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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.StringTokenizer;

/**
 * @author Pavel Mavrin
 */
public class B {

    private void solve() throws IOException {
        int n = nextInt();
        int s = nextInt();
        int l = nextInt();
        int[] a = new int[n];
        for (int i = 0; i < n; i++) {
            a[i] = nextInt();
        }
        int size = 1;
        while (size < n + 1) size *= 2;
        SegmentTree mins = new SegmentTree(size);
        SegmentTree maxs = new SegmentTree(size);
        for (int i = 0; i < n; i++) {
            mins.set(i, a[i]);
            maxs.set(i, -a[i]);
        }
        SegmentTree d = new SegmentTree(size);
        for (int i = 0; i < n; i++) {
            int rr = i - l + 1;
            int l1 = -1;
            int r1 = i;
            while (r1 > l1 + 1) {
                int m = (l1 + r1) / 2;
                int mx = -maxs.min(m, i + 1);
                int mn = mins.min(m, i + 1);
                int dd = mx - mn;
                if (dd > s) {
                    l1 = m;
                } else {
                    r1 = m;
                }
            }
            int ll = r1;
            int zz = Integer.MAX_VALUE;
            if (rr >= ll) {
                int z = d.min(ll, rr + 1);
                if (z < Integer.MAX_VALUE) {
                    zz = z + 1;
                }
            }
            d.set(i + 1, zz);
//            System.out.println(i + " " + ll + " " + rr + " " + zz);
        }
        int res = d.min(n, n + 1);
        if (res == Integer.MAX_VALUE) {
            out.println(-1);
        } else {
            out.println(res);
        }
    }


    class SegmentTree {

        private int[] a;
        private int size;

        public SegmentTree(int size) {
            this.size = size;
            a = new int[2 * size];
        }

        private void set(int i, int v) {
            set(0, 0, size, i, v);
        }

        private void set(int n, int l, int r, int i, int v) {
            if (r == l + 1) {
                a[n] = v;
            } else {
                int m = (l + r) / 2;
                if (i < m) {
                    set(n * 2 + 1, l, m, i, v);
                } else {
                    set(n * 2 + 2, m, r, i, v);
                }
                a[n] = Math.min(a[n * 2 + 1], a[n * 2 + 2]);
            }
        }

        private int get(int i) {
            return get(0, 0, size, i);
        }

        private int get(int n, int l, int r, int i) {
            if (r == l + 1) {
                return a[n];
            } else {
                int m = (l + r) / 2;
                if (i < m) {
                    return get(n * 2 + 1, l, m, i);
                } else {
                    return get(n * 2 + 2, m, r, i);
                }
            }
        }

        private int min(int l, int r) {
            return min(0, 0, size, l, r);
        }

        private int min(int n, int ll, int rr, int l, int r) {
            if (ll >= l && rr <= r) {
                return a[n];
            } else if (ll >= r || l >= rr) {
                return Integer.MAX_VALUE;
            } else {
                int m = (ll + rr) / 2;
                return Math.min(min(n * 2 + 1, ll, m, l, r), min(n * 2 + 2, m, rr, l, r));
            }
        }
    }

    BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
    StringTokenizer st;
    PrintWriter out = new PrintWriter(System.out);

    String next() throws IOException {
        while (st == null || !st.hasMoreTokens()) {
            st = new StringTokenizer(br.readLine());
        }
        return st.nextToken();
    }

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

    public static void main(String[] args) throws IOException {
        new B().run();
    }

    private void run() throws IOException {
        solve();
        out.close();
    }

}
