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.math.*;
import java.security.KeyStore.Entry;
import java.util.*;

public class CODEFORCES {
	private InputStream is;
	private PrintWriter out;

	long a[] = new long[(int) 1e6], b[] = new long[(int) 1e6];

	void update(int l, int r, int c, int ind, int val) {
		if (l == r) {
			a[c] = val;
			b[c] = val;
			return;
		}
		int mid = l + r >> 1;
		if (mid >= ind)
			update(l, mid, 2 * c + 1, ind, val);
		else
			update(mid + 1, r, 2 * c + 2, ind, val);
		a[c] = Math.min(a[2 * c + 1], a[2 * c + 2]);
		b[c] = Math.max(b[2 * c + 1], b[2 * c + 2]);
	}

	long max(int l, int r, int c, int x, int y) {
		if (l > r || x > y || l > y || x > r)
			return Integer.MIN_VALUE;
		if (x <= l && y >= r)
			return b[c];
		int mid = l + r >> 1;
		return Math.max(max(l, mid, 2 * c + 1, x, y), max(mid + 1, r, 2 * c + 2, x, y));
	}

	long min(int l, int r, int c, int x, int y) {
		if (l > r || x > y || l > y || x > r)
			return Integer.MAX_VALUE;
		if (x <= l && y >= r)
			return a[c];
		int mid = l + r >> 1;
		return Math.min(min(l, mid, 2 * c + 1, x, y), min(mid + 1, r, 2 * c + 2, x, y));
	}


	void solve() {
		int n = ni(), s = ni(), l = ni();
		int arr[] = new int[n];
		Arrays.fill(b, Integer.MIN_VALUE);
		Arrays.fill(a, Integer.MAX_VALUE);
		for (int i = 0; i < n; i++)
			arr[i] = ni();
		if (n < l) {
			out.println("-1");
			return;
		}
		int dp[] = new int[n], cou = 0;
		boolean u[] = new boolean[n];
		int pre[] = new int[n];
		int va[] = new int[n],nm = 0;
		for(int i=0;i<n;i++)
			va[i] = -1;
		for (int i = 0; i < n; i++) {
			update(0, n - 1, 0, i, arr[i]);
			int x = 0, y = i, tem = i;
			while (x <= y) {
				int mid = x + y >> 1;
				long ma = max(0, n - 1, 0, mid, i);
				long mi = min(0, n - 1, 0, mid, i);
				if (Math.abs(ma - mi) <= s) {
					y = mid - 1;
					tem = mid;
				} else {
					x = mid + 1;
				}
			}
			//out.println(tem+" "+arr[tem]+" "+i);
			if (i + 1 - tem >= l) {
				cou = 0;
				if(va[tem]!=-1){
					int ki = va[tem];
					if(pre[ki]==tem||tem==0||u[ki-1]||(tem!=0&&u[tem-1])){
						pre[i] = tem;
						u[i] = true;
						//out.println("if "+i);
					}
					else{
						tem=ki+1;
						if(i+1-tem>=l){
							u[i] = true;
							pre[i] = tem;
							//out.println("el "+i);
						}
					}
				}
				else{
					u[i] = true;
					pre[i] = tem;
				}
				if(u[i]){
					//out.println(i);
					for(int j=nm+1;j<=i;j++)
						va[j] = i;
					nm = i;
				}
			} else
				cou++;
			if (cou == l) {
				out.println("-1");
				return;
			}
			dp[i] = (tem != 0 ? dp[tem - 1] : 0) + 1;
		}
		int max = 0;
		for(int i=n-1;i>=0;i--){
			if(u[i]&&max>=0)
				max = i-pre[i];
			else
				max--;
			if(max<0){
				out.println("-1");
				return ;
			}
		}
		out.println(dp[n - 1]);
	}

	void soln() {
		is = System.in;
		out = new PrintWriter(System.out);
		long s = System.currentTimeMillis();
		solve();
		out.flush();
		tr(System.currentTimeMillis() - s + "ms");
	}

	public static void main(String[] args) throws Exception {
		new CODEFORCES().soln();
	}

	// To Get Input
	// Some Buffer Methods
	private byte[] inbuf = new byte[1024];
	public int lenbuf = 0, ptrbuf = 0;

	private int readByte() {
		if (lenbuf == -1)
			throw new InputMismatchException();
		if (ptrbuf >= lenbuf) {
			ptrbuf = 0;
			try {
				lenbuf = is.read(inbuf);
			} catch (IOException e) {
				throw new InputMismatchException();
			}
			if (lenbuf <= 0)
				return -1;
		}
		return inbuf[ptrbuf++];
	}

	private boolean isSpaceChar(int c) {
		return !(c >= 33 && c <= 126);
	}

	private int skip() {
		int b;
		while ((b = readByte()) != -1 && isSpaceChar(b))
			;
		return b;
	}

	private double nd() {
		return Double.parseDouble(ns());
	}

	private char nc() {
		return (char) skip();
	}

	private String ns() {
		int b = skip();
		StringBuilder sb = new StringBuilder();
		while (!(isSpaceChar(b))) { // when nextLine, (isSpaceChar(b) && b != '
									// ')
			sb.appendCodePoint(b);
			b = readByte();
		}
		return sb.toString();
	}

	private char[] ns(int n) {
		char[] buf = new char[n];
		int b = skip(), p = 0;
		while (p < n && !(isSpaceChar(b))) {
			buf[p++] = (char) b;
			b = readByte();
		}
		return n == p ? buf : Arrays.copyOf(buf, p);
	}

	private char[][] nm(int n, int m) {
		char[][] map = new char[n][];
		for (int i = 0; i < n; i++)
			map[i] = ns(m);
		return map;
	}

	private int[] na(int n) {
		int[] a = new int[n];
		for (int i = 0; i < n; i++)
			a[i] = ni();
		return a;
	}

	private int ni() {
		int num = 0, b;
		boolean minus = false;
		while ((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'))
			;
		if (b == '-') {
			minus = true;
			b = readByte();
		}

		while (true) {
			if (b >= '0' && b <= '9') {
				num = num * 10 + (b - '0');
			} else {
				return minus ? -num : num;
			}
			b = readByte();
		}
	}

	private long nl() {
		long num = 0;
		int b;
		boolean minus = false;
		while ((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'))
			;
		if (b == '-') {
			minus = true;
			b = readByte();
		}

		while (true) {
			if (b >= '0' && b <= '9') {
				num = num * 10 + (b - '0');
			} else {
				return minus ? -num : num;
			}
			b = readByte();
		}
	}

	private boolean oj = System.getProperty("ONLINE_JUDGE") != null;

	private void tr(Object... o) {
		if (!oj)
			System.out.println(Arrays.deepToString(o));
	}
}