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 strip {
  private static Reader in;
  private static PrintWriter out;
  
  
  static 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);
      }
    }
    
    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));
      }
    }
  }

  public static void main(String[] args) throws IOException {
    in = new Reader();
    out = new PrintWriter(System.out, true);
    int N = in.nextInt();
    int S = in.nextInt();
    int L = in.nextInt();
    
    int[] arr = new int[N+1];
    for (int i = 1; i <= N; i++)
      arr[i] = in.nextInt();
    SegmentTree max = new SegmentTree(0, N);
    SegmentTree min = new SegmentTree(0, N);
    for (int i = 1; i <= N; i++) {
      max.update(i, arr[i]);
      min.update(i, -arr[i]);
    }
    SegmentTree res = new SegmentTree(0, N);
    res.update(0, 0);
    for (int i = 1; i <= N; i++) {
      int lo = 1, hi = i;
      while (lo < hi) {
        int mid = (lo + hi) >> 1;
        if (max.query(mid, i)+min.query(mid, i) > S) {
          lo = mid+1;
        } else {
          hi = mid;
        }
      }
      int ans = (1 << 29);
      if (lo-1 <= i-L) ans = -res.query(lo-1, i-L)+1;
      res.update(i, -ans);
    }
    int ans = -res.query(N, N);
    out.println(ans > N ? -1 : ans);
    out.close();
    System.exit(0);
  }

  static class Reader {
    final private int BUFFER_SIZE = 1 << 16;
    private DataInputStream din;
    private byte[] buffer;
    private int bufferPointer, bytesRead;

    public Reader() {
      din = new DataInputStream(System.in);
      buffer = new byte[BUFFER_SIZE];
      bufferPointer = bytesRead = 0;
    }

    public Reader(String file_name) throws IOException {
      din = new DataInputStream(new FileInputStream(file_name));
      buffer = new byte[BUFFER_SIZE];
      bufferPointer = bytesRead = 0;
    }

    public String readLine() throws IOException {
      byte[] buf = new byte[1024];
      int cnt = 0;
      byte c = read();
      while (c <= ' ')
        c = read();
      do {
        buf[cnt++] = c;
      } while ((c = read()) != '\n');
      return new String(buf, 0, cnt);
    }

    public String next() throws IOException {
      byte[] buf = new byte[1024];
      int cnt = 0;
      byte c = read();
      while (c <= ' ')
        c = read();
      do {
        buf[cnt++] = c;
      } while ((c = read()) > ' ');
      return new String(buf, 0, cnt);
    }

    public int nextInt() throws IOException {
      int ret = 0;
      byte c = read();
      while (c <= ' ')
        c = read();
      boolean neg = (c == '-');
      if (neg)
        c = read();
      do {
        ret = ret * 10 + c - '0';
      } while ((c = read()) >= '0' && c <= '9');
      if (neg)
        return -ret;
      return ret;
    }

    public long nextLong() throws IOException {
      long ret = 0;
      byte c = read();
      while (c <= ' ')
        c = read();
      boolean neg = (c == '-');
      if (neg)
        c = read();
      do {
        ret = ret * 10 + c - '0';
      } while ((c = read()) >= '0' && c <= '9');
      if (neg)
        return -ret;
      return ret;
    }

    public double nextDouble() throws IOException {
      double ret = 0, div = 1;
      byte c = read();
      while (c <= ' ')
        c = read();
      boolean neg = (c == '-');
      if (neg)
        c = read();
      do {
        ret = ret * 10 + c - '0';
      } while ((c = read()) >= '0' && c <= '9');
      if (c == '.')
        while ((c = read()) >= '0' && c <= '9')
          ret += (c - '0') / (div *= 10);
      if (neg)
        return -ret;
      return ret;
    }

    private void fillBuffer() throws IOException {
      bytesRead = din.read(buffer, bufferPointer = 0, BUFFER_SIZE);
      if (bytesRead == -1)
        buffer[0] = -1;
    }

    private byte read() throws IOException {
      if (bufferPointer == bytesRead)
        fillBuffer();
      return buffer[bufferPointer++];
    }

    public void close() throws IOException {
      if (din == null)
        return;
      din.close();
    }
  }


}
