Friendly Rabbits

There are N rabbits, numbered 1 through N.

The i-th (1≤i≤N) rabbit likes rabbit a_i. Note that no rabbit can like itself, that is, a_i≠i.

For a pair of rabbits i and j (i＜j), we call the pair (i，j) a friendly pair if the following condition is met.

• Rabbit i likes rabbit j and rabbit j likes rabbit i.

Calculate the number of the friendly pairs.

Constraints

• 2≤N≤10^5
• 1≤a_i≤N
• a_i≠i

Input

The input is given from Standard Input in the following format:

N a_1 a_2 ... a_N

Output

Print the number of the friendly pairs.

Examples

Input

4 2 1 4 3

Output

2

Input

3 2 3 1

Output

0

Input

5 5 5 5 5 1

Output

1

inputFormat

Input

The input is given from Standard Input in the following format:

N a_1 a_2 ... a_N

outputFormat

Output

Print the number of the friendly pairs.

Examples

Input

4 2 1 4 3

Output

2

Input

3 2 3 1

Output

0

Input

5 5 5 5 5 1

Output

1

样例

3
2 3 1

0