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.ByteArrayInputStream;
import java.io.File;
import java.io.FileInputStream;
import java.io.FileNotFoundException;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.nio.charset.StandardCharsets;
import java.util.Arrays;
import java.util.InputMismatchException;
import java.util.TreeMap;

public class B487 {

	static class Solver {

		int N, S, L, a[], f[], memo[];

		void solve(FastScanner s, PrintWriter out) {
			N = s.nextInt();
			S = s.nextInt();
			L = s.nextInt();
			a = s.nextIntArray(N);

			f = new int[N];
			TreeMap<Integer, Integer> mts = new TreeMap<>();
			mts.put(a[0], 1);
			int q = 1;
			for (int p = 0; p < N; p++) {
				while (q < N && (q <= p || (a[q] - mts.firstKey() <= S && mts.lastKey() - a[q] <= S))) {
					mts.put(a[q], mts.getOrDefault(a[q], 0) + 1);
					q++;
				}
				if (mts.lastKey() - mts.firstKey() <= S && q - p >= L)
					f[p] = q;
				else
					f[p] = -1;
				int rem = a[p];
				if (mts.put(rem, mts.get(rem) - 1) == 1)
					mts.remove(rem);
			}

			Node st = new Node(0, N);
			st.set(N, 0);
			for (int i = N - L; i >= 0; i--) {
				int l = i + L, r = f[i];
				if (r < l)
					continue;
				st.set(i, 1 + st.rmin(l, r));
			}

			int ans = st.get(0);
			out.println(ans > N ? -1 : ans);

		}

		class Node {

			int l, m, r, min, oo = 987654321;
			Node L, R;

			Node(int ll, int rr) {
				l = ll;
				r = rr;
				m = l + (r - l) / 2;
				min = oo;
				if (ll == rr)
					return;
				L = new Node(l, m);
				R = new Node(m + 1, r);
			}

			int set(int x, int v) {
				if (l == x && r == x) {
					return min = v;
				}
				if (x <= m)
					return min = min(min, L.set(x, v));
				else
					return min = min(min, R.set(x, v));
			}

			int get(int x) {
				if (l == x && r == x)
					return min;
				return x <= m ? L.get(x) : R.get(x);
			}

			int rmin(int s, int e) {
				if (s <= l && r <= e)
					return min;
				int min = oo;
				if (s <= m)
					min = min(min, L.rmin(s, e));
				if (m < e)
					min = min(min, R.rmin(s, e));
				return min;
			}

		}

		int min(int a, int b) {
			return a < b ? a : b;
		}

	}

	public static void main(String[] args) {

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

		Solver solver = new Solver();
		solver.solve(s, out);

		out.close();

	}

	static int swap(int a, int b) {
		return a;
	}

	static Object swap(Object a, Object b) {
		return a;
	}

	static String ts(Object... o) {
		return Arrays.deepToString(o);
	}

	static class FastScanner {
		private InputStream stream;
		private byte[] buf = new byte[1024];
		private int curChar;
		private int numChars;

		public FastScanner(InputStream stream) {
			this.stream = stream;
		}

		public FastScanner(File f) throws FileNotFoundException {
			this(new FileInputStream(f));
		}

		public FastScanner(String s) {
			this.stream = new ByteArrayInputStream(s.getBytes(StandardCharsets.UTF_8));
		}

		int read() {
			if (numChars == -1)
				throw new InputMismatchException();
			if (curChar >= numChars) {
				curChar = 0;
				try {
					numChars = stream.read(buf);
				} catch (IOException e) {
					throw new InputMismatchException();
				}
				if (numChars <= 0)
					return -1;
			}
			return buf[curChar++];
		}

		boolean isSpaceChar(int c) {
			return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
		}

		boolean isEndline(int c) {
			return c == '\n' || c == '\r' || c == -1;
		}

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

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

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

		public String next() {
			int c = read();
			while (isSpaceChar(c))
				c = read();
			StringBuilder res = new StringBuilder();
			do {
				res.appendCodePoint(c);
				c = read();
			} while (!isSpaceChar(c));
			return res.toString();
		}

		public String nextLine() {
			int c = read();
			while (isEndline(c))
				c = read();
			StringBuilder res = new StringBuilder();
			do {
				res.appendCodePoint(c);
				c = read();
			} while (!isEndline(c));
			return res.toString();
		}

		// Jacob Garbage

		public int[] nextIntArray(int N) {
			int[] ret = new int[N];
			for (int i = 0; i < N; i++)
				ret[i] = this.nextInt();
			return ret;
		}

		public int[][] next2DIntArray(int N, int M) {
			int[][] ret = new int[N][];
			for (int i = 0; i < N; i++)
				ret[i] = this.nextIntArray(M);
			return ret;
		}

		public long[] nextLongArray(int N) {
			long[] ret = new long[N];
			for (int i = 0; i < N; i++)
				ret[i] = this.nextLong();
			return ret;
		}

		public long[][] next2DLongArray(int N, int M) {
			long[][] ret = new long[N][];
			for (int i = 0; i < N; i++)
				ret[i] = nextLongArray(M);
			return ret;
		}

		public double[] nextDoubleArray(int N) {
			double[] ret = new double[N];
			for (int i = 0; i < N; i++)
				ret[i] = this.nextDouble();
			return ret;
		}

		public double[][] next2DDoubleArray(int N, int M) {
			double[][] ret = new double[N][];
			for (int i = 0; i < N; i++)
				ret[i] = this.nextDoubleArray(M);
			return ret;
		}

	}

}