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.Arrays;
import java.util.StringTokenizer;


public class Task {
    final int INF = (int)1e9 + 10;

    class SegmentTree {
        int[] data;
        int size;

        SegmentTree(int size) {
            data = new int[size * 4 + 10];
            Arrays.fill(data, INF);
            this.size = size;
        }

        void put(int i, int tl, int tr, int pos, int val) {
            if (tl == tr) {
                data[i] = val;
                return;
            }
            int m = (tl + tr) / 2;
            if (pos <= m)
                put(2 * i + 1, tl, m, pos, val);
            else
                put(2 * i + 2, m + 1, tr, pos, val);
            data[i] = Math.min(data[2 * i + 1], data[2 * i + 2]);
        }

        void put(int pos, int val) {
            put(0, 0, size - 1, pos, val);
        }

        int get(int i, int tl, int tr, int l, int r) {
            if (l == tl && r == tr)
                return data[i];
            int m = (tl + tr) / 2;
            int sl = INF;
            int sr = INF;
            if (l <= m)
                sl = get(2 * i + 1, tl, m, l, Math.min(r, m));
            if (r > m)
                sr = get(2 * i + 2, m + 1, tr, Math.max(m + 1, l), r);
            return Math.min(sl, sr);
        }

        int get(int l, int r) {
            return get(0, 0, size - 1, l, r);
        }
    }

    public void solve(FastScanner in, PrintWriter out) throws IOException {
        int n = in.nextInt();
        int s = in.nextInt();
        int len = in.nextInt();
        int[] a = new int[n];
        SegmentTree min = new SegmentTree(n);
        SegmentTree max = new SegmentTree(n);
        SegmentTree dpTree = new SegmentTree(n + 1);
        for (int i = 0; i < n; i++) {
            a[i] = in.nextInt();
            min.put(i, a[i]);
            max.put(i, -a[i]);
        }
        int[] dp = new int[n + 1];
        dpTree.put(0, 0);
        Arrays.fill(dp, INF);
        dp[0] = 0;
        int l = 0;
        for (int r = 0; r < n; r++) {
            while (-max.get(l, r) - min.get(l, r) > s)
                l++;
            int first = l;
            int last = r - len + 1;
            if (first <= last)
                dp[r + 1] = dpTree.get(first, last) + 1;
            dpTree.put(r + 1, dp[r + 1]);
        }
        int res = dp[n];
        if (res >= INF)
            res = -1;
        out.println(res);
    }

    public static void main(String[] args) throws IOException {
        FastScanner in = new FastScanner(System.in);
        PrintWriter out = new PrintWriter(System.out);
        int t = 1;
        for (int i = 0; i < t; i++)
            new Task().solve(in, out);
        out.flush();
    }

    static class FastScanner {
        private StringTokenizer tokenizer;
        private BufferedReader reader;

        public FastScanner(InputStream inputStream) {
            reader = new BufferedReader(new InputStreamReader(inputStream));
        }

        public String next() throws IOException {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                String line = reader.readLine();
                if (line == null)
                    throw new IOException();
                tokenizer = new StringTokenizer(line);
            }
            return tokenizer.nextToken();
        }

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

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

        public void close() {
            try {
                reader.close();
            } catch (IOException e) {
                // ignore
            }
        }
    }
}
