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.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.InputMismatchException;
import java.io.IOException;
import java.util.TreeSet;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        ProblemBStrip solver = new ProblemBStrip();
        solver.solve(1, in, out);
        out.close();
    }

    static class ProblemBStrip {
        private static final int INF = (int) 2e9;
        int[] tree;
        int n;

        public void solve(int testNumber, InputReader in, PrintWriter out) {
            n = in.readInt();
            int s = in.readInt();
            int l = in.readInt();

            int[] a = in.readIntArray(n);
            int[] range = new int[n + 1];
            TreeSet<Integer> set = new TreeSet<>(((o1, o2) -> a[o1] == a[o2] ? o1 - o2 : a[o1] - a[o2]));
            tree = new int[5 * n];

            int start = n - 1;
            for (int i = n - 1; i >= 0; i--) {
                set.add(i);
                while (set.size() > 0 && a[set.last()] - a[set.first()] > s) {
                    set.remove(start--);
                }
                range[i] = start - i + 1;
            }

            for (int i = n - 1; i > 0 && n - i < l; i--) {
                update(1, 1, n, i + 1, INF);
            }

            int ans = INF;
            for (int i = n - l; i >= 0; i--) {
                if (range[i] < l) {
                    update(1, 1, n, i + 1, INF);
                    ans = INF;
                } else {
                    int v = query(1, 1, n, i + l + 1, i + range[i] + 1);
                    if (v != INF) v++;
                    update(1, 1, n, i + 1, v);
                    ans = v;
                }
            }
            out.print(ans == INF ? -1 : ans);

        }

        int query(int node, int s, int e, int l, int r) {
            if (r > n) return 0;
            if (r < s || l > e) return INF;
            if (l <= s && r >= e) return tree[node];

            int v1 = query(node * 2, s, (s + e) / 2, l, r);
            int v2 = query(node * 2 + 1, (s + e) / 2 + 1, e, l, r);
            return Math.min(v1, v2);
        }

        void update(int node, int s, int e, int pos, int val) {
            if (pos < s || pos > e) return;
            if (s == e) {
                tree[node] = val;
                return;
            }

            update(node * 2, s, (s + e) / 2, pos, val);
            update(node * 2 + 1, (s + e) / 2 + 1, e, pos, val);
            tree[node] = Math.min(tree[node * 2], tree[node * 2 + 1]);
        }

    }

    static class InputReader {
        private InputStream stream;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;
        private InputReader.SpaceCharFilter filter;

        public InputReader(InputStream stream) {
            this.stream = stream;
        }

        public int read() {
            if (numChars == -1)
                throw new InputMismatchException();
            if (curChar >= numChars) {
                curChar = 0;
                try {
                    numChars = stream.read(buf);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }
                if (numChars <= 0)
                    return -1;
            }
            return buf[curChar++];
        }

        public int readInt() {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            int res = 0;
            do {
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = read();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

        public boolean isSpaceChar(int c) {
            if (filter != null)
                return filter.isSpaceChar(c);
            return isWhitespace(c);
        }

        public static boolean isWhitespace(int c) {
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

        public int[] readIntArray(int size) {
            int[] ans = new int[size];
            for (int i = 0; i < size; i++) ans[i] = readInt();
            return ans;
        }

        public interface SpaceCharFilter {
            public boolean isSpaceChar(int ch);

        }

    }
}

