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.InputStreamReader;
import java.io.IOException;
import java.util.Arrays;
import java.io.BufferedReader;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.util.StringTokenizer;
import java.io.InputStream;

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

class TaskB {
	public void solve(int testNumber, FastScanner in, PrintWriter out) {
		int n = in.nextInt();
		int s = in.nextInt();
		int len = in.nextInt();
		int[] a = new int[n];
		for (int i = 0; i < n; i++) {
			a[i] = in.nextInt();
		}
		int p = 0;
		int[] left = new int[n];
		int[] right = new int[n];
		MinMaxQueue q = new MinMaxQueue(n);
		for (int i = 0; i < n; i++) {
			while (p < n) {
				if (q.size() == 0) {
					q.add(a[p]);
					++p;
				} else if (Math.max(q.max(), a[p]) - Math.min(q.min(), a[p]) <= s) {
					q.add(a[p]);
					++p;
				} else {
					break;
				}
			}
			left[i] = i + len - 1;
			right[i] = p - 1;
			if (q.size() == 0) {
				throw new AssertionError();
			}
			q.pop();
		}
		int[] d = new int[n + 1];
		final int infinity = 1000000000;
		Arrays.fill(d, infinity);
		d[n] = 0;
		MinTree t = new MinTree(n + 1);
		t.set(n, d[n]);
		for (int i = n - 1; i >= 0; i--) {
			if (left[i] <= right[i] && left[i] < n) {
				d[i] = 1 + t.getMin(left[i] + 1, right[i] + 1);
			}
			t.set(i, d[i]);
		}
		if (d[0] > infinity / 2) {
			out.println(-1);
		} else {
			out.println(d[0]);
		}
	}

	class MinMaxQueue {
		int[] st1, st2;
		int[] min1, min2;
		int[] max1, max2;
		int p1, p2;

		MinMaxQueue(int n) {
			st1 = new int[n];
			st2 = new int[n];
			min1 = new int[n];
			min2 = new int[n];
			max1 = new int[n];
			max2 = new int[n];
			p1 = p2 = 0;
		}

		void add(int x) {
			st1[p1] = x;
			min1[p1] = x;
			max1[p1] = x;
			if (p1 > 0) {
				min1[p1] = Math.min(min1[p1], min1[p1 - 1]);
				max1[p1] = Math.max(max1[p1], max1[p1 - 1]);
			}
			++p1;
		}

		void update() {
			if (p2 == 0) {
				while (p1 > 0) {
					int x = st1[--p1];
					st2[p2] = x;
					min2[p2] = x;
					max2[p2] = x;
					if (p2 > 0) {
						min2[p2] = Math.min(min2[p2], min2[p2 - 1]);
						max2[p2] = Math.max(max2[p2], max2[p2 - 1]);
					}
					++p2;
				}
			}
		}
		int min() {
			int res = Integer.MAX_VALUE;
			if (p1 > 0 && res > min1[p1 - 1]) {
				res = min1[p1 - 1];
			}
			if (p2 > 0 && res > min2[p2 - 1]) {
				res = min2[p2 - 1];
			}
			return res;
		}
		int max() {
			int res = Integer.MIN_VALUE;
			if (p1 > 0 && res < max1[p1 - 1]) {
				res = max1[p1 - 1];
			}
			if (p2 > 0 && res < max2[p2 - 1]) {
				res = max2[p2 - 1];
			}
			return res;
		}
		void pop() {
			update();
			--p2;
		}
		int size() {
			return p1 + p2;
		}
	}

	class MinTree {
		int[] a;
		int n;
		MinTree(int size) {
			n = 1;
			while (n < size) {
				n *= 2;
			}
			a = new int[2 * n];
		}
		void set(int pos, int val) {
			pos += n;
			a[pos] = val;
			while (pos > 1) {
				pos /= 2;
				a[pos] = Math.min(a[2 * pos], a[2 * pos + 1]);
			}
		}
		int getMin(int l, int r) {
			if (l > r) {
				return 0;
			}
			l += n;
			r += n;
			if (l == r) {
				return a[l];
			}
			int lm = a[l];
			int rm = a[r];
			while (r - l > 1) {
				if (l % 2 == 0) {
					lm = Math.min(lm, a[l + 1]);
				}
				if (r % 2 == 1) {
					rm = Math.min(rm, a[r - 1]);
				}
				l /= 2;
				r /= 2;
			}
			return Math.min(lm, rm);
		}
	}

}

class FastScanner {

	private BufferedReader in;
	private StringTokenizer st;

	public FastScanner(InputStream stream) {
		in = new BufferedReader(new InputStreamReader(stream));
	}

	public String next() {
		while (st == null || !st.hasMoreTokens()) {
			try {
				String rl = in.readLine();
				if (rl == null) {
					return null;
				}
				st = new StringTokenizer(rl);
			} catch (IOException e) {
				throw new RuntimeException(e);
			}
		}
		return st.nextToken();
	}

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

}

