Shane has just become a new swimming coach. One may even say he is very qual-leaf-fied for the job, since he has won several swimming competitions. However, because he is 16, he can only coach little children.

Shane has ~N~ potential children he can coach for money. However, he must prove to the child's parent that he is qual-leaf-fied to teach. Shane will only be able to coach the ~i^{th}~ child if their parent sees that Shane has coached at least ~A_i~ children.

Shane is poor, so he wants to teach all ~N~ children for money. He has no experience, so he decides to teach ~K~ other children for free first to rack up experience. Shane is also lazy, so he wants to know what the minimum value of ~K~ is, so he can earn money as soon as possible.

Constraints

~1 \le N \le 10^6~

~0 \le A_i \le 10^9~

Input Specification

The first line will contain a single integer ~N~, the number of potential children Shane can coach for money.

The next line will contain ~A~, represented by ~N~ space-separated integers. ~A_i~ is the minimum amount of children Shane must coach to be qual-leaf-fied to teach the ~i^{th}~ child.

Output Specification

Output ~K~, the minimum amount of children Shane must coach for free in order to coach all ~N~ children for money.

Sample Input 1

5
5 3 1 2 3

Sample Output 1

1

Sample Explanation 1

If Shane teaches one child for free, he can teach the ~3^{rd}~ child for money, while also gaining another coaching experience. Then, he can teach the ~4^{th}~ child he now has coached two children. He can then coach the ~5^{th}~ and ~2^{nd}~ child, before finally teaching the ~1^{st}~ child. Note that if Shane does not coach one child for free, he cannot teach any of the ~N~ children for money.

Sample Input 2

20
2 3 53 6 12 6 3 21 6 2 3 42 2 6 12 3 5 6 1 34

Sample Output 2

34