Recently, Tokitsukaze found an interesting game. Tokitsukaze had n items at the beginning of this game. However, she thought there were too many items, so now she wants to discard m (1 ≤ m ≤ n) special items of them.

These n items are marked with indices from 1 to n. In the beginning, the item with index i is placed on the i-th position. Items are divided into several pages orderly, such that each page contains exactly k positions and the last positions on the last page may be left empty.

Tokitsukaze would do the following operation: focus on the first special page that contains at least one special item, and at one time, Tokitsukaze would discard all special items on this page. After an item is discarded or moved, its old position would be empty, and then the item below it, if exists, would move up to this empty position. The movement may bring many items forward and even into previous pages, so Tokitsukaze would keep waiting until all the items stop moving, and then do the operation (i.e. check the special page and discard the special items) repeatedly until there is no item need to be discarded.

<image> Consider the first example from the statement: n=10, m=4, k=5, p=[3, 5, 7, 10]. The are two pages. Initially, the first page is special (since it is the first page containing a special item). So Tokitsukaze discards the special items with indices 3 and 5. After, the first page remains to be special. It contains [1, 2, 4, 6, 7], Tokitsukaze discards the special item with index 7. After, the second page is special (since it is the first page containing a special item). It contains [9, 10], Tokitsukaze discards the special item with index 10.

Tokitsukaze wants to know the number of operations she would do in total.

Input

The first line contains three integers n, m and k (1 ≤ n ≤ 10^{18}, 1 ≤ m ≤ 10^5, 1 ≤ m, k ≤ n) — the number of items, the number of special items to be discarded and the number of positions in each page.

The second line contains m distinct integers p_1, p_2, …, p_m (1 ≤ p_1 < p_2 < … < p_m ≤ n) — the indices of special items which should be discarded.

Output

Print a single integer — the number of operations that Tokitsukaze would do in total.

Examples

Input


10 4 5
3 5 7 10


Output


3


Input


13 4 5
7 8 9 10


Output


1

Note

For the first example:

  * In the first operation, Tokitsukaze would focus on the first page [1, 2, 3, 4, 5] and discard items with indices 3 and 5; 
  * In the second operation, Tokitsukaze would focus on the first page [1, 2, 4, 6, 7] and discard item with index 7; 
  * In the third operation, Tokitsukaze would focus on the second page [9, 10] and discard item with index 10. 



For the second example, Tokitsukaze would focus on the second page [6, 7, 8, 9, 10] and discard all special items at once.
import java.io.*;
import java.util.*;
public class tr3 {
	public static void main(String[] args) throws Exception {
		Scanner sc = new Scanner(System.in);
		PrintWriter out = new PrintWriter(System.out);
		long n=sc.nextLong();
		int m=sc.nextInt();
		long k=sc.nextLong();
		long []a=new long[m];
		for(int i=0;i<m;i++)
			a[i]=sc.nextLong();
		int ans=0;
		long shift=0;
		long page=1;
		for(int i=0;i<m;i++) {
			long c=0;
			int j=i;
			page=(a[j]-shift-1)/k+1;
			for(;j<m && (a[j]-shift-1)/k+1==page;j++) {
				c++;
			}
			shift+=c;
			i=j-1;
			//System.out.println(i+" "+shift+" "+page);
			ans++;
		}
		out.println(ans);
		out.flush();
	}
	static final double EPS = 1e-9;
static public class Circle { 	//equation: (x-c.x)^2 + (y-c.y)^2 = r^2

	static final double EPS = 1e-9;
	
	Point c;
	double r;

	Circle(Point p, double k) { c = p; r = k; }

	int inside(Point p)	//1 for inside, 0 for border, -1 for outside
	{
		double d = p.dist(c);

		return d + EPS < r ? 1 : Math.abs(d - r) < EPS ? 0 : -1;
	}

	double circum()	{ return 2 * Math.PI * r; }

	double area() { return Math.PI * r * r; }

	double arcLength(double deg) { return deg / 360.0 * circum(); }		//major and minor chords exist
	double sectorArea(double deg) { return deg / 360.0 * area(); }
	boolean intersect(Circle cir)
	{
		return c.dist(cir.c) <= r + cir.r + EPS && c.dist(cir.c) + EPS >= Math.abs(r - cir.r);
	}
	//returns true if the circle intersects with the line segment defined by p and q at one or two points
	boolean intersect(Point p, Point q)
	{
		Line l = new Line(p, q);
		if(Math.abs(l.b) < EPS)
		{
			if(l.c * l.c > r * r + EPS)
				return false;

			double y1 = Math.sqrt(Math.abs(r * r - l.c * l.c)), y2 = -y1;
			return new Point(-l.c, y1).between(p, q) && new Point(-l.c, y2).between(p, q);
		}
		double a = l.a * l.a + 1, b = 2 * l.a * l.c, c = l.c * l.c - r * r;
		if(b * b - 4 * a * c + EPS < 0)
			return false;

		double dis = b * b - 4 * a * c;

		double x1 = (-b + Math.sqrt(dis)) / (2.0 * a), x2 = (-b - Math.sqrt(dis)) / (2.0 * a);

		return new Point(x1, - l.a * x1 - l.c).between(p, q) || new Point(x2, - l.a * x2 - l.c).between(p, q);
	}

	static Point findCenter(Point p, Point q, double r)		//for the other center, swap p and q
	{
		double d2 = (p.x - q.x) * (p.x - q.x) + (p.y - q.y) * (p.y - q.y);
		double det = r * r / d2 - 0.25;
		if(Math.abs(det) < EPS)
			det = 0.0;
		if(det < 0.0)
			return null;
		double h = Math.sqrt(det);
		return new Point((p.x + q.x) / 2.0 + (p.y - q.y) * h, (p.y + q.y) / 2.0 + (q.x - p.x) * h);
	}

}	
static public class Line {

		static final double INF = 1e9, EPS = 1e-9;
		
		double a, b, c;
		
		Line(Point p, Point q)
		{
			if(Math.abs(p.x - q.x) < EPS) {	a = 1; b = 0; c = -p.x;	}
			else
			{
				a = (p.y - q.y) / (q.x - p.x);
				b = 1.0;
				c = -(a * p.x + p.y);
			}
						
		}
		
		Line(Point p, double m) { a = -m; b = 1; c =  -(a * p.x + p.y); } 
		
		boolean parallel(Line l) { return Math.abs(a - l.a) < EPS && Math.abs(b - l.b) < EPS; }
		
		boolean same(Line l) { return parallel(l) && Math.abs(c - l.c) < EPS; }
		
		Point intersect(Line l)
		{
			if(parallel(l))
				return null;
			double x = (b * l.c - c * l.b) / (a * l.b - b * l.a);
			double y;
			if(Math.abs(b) < EPS)
				 y = -l.a * x - l.c;
			else
				y = -a * x - c;
			
			return new Point(x, y);
		}
		
		Point closestPoint(Point p)
		{
			if(Math.abs(b) < EPS) return new Point(-c, p.y);
			if(Math.abs(a) < EPS) return new Point(p.x, -c);
			return intersect(new Line(p, 1 / a));
		}
				
	}  
static public class Point implements Comparable<Point>{

	static final double EPS = 1e-9;

	double x, y;                  

	Point(double a, double b) { x = a; y = b; }  
	
	public int compareTo(Point p)
	{
		if(Math.abs(x - p.x) > EPS) return x > p.x ? 1 : -1;
		if(Math.abs(y - p.y) > EPS) return y > p.y ? 1 : -1;
		return 0;
	}
	public String toString () {
		return x+" "+y;
	}
	public double dist(Point p) { return Math.sqrt(sq(x - p.x) + sq(y - p.y)); }
	
	static double sq(double x) { return x * x; }
	
	Point rotate(double angle)
	{
		double c = Math.cos(angle), s = Math.sin(angle);
		return new Point(x * c - y * s, x * s + y * c);
	}
	// for integer points and rotation by 90 (counterclockwise) : swap x and y, negate x
	boolean between(Point p, Point q)
	{
		return x < Math.max(p.x, q.x) + EPS && x + EPS > Math.min(p.x, q.x)
				&& y < Math.max(p.y, q.y) + EPS && y + EPS > Math.min(p.y, q.y);
	}
}
	static class Scanner {
		StringTokenizer st;
		BufferedReader br;

		public Scanner(InputStream system) {
			br = new BufferedReader(new InputStreamReader(system));
		}

		public Scanner(String file) throws Exception {
			br = new BufferedReader(new FileReader(file));
		}

		public String next() throws IOException {
			while (st == null || !st.hasMoreTokens())
				st = new StringTokenizer(br.readLine());
			return st.nextToken();
		}

		public String nextLine() throws IOException {
			return br.readLine();
		}

		public int nextInt() throws IOException {
			return Integer.parseInt(next());
		}

		public double nextDouble() throws IOException {
			return Double.parseDouble(next());
		}

		public char nextChar() throws IOException {
			return next().charAt(0);
		}

		public Long nextLong() throws IOException {
			return Long.parseLong(next());
		}

		public boolean ready() throws IOException {
			return br.ready();
		}

		public void waitForInput() throws InterruptedException {
			Thread.sleep(3000);
		}
	}
}