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.util.Scanner;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.io.IOException;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 * @author about@manhquynh.net
 */
public class Main {
	public static void main(String[] args) {
		InputStream inputStream = System.in;
		OutputStream outputStream = System.out;
		Scanner in = new Scanner(inputStream);
		PrintWriter out = new PrintWriter(outputStream);
		TaskD solver = new TaskD();
		solver.solve(1, in, out);
		out.close();
	}
}

class TaskD {
    int n, s, l, MinValue, MaxValue;
    int[] a;
    int[] optimize;
    Node[] IntervalTree;

    class Node<A, B> {
        int A;
        int B;
        Node(int A, int B) {
            this.A = A;
            this.B = B;
        }
    }

    void buildIntervalTree(int node, int left, int right) {
        if (left == right) {
            IntervalTree[node].A = a[left];
            IntervalTree[node].B = a[left];
            return;
        }
        int mid = (left + right) >> 1;
        buildIntervalTree(node * 2, left, mid);
        buildIntervalTree(node * 2 + 1, mid + 1, right);
        IntervalTree[node].A = Math.max(IntervalTree[node * 2].A, IntervalTree[node * 2 + 1].A);
        IntervalTree[node].B = Math.min(IntervalTree[node * 2].B, IntervalTree[node * 2 + 1].B);
    }

    void QueryIntervalTree(int node, int left, int right, int realleft, int realright) {
        if (realleft > right || realright < left)
            return;
        if (realleft <= left && right <= realright) {
            MaxValue = Math.max(MaxValue, IntervalTree[node].A);
            MinValue = Math.min(MinValue, IntervalTree[node].B);
            return;
        }
        int mid = (left + right) >> 1;
        QueryIntervalTree(node * 2, left, mid, realleft, realright);
        QueryIntervalTree(node * 2 + 1, mid + 1, right, realleft, realright);
    }

    public void solve(int testNumber, Scanner in, PrintWriter out) {
        n = in.nextInt();
        s = in.nextInt();
        l = in.nextInt();
        a = new int[n + 1];
        optimize = new int[n + 1];
        IntervalTree = new Node[n * 4 + 1];
        for (int i = 1; i <= n * 4; ++i)
            IntervalTree[i] = new Node(0, 0);
        for (int i = 1; i <= n; ++i)
            a[i] = in.nextInt();
        buildIntervalTree(1, 1, n);
        int dequeue[] = new int[n + 1];
        int head = 1;
        int tail = 0;
        for (int i = l; i <= n; ++i) {
            int left = 1;
            int right = i - l + 1;
            int front = -1;
            while (left <= right) {
                int mid = (left + right) >> 1;
                MaxValue = -2000000000;
                MinValue = 2000000000;
                QueryIntervalTree(1, 1, n, mid, i);
                if (Math.abs(MaxValue - MinValue) <= s) {
                    front = mid;
                    right = mid - 1;
                } else
                    left = mid + 1;

            }
//            out.println( (front - 1) + " " + (i - l));
            if (front == -1)
                continue;
            --front;
            if (i == l ||optimize[i - l] != 0) {
                while (tail >= head && optimize[dequeue[tail]] >= optimize[i - l])
                    --tail;
                dequeue[++tail] = i - l;
            }
//            out.print("E ");
            while (tail >= head && dequeue[head] < front)
                ++head;
//            for (int j = head; j <= tail; ++j)
//                out.print(dequeue[j] + " ");
//            out.println();
            if (head <= tail)
                optimize[i] = optimize[dequeue[head]] + 1;

        }
        if (optimize[n] == 0)
            out.println(-1);
        else
            out.println(optimize[n]);
    }
}

