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.BufferedOutputStream;
import java.io.BufferedReader;
import java.io.BufferedWriter;
import java.io.FileInputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.OutputStream;
import java.io.OutputStreamWriter;
import java.io.PrintWriter;
import java.util.Comparator;
import java.util.PriorityQueue;
import java.util.StringTokenizer;

/**
 * @author Jens Staahl
 */

public class Prac {

	// some local config
	// static boolean test = false ;
	private boolean test = System.getProperty("ONLINE_JUDGE") == null;
	static String testDataFile = "testdata.txt";
	// static String testDataFile = "testdata.txt";
	private static String ENDL = "\n";

	// Just solves the acutal kattis-problem
	ZKattio io;
	class SegmentTree {
		public SegmentTree left, right;
		public int start, end, max;
		
		public SegmentTree(int start, int end) {
			this. start = start;
			this.end = end;
			max = -(1<<29);
			if(start != end) {
				int mid = (start+end)>>1;
				left = new SegmentTree(start, mid);
				right = new SegmentTree(mid+1, end);
			}
		}
		
		//p = pos, v = value
		public void update(int p, int v) {
			if(start == p && end == p){
				this.max = v;
				return;
			}
			int mid = (start + end) >> 1;
			if (mid >= p) {
				left.update(p, v);
			} else {
				right.update(p, v);
			}
			this.max = Math.max(left.max, right.max);
		}
		
		public int query(int s, int e) {
			if (start == s && end == e) {
				return max;
			}
			int mid = (start + end) >> 1;
			if ( mid >= e) return left.query(s, e);
			else if(mid < s) return right.query(s, e);
			else {
				return Math.max(left.query(s, mid), right.query(mid+1, e));
			}
		}
	}

	private void solve() throws Throwable {
		io = new ZKattio(stream);
		int n = io.getInt(), s = io.getInt(), l = io.getInt();
		
		int[] r = new int[n+1];
		for (int i = 0; i < n; i++) {
			r[i+1] = io.getInt();
		}
		SegmentTree min = new SegmentTree(0, n);
		SegmentTree max = new SegmentTree(0, n);
		for (int i = 1; i <= n; i++) {
			min.update(i, -r[i]);
			max.update(i, r[i]);
		}
		SegmentTree result = new SegmentTree(0, n);
		result.update(0, 0);
		for (int i = 1; i <= n; i++) {
			int lo = 1, hi = i;

			int rightmostOk = i - l;
			while(lo < hi) {
				int mid = (lo + hi)>>1;
				int minQ = min.query(mid, i);
				int maxQ = max.query(mid, i);
				if(minQ + maxQ > s) {
					lo = mid + 1;
				} else {
					hi = mid;
				}
			}
			int ans = (1<<29);
			if(lo - 1 <= rightmostOk) {
				ans = -result.query(lo-1, rightmostOk) + 1;
			}
			result.update(i, -ans);
		}
		int query = -result.query(n, n);
		if(query < 1<<29){ 
			System.out.println(query);
		} else {
			System.out.println(-1);
		}
	}

	public static void main(String[] args) throws Throwable {
		new Prac().solve();
	}

	public Prac() throws Throwable {
		if (test) {
			stream = new FileInputStream(testDataFile);
		}
	}

	InputStream stream = System.in;
	BufferedWriter out = new BufferedWriter(new OutputStreamWriter(System.out));// outStream

	public class ZKattio extends PrintWriter {
		public ZKattio(InputStream i) {
			super(new BufferedOutputStream(System.out));
			r = new BufferedReader(new InputStreamReader(i));
		}

		public ZKattio(InputStream i, OutputStream o) {
			super(new BufferedOutputStream(o));
			r = new BufferedReader(new InputStreamReader(i));
		}

		public boolean hasMoreTokens() {
			return peekToken() != null;
		}

		public int getInt() {
			return Integer.parseInt(nextToken());
		}

		public double getDouble() {
			return Double.parseDouble(nextToken());
		}

		public long getLong() {
			return Long.parseLong(nextToken());
		}

		public String getWord() {
			return nextToken();
		}

		private BufferedReader r;
		private String line;
		private StringTokenizer st;
		private String token;

		private String peekToken() {
			if (token == null)
				try {
					while (st == null || !st.hasMoreTokens()) {
						line = r.readLine();
						if (line == null)
							return null;
						st = new StringTokenizer(line);
					}
					token = st.nextToken();
				} catch (IOException e) {
				}
			return token;
		}

		private String nextToken() {
			String ans = peekToken();
			token = null;
			return ans;
		}
	}
	// System.out;

}