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.util.*;
import java.io.*;
public class B {
    public static PrintStream out = System.out;
    public static InputReader in = new InputReader(System.in);
    public static void main(String args[]) {
        int N, S, L;
        N = in.nextInt();
        S = in.nextInt();
        L = 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 r = N - 1;
        dpTree.put(N, 0);
        // out.println(dpTree.get(7, 7));
        for (int i = N - 1; i >= 0; i--) {
            // check i ~ i + L - 1 is good
            while (true) {
                // out.println(i + " " + (i + L - 1) + " " + Arrays.toString(minMax));
                if (-max.get(i, r) - min.get(i, r) > S) {
                    r--;
                } else {
                    break;
                }
            }
            // out.println(i + " " + r);
            if (r - i + 1 >= L) { // i ~ r. i ~ r - L + 1. i + L ~ r + 1
                dpTree.put(i, dpTree.get(i + L, r + 1) + 1);
            }
        }
        int ret = dpTree.get(0, 0);
        if (ret >= SegmentTree.EMPTY) out.println(-1);
        else out.println(ret);
    }
    static class SegmentTree {
        static int EMPTY = (int) 1e9 + 7; // MINIMUM RANGE QUERY so use MAX_VALUE for garbage
        int[] ans;
        int[] vals;
        int size;
        SegmentTree(int[] vals) {
            this.vals = vals;
            this.size = vals.length - 1;
            ans = new int[size * 4 + 10];
            build(0, 0, size - 1);
        }
        SegmentTree(int size) {
            this.vals = null;
            this.size = size;
            ans = new int[size * 4 + 10];
            Arrays.fill(ans, EMPTY);
        }
        int unite(int val1, int val2) {
            return Math.min(val1, val2);
        }
        void build(int v, int l, int r) { // O(N)
            if (l == r) {
                ans[v] = vals[l];
            } else {
                int m = (l + r) / 2;
                build(v * 2 + 1, l, m);
                build(v * 2 + 2, m + 1, r);
                ans[v] = unite(ans[v * 2 + 1], ans[v * 2 + 2]);
            }
        }
        int get(int needL, int needR) {
            return get(0, 0, size - 1, needL, needR);
        }
        int get(int v, int l, int r, int needL, int needR) { // O(log N)
            if (needL > r || needR < l) {
                return EMPTY;
            }
            if (needL <= l && needR >= r) {
                return ans[v];
            }
            int mid = (l + r) / 2;
            return unite(get(v * 2 + 1, l, mid, needL, needR),
                         get(v * 2 + 2, mid + 1, r, needL, needR));
        }
        void put(int i, int tl, int tr, int pos, int val) { // O(log N)
            if (tl == tr) {
                ans[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);
            ans[i] = unite(ans[2 * i + 1], ans[2 * i + 2]);
        }
        void put(int pos, int val) {
            put(0, 0, size - 1, pos, val);
        }
    }
}
class InputReader {
    public BufferedReader reader;
    public StringTokenizer tokenizer;
    public InputReader(InputStream stream) {
	reader = new BufferedReader(new InputStreamReader(stream), 32768);
	tokenizer = null;
    }
    public String next() {
	while (tokenizer == null || !tokenizer.hasMoreTokens()) {
	    try {
		tokenizer = new StringTokenizer(reader.readLine());
	    } catch (IOException e) {
		throw new RuntimeException(e);
	    }
	}
	return tokenizer.nextToken();
    }
    public double nextDouble() {
	return Double.parseDouble(next());
    }
    public long nextLong() {
	return Long.parseLong(next());
    }
    public int nextInt() {
	return Integer.parseInt(next());
    }
}
