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.awt.print.Book;
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.lang.Thread.State;
import java.math.BigInteger;
import java.nio.file.attribute.AclEntry.Builder;
import java.util.Arrays;
import java.util.StringTokenizer;
import java.util.TreeSet;
import javax.print.CancelablePrintJob;
import javax.swing.text.DefaultEditorKit.InsertBreakAction;

public class A {
	final static int MAX = 1000000000;
	final static int MOD = 1000000007;
	static int arr[];
	static int min_sgTree[];
	static int max_sgTree[];
	static int min_dp[];

	public static void main(String[] args) throws IOException {
		br = new BufferedReader(new InputStreamReader(System.in));
		out = new PrintWriter(System.out);
		sc = new StringTokenizer("");
		min_sgTree = new int[262144];
		max_sgTree = new int[262144];
		min_dp = new int[262144];

		Arrays.fill(min_dp, MAX + 2);
		Arrays.fill(min_sgTree, MAX + 2);
		Arrays.fill(max_sgTree, -MAX - 2);

		int n, s, l;
		n = nxtInt();
		s = nxtInt();
		l = nxtInt();
		arr = nxtIntArr(n);
		if (l > n) {
			out.print(-1);
			br.close();
			out.close();
			return;

		}
		if (n == 1) {
			out.print(l == 1 ? 1 : -1);
			br.close();
			out.close();
			return;
		}
		int dp[] = new int[n];
		int First[] = new int[n];
		Arrays.fill(dp, MAX + 2);
		Arrays.fill(First, MAX + 2);
		build(1, 0, n - 1);

		int l1 = 0, r = l - 1;
		while (r < n) {

			int Max = getMax(1, 0, n - 1, l1, r);
			int Min = getMin(1, 0, n - 1, l1, r);
			if (r - l1 + 1 < l) {
				r++;
				continue;
			}
			if (Max - Min <= s) {
				First[r] = l1;
				r++;
			} else
				l1++;
		}
		// for (int i = 0; i < First.length; i++) {
		// System.out.print(First[i] + " ");
		// }
		// System.out.println();
		for (int i = 0; i < l - 1; i++)
			Insert(1, 0, n - 1, i, i, dp[i]);

		for (int i = l - 1; i < n; i++) {
			if (First[i] - 1 >= 0 && i - l >= 0 && i - First[i] + 1 >= l) {
				int c = getMinDp(1, 0, n - 1, First[i] - 1, i - l);
				dp[i] = c == MAX + 2 ? c : c + 1;

				Insert(1, 0, n - 1, i, i, dp[i]);

			} else if (First[i] == 0) {
				dp[i] = 1;
				Insert(1, 0, n - 1, i, i, dp[i]);
			}

		}

		out.print(dp[n - 1] == MAX + 2 ? -1 : dp[n - 1]);

		br.close();
		out.close();
	}

	private static int getMinDp(int node, int l, int r, int i, int j) {
		if (l >= i && r <= j)
			return min_dp[node];

		if (i > (l + r) / 2)
			return getMinDp(node * 2 + 1, (l + r) / 2 + 1, r, i, j);
		else if (j <= (l + r) / 2)
			return getMinDp(node * 2, l, (l + r) / 2, i, j);
		else {
			return Math.min(getMinDp(node * 2, l, (l + r) / 2, i, j),
					getMinDp(node * 2 + 1, (l + r) / 2 + 1, r, i, j));
		}

	}

	private static void Insert(int node, int l, int r, int i, int j, int value) {

		if (l >= i && r <= j) {
			min_dp[node] = value;
			return;
		}

		if (i > (l + r) / 2)
			Insert(node * 2 + 1, (l + r) / 2 + 1, r, i, j, value);
		else
			Insert(node * 2, l, (l + r) / 2, i, j, value);

		min_dp[node] = Math.min(min_dp[node * 2], min_dp[node * 2 + 1]);

	}

	private static void build(int node, int l, int r) {
		if (l == r) {
			min_sgTree[node] = arr[l];
			max_sgTree[node] = arr[l];
			return;
		}
		build(node * 2, l, (l + r) / 2);
		build(node * 2 + 1, (l + r) / 2 + 1, r);
		min_sgTree[node] = Math.min(min_sgTree[node * 2],
				min_sgTree[node * 2 + 1]);
		max_sgTree[node] = Math.max(max_sgTree[node * 2],
				max_sgTree[node * 2 + 1]);

	}

	private static int getMin(int node, int l, int r, int i, int j) {
		// TODO Auto-generated method stub

		if (l >= i && r <= j)
			return min_sgTree[node];

		if (i > (l + r) / 2)
			return getMin(node * 2 + 1, (l + r) / 2 + 1, r, i, j);
		else if (j <= (l + r) / 2)
			return getMin(node * 2, l, (l + r) / 2, i, j);
		else {
			return Math.min(getMin(node * 2, l, (l + r) / 2, i, j),
					getMin(node * 2 + 1, (l + r) / 2 + 1, r, i, j));
		}

	}

	private static int getMax(int node, int l, int r, int i, int j) {
		if (l >= i && r <= j)
			return max_sgTree[node];

		if (i > (l + r) / 2)
			return getMax(node * 2 + 1, (l + r) / 2 + 1, r, i, j);
		else if (j <= (l + r) / 2)
			return getMax(node * 2, l, (l + r) / 2, i, j);
		else {
			return Math.max(getMax(node * 2, l, (l + r) / 2, i, j),
					getMax(node * 2 + 1, (l + r) / 2 + 1, r, i, j));
		}
	}

	static String nxtTok() throws IOException {
		while (!sc.hasMoreTokens()) {
			String s = br.readLine();
			if (s == null)
				return null;
			sc = new StringTokenizer(s.trim());
		}
		return sc.nextToken();
	}

	static BufferedReader br;
	static StringTokenizer sc;
	static PrintWriter out;

	static int nxtInt() throws IOException {
		return Integer.parseInt(nxtTok());
	}

	static long nxtLng() throws IOException {
		return Long.parseLong(nxtTok());
	}

	static double nxtDbl() throws IOException {
		return Double.parseDouble(nxtTok());
	}

	static int[] nxtIntArr(int n) throws IOException {
		int[] a = new int[n];
		for (int i = 0; i < n; i++)
			a[i] = nxtInt();
		return a;
	}

	static long[] nxtLngArr(int n) throws IOException {
		long[] a = new long[n];
		for (int i = 0; i < n; i++)
			a[i] = nxtLng();
		return a;
	}

	static char[] nxtCharArr() throws IOException {
		return nxtTok().toCharArray();
	}

}