Problem:
Score : 300 points

Problem Statement

You are given a sequence of positive integers of length N, a = (a_1, a_2, ..., a_N).
Your objective is to remove some of the elements in a so that a will be a good sequence.

Here, an sequence b is a good sequence when the following condition holds true:

For each element x in b, the value x occurs exactly x times in b.

For example, (3, 3, 3), (4, 2, 4, 1, 4, 2, 4) and () (an empty sequence) are good sequences, while (3, 3, 3, 3) and (2, 4, 1, 4, 2) are not.

Find the minimum number of elements that needs to be removed so that a will be a good sequence.

Constraints

1 \leq N \leq 10^5

a_i is an integer.

1 \leq a_i \leq 10^9

Input

Input is given from Standard Input in the following format:

N
a_1 a_2 ... a_N

Output

Print the minimum number of elements that needs to be removed so that a will be a good sequence.

Sample Input 1

4
3 3 3 3

Sample Output 1

1

We can, for example, remove one occurrence of 3. Then, (3, 3, 3) is a good sequence.

Sample Input 2

5
2 4 1 4 2

Sample Output 2

2

We can, for example, remove two occurrences of 4. Then, (2, 1, 2) is a good sequence.

Sample Input 3

6
1 2 2 3 3 3

Sample Output 3

0

Sample Input 4

1
1000000000

Sample Output 4

1

Remove one occurrence of 10^9. Then, () is a good sequence.

Sample Input 5

8
2 7 1 8 2 8 1 8

Sample Output 5

5

Solution in Kotlin (1.0.0) (judge verdict: Accepted)

fun main(args: Array<String>) {
    val n = readLine()?.toInt() ?: return

    // a値とその個数のmapにする
    // この時点で、a = 個数 のものは除外しておく
    val aMap: Map<Long, Long> = readLine()
        ?.split(" ")
        ?.map { it.toLong() }
        ?.groupBy { it }
        ?.mapValues { it.value.size.toLong() }
        ?.filter { it.key != it.value }
        ?: return

    // a値の個数がa以下の場合には、aはすべて削除する必要がある
    val less: Long = aMap
        .filter { it.key > it.value }
        .values
        .sum()

    // a値の個数がa以上の場合には、(個数-a）個を削除する必要がある
    val more: Long = aMap
        .filter { it.key < it.value }
        .map { it.value - it.key }
        .sum()

    println(less + more)
}