2009 Bulgarian Olympiad in Informatics

Task 2: Money-boxen

The programmer Pesho is a very thrifty person. The money which he earns from web-site design he stores in N money boxen (1 ≤ N ≤ 100,000), labeled by the integers from 1 to N. The intention of Pesho is to buy a new super-computer. In order to avoid the temptation to spend the money for rubbis, before the necessary sum is collected, he dropped all keys of the money-boxen in a random way inside the boxen themselves.

Fortunately, Pesho marked on a list of paper where the key for each money-box is stored. Now, the necessary money is finally collected and Pesho has to open all the money-boxen to take the money.

Unfortunately, no keys are available: Pesho must break the boxen! Pesho doesn't like breaking things, so he'd like to break as few boxen as possible. He realized that when a broken money-box contains a key of another money-box then the second money-box could be simply unlocked.

Write a program to determine the minimal number of money-boxen that have to be broken in order to collect all the stored money.

Input

The program has to solve two test cases for each run. Each test case starts with a line containing the number N of money-boxen. Then N lines follow with one integer from 1 to N - on the i^th line is the box in which the key for the i^th box is stored.

Output

Output the minimal number of boxen that must be broken.
Separate the numbers with a space.

Sample Input

4
2
1
2
4
3
3
3
3

Sample Output

2 1

Explanation

In the first test case the 4th box must be broken, because it contains its own key. Then, you can simply break the 1st box - it contains the key for box 2, which contains the key for box 3.

In the second case, you can just break box 3 to enter everything.

All Submissions
Best Solutions

Point Value: 20
Time Limit: 1.00s
Memory Limit: 32M
Added: May 10, 2009

Languages Allowed:
C++03, PAS, C, HASK, ASM, RUBY, PYTH2, JAVA, PHP, SCM, CAML, PERL, C#, C++11, PYTH3

Comments (Search)

It's quiet in here...