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.math.BigDecimal;
import java.math.BigInteger;
import java.util.*;


public class Main {
    static int inf = (int) 1e9 + 7;

    public static void main(String[] args) throws IOException {
        sc = new Scanner(System.in);
        pw = new PrintWriter(System.out);
        int n = sc.nextInt();
        int s = sc.nextInt();
        int l = sc.nextInt();
        int a[] = new int [n];
        int dp[] = new int [n];
        for(int i = 0;i < n;i++) dp[i] = inf;

        for(int i = 0;i < n;i++) a[i] = sc.nextInt();

        segment_tree a1 = new segment_tree(a);
        segment_tree dp1 = new segment_tree(dp);

        for(int i = 0;i < n;i++) {
            int id = a1.get_dist(i, s);
            if (i - id + 1 < l) continue;
            if (id == 0) dp[i] = 1;
            else {
                int left = i - l + 1;
                dp[i] = dp1.get_min(id - 1, left - 1) + 1;
            }
            dp1.set(i, dp[i]);
        }

        if (dp[n - 1] >= inf) pw.println(-1);
        else pw.println(dp[n - 1]);
        pw.close();
    }

    static Scanner sc;
    static PrintWriter pw;

    static class Scanner {
        BufferedReader br;
        StringTokenizer st = new StringTokenizer("");

        Scanner(InputStream in) throws FileNotFoundException {
            br = new BufferedReader(new InputStreamReader(in));
        }

        Scanner(String in) throws FileNotFoundException {
            br = new BufferedReader(new FileReader(in));
        }

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

class segment_tree {
    static int inf = (int) 1e9 + 7;
    int min[], max[];
    int last;

    segment_tree(int a[]) {
        int n = a.length;
        min = new int [4 * n];
        max = new int [4 * n];
        last = n - 1;
        build(0, 0, last, a);
    }

    void update(int v) {
        min[v] = Math.min(min[v * 2 + 1], min[v * 2 + 2]);
        max[v] = Math.max(max[v * 2 + 1], max[v * 2 + 2]);
    }

    void build(int v, int l, int r, int a[]) {
        if (l == r) {
            min[v] = a[l];
            max[v] = a[l];
            return;
        }
        int m = ((l + r) >> 1);
        build(v * 2 + 1, l, m, a);
        build(v * 2 + 2, m + 1, r, a);
        update(v);
    }

    void set(int id, int x) {
        set(0, 0, last, id, x);
    }

    void set(int v, int l, int r, int id, int x) {
        if (l > id || r < id) return;
        if (l == id && r == id) {
            min[v] = x;
            max[v] = x;
            return;
        }
        int m = ((l + r) >> 1);
        set(v * 2 + 1, l, m, id, x);
        set(v * 2 + 2, m + 1, r, id, x);
        update(v);
    }

    int get_min(int l, int r) {
        return get_min(0, 0, last, l, r);
    }

    int get_min(int v, int l, int r, int left, int right) {
        if (l > right || r < left) return inf;
        if (l >= left && r <= right) return min[v];

        int m = ((l + r) >> 1);

        return Math.min(get_min(v * 2 + 1, l, m, left, right), get_min(v * 2 + 2, m + 1, r, left, right));
    }

    int get_max(int l, int r) {
        return get_max(0, 0, last, l, r);
    }

    int get_max(int v, int l, int r, int left, int right) {
        if (l > right || r < left) return -inf;
        if (l >= left && r <= right) return max[v];

        int m = ((l + r) >> 1);

        return Math.max(get_max(v * 2 + 1, l, m, left, right), get_max(v * 2 + 2, m + 1, r, left, right));
    }

    int get_dist(int r, int s) {
        return get_dist(0, 0, last, r, s, inf, -inf) + 1;
    }

    int get_dist(int v, int l, int r, int right, int s, int min1, int max1) {
        if (l > right) return -1;
        if (Math.max(max[v], max1) - Math.min(min[v], min1) <= s) return -1;
        if (l == r) return l;
        int m = ((l + r) >> 1);

        int ans = get_dist(v * 2 + 2, m + 1, r, right, s, min1, max1);
        min1 = Math.min(min1, get_min(m + 1, Math.min(r, right)));
        max1 = Math.max(max1, get_max(m + 1, Math.min(r, right)));
        if (ans == -1) ans = get_dist(v * 2 + 1, l, m, right, s, min1, max1);
        return ans;
    }

}