Alice has recently found an array a containing N integers. As we all know Alice loves sorted array so, he wants to sort the array. To sort an array Alice can add 1 to any integer in the array in 1 move.

Alice wants to find minimum number of moves needed to sort this array. Remember that after sorting the array, all elements in it should be distinct.

INPUT CONSTRAINTS

• \(1 \le N \le 10^5\)
• \(1 \le a_i \le 10^6\)

INPUT FORMAT
First line of input contains a single integer N.
Second line of input contains N space separated inegers, elements of array a.

OUTPUT FORMAT
Output a single integer, denoting number of moves needed to sort the given array.