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.*;
import java.util.*;

public class CF {
	FastScanner in;
	PrintWriter out;

	int it;

	class O implements Comparable<O> {
		int id;
		int value;

		O(int value) {
			id = it++;
			this.value = value;
		}

		@Override
		public int compareTo(O o) {
			return value == o.value ? Integer.compare(id, o.id) : Integer
					.compare(value, o.value);
		}
	}

	class SegmentTree {
		int[] min;

		SegmentTree(int n) {
			min = new int[n * 4];
			Arrays.fill(min, Integer.MAX_VALUE);
		}

		int get(int v, int l, int r, int needL, int needR) {
			if (needL > needR) {
				return Integer.MAX_VALUE;
			}
			if (l == needL && r == needR) {
				return min[v];
			}
			int mid = (l + r) >> 1;
			int res = get(v * 2 + 1, l, mid, needL, Math.min(needR, mid));
			res = Math
					.min(res,
							get(v * 2 + 2, mid + 1, r,
									Math.max(needL, mid + 1), needR));
			return res;
		}

		void set(int v, int l, int r, int pos, int value) {
			if (l == r) {
				min[v] = value;
			} else {
				int mid = (l + r) >> 1;
				if (mid >= pos) {
					set(v * 2 + 1, l, mid, pos, value);
				} else {
					set(v * 2 + 2, mid + 1, r, pos, value);
				}
				min[v] = Math.min(min[v * 2 + 1], min[v * 2 + 2]);
			}
		}
	}

	void solve() {
		int n = in.nextInt();
		int s = in.nextInt();
		int l = in.nextInt();
		O[] a = new O[n];
		for (int i = 0; i < n; i++) {
			a[i] = new O(in.nextInt());
		}
		SegmentTree st = new SegmentTree(n + 1);
		st.set(0, 0, n, 0, 0);
		int from = 0;
		TreeSet<O> ts = new TreeSet<>();
		for (int i = 0; i < n; i++) {
			ts.add(a[i]);
			while (ts.last().value - ts.first().value > s) {
				ts.remove(a[from++]);
			}
			int max = i - l + 1;
			int res = st.get(0, 0, n, from, max);
			if (res != Integer.MAX_VALUE) {
				st.set(0, 0, n, i + 1, res + 1);
			}
		}
		int result = st.get(0, 0, n, n, n);
		out.println(result == Integer.MAX_VALUE ? -1 : result);
	}

	void run() {
		try {
			in = new FastScanner(new File("CF.in"));
			out = new PrintWriter(new File("CF.out"));

			solve();

			out.close();
		} catch (FileNotFoundException e) {
			e.printStackTrace();
		}
	}

	void runIO() {

		in = new FastScanner(System.in);
		out = new PrintWriter(System.out);

		solve();

		out.close();
	}

	class FastScanner {
		BufferedReader br;
		StringTokenizer st;

		public FastScanner(File f) {
			try {
				br = new BufferedReader(new FileReader(f));
			} catch (FileNotFoundException e) {
				e.printStackTrace();
			}
		}

		public FastScanner(InputStream f) {
			br = new BufferedReader(new InputStreamReader(f));
		}

		String next() {
			while (st == null || !st.hasMoreTokens()) {
				String s = null;
				try {
					s = br.readLine();
				} catch (IOException e) {
					e.printStackTrace();
				}
				if (s == null)
					return null;
				st = new StringTokenizer(s);
			}
			return st.nextToken();
		}

		boolean hasMoreTokens() {
			while (st == null || !st.hasMoreTokens()) {
				String s = null;
				try {
					s = br.readLine();
				} catch (IOException e) {
					e.printStackTrace();
				}
				if (s == null)
					return false;
				st = new StringTokenizer(s);
			}
			return true;
		}

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

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

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

	public static void main(String[] args) {
		new CF().runIO();
	}
}