Grammy arrives on a planet inhabited by mythical creatures, including a species called Nailoong. Through her interactions, she discovers two rules:

• Nailoongs always lie.

• All other creatures may either tell the truth or lie.

There are $n$ creatures on the planet. The $i$-th creature claims: “The creature numbered $a_i$ is a Nailoong.”

Please determine the maximum possible number of Nailoongs among these creatures that could possibly exist under these rules.

Input

The first line of input contains one integer $n$ ($1\le n\le 10^5$).

The second line contains $n$ integers $a_1,a_2,\ldots,a_n$ ($1\le a_i\le n$), where the $i$-th creature claims that the $a_i$-th creature is a Nailoong.

Output

Output one integer, the maximum possible number of Nailoongs among these creatures that could possibly exist under these rules.

Examples

Input 1

6
4 1 1 5 6 5

Output 1

4