sample input:
5
3
0 1 1
8
0 1 1 2 2 3 3 3
5
0 1 2 3 4
9
0 1 2 3 4 5 5 5 5
8
0 1 1 1 1 2 2 2


Sample output:
Case #1: 4
Case #2: 10
Case #3: 7
Case #4: 12
Case #5: 11