Alexandra has a paper strip with n numbers on it. Let's call them ai from left to right.

Now Alexandra wants to split it into some pieces (possibly 1). For each piece of strip, it must satisfy:

  * Each piece should contain at least l numbers.
  * The difference between the maximal and the minimal number on the piece should be at most s.



Please help Alexandra to find the minimal number of pieces meeting the condition above.

Input

The first line contains three space-separated integers n, s, l (1 ≤ n ≤ 105, 0 ≤ s ≤ 109, 1 ≤ l ≤ 105).

The second line contains n integers ai separated by spaces ( - 109 ≤ ai ≤ 109).

Output

Output the minimal number of strip pieces.

If there are no ways to split the strip, output -1.

Examples

Input

7 2 2
1 3 1 2 4 1 2


Output

3


Input

7 2 2
1 100 1 100 1 100 1


Output

-1

Note

For the first sample, we can split the strip into 3 pieces: [1, 3, 1], [2, 4], [1, 2].

For the second sample, we can't let 1 and 100 be on the same piece, so no solution exists.
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.Stack;
import java.util.StringTokenizer;



public class Abood2C {


	public static void main(String[] args) throws IOException {
		Scanner sc = new Scanner(System.in);
		PrintWriter out = new PrintWriter(System.out);

		int n = sc.nextInt();
		int s = sc.nextInt();
		int l = sc.nextInt();

		int[] a = new int[n];

		for (int i = 0; i < n; i++)
			a[i] = sc.nextInt();
		
		int res = -1;
		for (int k = 0; k < 2; k++) {
			Stack<ArrayList<Integer>> stack = new Stack<>();

			int min = 0;
			int max = 0;

			for (int i = 0; i < n; i++) {
				if(stack.isEmpty() || a[i] > min && a[i] - min > s || a[i] < max && max - a[i] > s) {
					ArrayList<Integer> cur = new ArrayList<>();
					cur.add(a[i]);
					stack.push(cur);
					min = a[i];
					max = a[i];
				} else {
					stack.peek().add(a[i]);
					min = Math.min(min, a[i]);
					max = Math.max(max, a[i]);
				}
			}

			int ans = 0;
			boolean f = true;
			while(!stack.isEmpty() && f) {
				ArrayList<Integer> cur = stack.pop();
				if(cur.size() == 0)
					continue;

				int maxC = cur.get(0);
				int minC = maxC;

				for (int i = 1; i < cur.size(); i++) {
					minC = Math.min(minC, cur.get(i));
					maxC = Math.max(maxC, cur.get(i));
				}

				while(cur.size() < l){
					if(stack.isEmpty() && cur.size() >= l)
						break;

					if(stack.isEmpty()) {
						f = false;
						break;
					}


					ArrayList<Integer> nxt = stack.peek();
					if(nxt.size() == 0) {
						stack.pop();
						continue;
					}

					if(nxt.get(nxt.size() - 1) > minC && nxt.get(nxt.size() - 1) - minC > s || nxt.get(nxt.size() - 1) < maxC && maxC - nxt.get(nxt.size() - 1) > s) {
						f = false;
						break;
					}
					int N = nxt.remove(nxt.size() - 1);
					cur.add(N);
					maxC = Math.max(maxC, N);
					minC = Math.min(minC, N);
				}
				if(!f) {
					ans = -1;
					break;
				}
				ans++;

			}

			res = Math.max(ans, res);

			int[] tmp = new int[n];
			for (int i = 0; i < n; i++)
				tmp[i] = a[n - i - 1];
			a = tmp;
		}

		out.println(res);

		out.flush();
		out.close();
	}




	static class Scanner 



	{
		StringTokenizer st;
		BufferedReader br;

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

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

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

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

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


		public double nextDouble() throws IOException
		{
			String x = next();
			StringBuilder sb = new StringBuilder("0");
			double res = 0, f = 1;
			boolean dec = false, neg = false;
			int start = 0;
			if(x.charAt(0) == '-')
			{
				neg = true;
				start++;
			}
			for(int i = start; i < x.length(); i++)
				if(x.charAt(i) == '.')
				{
					res = Long.parseLong(sb.toString());
					sb = new StringBuilder("0");
					dec = true;
				}
				else
				{
					sb.append(x.charAt(i));
					if(dec)
						f *= 10;
				}
			res += Long.parseLong(sb.toString()) / f;
			return res * (neg?-1:1);
		}

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



	}

}