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.*;

import static java.lang.Math.*;

public class Main extends PrintWriter {
    BufferedReader in;
    StringTokenizer stok;
    final Random rand = new Random(31);
    final int inf = (int) 1e9;
    final long linf = (long) 1e18;

    class MinMaxStack {
        Deque<Integer> a = new ArrayDeque<>();
        Deque<Integer> min = new ArrayDeque<>();
        Deque<Integer> max = new ArrayDeque<>();

        void add(int x) {
            min.addLast(min(x, getMin()));
            max.addLast(max(x, getMax()));
            a.addLast(x);
        }

        int poll() {
            if (!isEmpty()) {
                min.pollLast();
                max.pollLast();
                return a.pollLast();
            }
            return inf;
        }

        int getMin() {
            if (isEmpty()) {
                return inf;
            }
            return min.getLast();
        }

        int getMax() {
            if (isEmpty()) {
                return -inf;
            }
            return max.getLast();
        }

        boolean isEmpty() {
            return a.isEmpty();
        }

        int size() {
            return a.size();
        }

        @Override
        public String toString() {
            return a.toString();
        }
    }

    class MinMaxQueue {
        MinMaxStack a = new MinMaxStack();
        MinMaxStack b = new MinMaxStack();

        void add(int x) {
            b.add(x);
        }

        int poll() {
            if (a.isEmpty()) {
                transfer();
            }
            return a.poll();
        }

        int getMin() {
            return min(a.getMin(), b.getMin());
        }

        int getMax() {
            return max(a.getMax(), b.getMax());
        }

        void transfer() {
            while (!b.isEmpty()) {
                a.add(b.poll());
            }
        }

        boolean isEmpty() {
            return a.isEmpty() && b.isEmpty();
        }

        int size() {
            return a.size() + b.size();
        }

        @Override
        public String toString() {
            return "a: " + a.toString() + ", b: " + b.toString();
        }
    }

    public void solve() throws IOException {
        int n = nextInt();
        int s = nextInt();
        int l = nextInt();
        int[] a = nextIntArray(n);
        MinMaxQueue q = new MinMaxQueue();
        MinMaxQueue b = new MinMaxQueue();
        int[] d = new int[n];
        for (int i = 0; i < n; i++) {
            q.add(a[i]);
            if (q.size() - l + 1 > b.size()) {
                if (i >= l) {
                    b.add(d[i - l]);
                } else {
                    b.add(0);
                }
            }
            boolean fl = false;
            while (q.getMax() - q.getMin() > s) {
                q.poll();
                if (fl) {
                    fl = false;
                } else {
                    b.poll();
                }
            }
            d[i] = min(inf, b.getMin() + 1);
        }
        println(d[n - 1] == inf ? -1 : d[n - 1]);
    }

    public void run() {
        try {
            solve();
            close();
        } catch (Exception e) {
            e.printStackTrace();
            System.exit(abs(-1));
        }
    }

    Main() throws IOException {
        super(System.out);
        in = new BufferedReader(new InputStreamReader(System.in));
    }

    Main(String s) throws IOException {
        super("".equals(s) ? "output.txt" : (s + ".out"));
        in = new BufferedReader(new FileReader("".equals(s) ? "input.txt" : (s + ".in")));
    }

    public static void main(String[] args) throws IOException {
        try {
            Locale.setDefault(Locale.US);
        } catch (Exception ignored) {
        }
        new Main().run();
    }

    String next() throws IOException {
        while (stok == null || !stok.hasMoreTokens()) {
            String s = in.readLine();
            if (s == null) {
                return null;
            }
            stok = new StringTokenizer(s);
        }
        return stok.nextToken();
    }

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

    long nextLong() throws IOException {
        return Long.parseLong(next());
    }

    double nextDouble() throws IOException {
        return Double.parseDouble(next());
    }

    int[] nextIntArray(int len) throws IOException {
        int[] a = new int[len];
        for (int i = 0; i < len; i++) {
            a[i] = nextInt();
        }
        return a;
    }

    void shuffle(int[] a) {
        for (int i = 1; i < a.length; i++) {
            int x = rand.nextInt(i + 1);
            int t = a[i];
            a[i] = a[x];
            a[x] = t;
        }
    }

    boolean nextPerm(int[] p) {
        for (int a = p.length - 2; a >= 0; --a)
            if (p[a] < p[a + 1])
                for (int b = p.length - 1; ; --b)
                    if (p[b] > p[a]) {
                        int t = p[a];
                        p[a] = p[b];
                        p[b] = t;
                        for (++a, b = p.length - 1; a < b; ++a, --b) {
                            t = p[a];
                            p[a] = p[b];
                            p[b] = t;
                        }
                        return true;
                    }
        return false;
    }

    <T> List<T>[] createAdjacencyList(int countVertex) {
        List<T>[] res = new List[countVertex];
        for (int i = 0; i < countVertex; i++) {
            res[i] = new ArrayList<T>();
        }
        return res;
    }
}
