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.*;

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);
        TaskB solver = new TaskB();
        solver.solve(1, in, out);
        out.close();
    }
}

class TaskB {

    int inf = (int) 1e9 + 10;

    int n, s, l;
    int[] a;

    int[] itMin, itMax, itF;
    int[] id;

    void buildIT(int i, int l, int r) {
        itF[i] = n + 1;
        if (l == r) {
            itMin[i] = itMax[i] = a[l];
            id[l] = i;
            return;
        }
        int mid = (l + r) / 2;
        buildIT(i * 2, l, mid);
        buildIT(i * 2 + 1, mid + 1, r);

        itMin[i] = Math.min(itMin[i * 2], itMin[i * 2 + 1]);
        itMax[i] = Math.max(itMax[i * 2], itMax[i * 2 + 1]);
    }

    int getMax(int i, int l, int r, int u, int v) {
        if (r < u || v < l) return -inf;
        if (u <= l && r <= v) return itMax[i];
        int mid = (l + r) / 2;
        return Math.max(getMax(i * 2, l, mid, u, v), getMax(i * 2 + 1, mid + 1, r, u, v));
    }

    int getMin(int i, int l, int r, int u, int v) {
        if (r < u || v < l) return inf;
        if (u <= l && r <= v) return itMin[i];
        int mid = (l + r) / 2;
        return Math.min(getMin(i * 2, l, mid, u, v), getMin(i * 2 + 1, mid + 1, r, u, v));
    }

    void updateF(int i, int v) {
        i = id[i];
        itF[i] = v;
        for (i /= 2; i >= 1; i /= 2)
            itF[i] = Math.min(itF[i * 2], itF[i * 2 + 1]);
    }

    int getF(int i, int l, int r, int u, int v) {
        if (r < u || v < l) return inf;
        if (u <= l && r <= v) return itF[i];
        int mid = (l + r) / 2;
        return Math.min(getF(i * 2, l, mid, u, v), getF(i * 2 + 1, mid + 1, r, u, v));
    }

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

        a = new int[n + 10];
        for (int i = 1; i <= n; i++)
            a[i] = in.nextInt();

        itMin = new int[n * 4];
        itMax = new int[n * 4];
        itF = new int[n * 4];
        id = new int[n + 10];

        buildIT(1, 0, n);
        updateF(0, 0);
        for (int i = l, j = 1; i <= n; i++) {
            while (getMax(1, 0, n, j, i) - getMin(1, 0, n, j, i) > s) j++;

            if (j <= i - l + 1) {
                int fCur = getF(1, 0, n, j - 1, i - l) + 1;
                updateF(i, fCur);
//              out.println(i + " " + j + " " + fCur);
            }

        }

        int ans = getF(1, 0, n, n, n);
        if (ans > n) ans = -1;
        out.println(ans);
    }
}

class InputReader {
    private BufferedReader reader;
    private StringTokenizer tokenizer;

    public InputReader(InputStream stream) {
        reader = new BufferedReader(new InputStreamReader(stream));
        tokenizer = null;
    }

    public String nextLine() {
        try {
            return reader.readLine();
        } catch (IOException e) {
            throw new RuntimeException(e);
        }
    }

    public String next() {
        while (tokenizer == null || !tokenizer.hasMoreTokens())
            tokenizer = new StringTokenizer(nextLine());
        return tokenizer.nextToken();
    }

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

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

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

 	   		   	 	 	 	 		 	    	 			