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Rabbits In The Forest

1. There are some rabbits in the forest and each rabbit has some color. 2. Some(possibly all) rabbits are selected from them and they tell you about the number of other rabbits having the same color as them. 3. You are given an array(arr) that contains the answers of all selected rabbits. 4. You have to find the minimum number of rabbits that could be in the forest.

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Rabbits In The Forest

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1. There are some rabbits in the forest and each rabbit has some color. 2. Some(possibly all) rabbits are selected from them and they tell you about the number of other rabbits having the same color as them. 3. You are given an array(arr) that contains the answers of all selected rabbits. 4. You have to find the minimum number of rabbits that could be in the forest.

Constraints

1 <= N <= 1000 0 <= arr[i] <= 1000

Format

Input

A number N arr1 arr2.. N numbers

Output

A number representing the minimum number of rabbits in the forest.

Example

Sample Input

5 1 0 1 0 0

Sample Output

5

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