There are $M$ rows of benches in a classroom. $N$ students come to the classroom one-by-one and take a seat. Every student contains a preferred number. The rows are numbered from $1$ to $N$ and the maximum capacity of all the rows is $K$. The students come to the class in a sequential manner starting from $1$ to $N$ and follow these rules for the seating arrangement:

• Every student must sit in his or her preferred row (if the row is not full)
• If the preferred row is fully occupied, then the student must sit in the next vacant row (next row for $N$ will be $1$)
• If all the seats are occupied, then the student cannot sit anywhere.

Your task is to determine the total number of students who cannot sit in their preferred row.

Note: This includes the students that did not get a seat at all.

Input format

• First line: Three integers $N$, $M$, and $K$ that denotes the number of students, number of rows, and maximum capacity of a row respectively
• Next line: $N$ space-separated integers $A_{i}$ that denote the preferred row of the $i^{th}$ student

Output format

Print the total number of students who cannot sit in their preferred row.

Constraints

$1 ≤N, M ≤ 10^{5}$

$1 ≤ K ≤ 500$

$1 ≤ A_{i} ≤ M$