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.Random;
import java.util.StringTokenizer;
import java.util.TreeMap;

public class B {

    final boolean ONLINE_JUDGE = System.getProperty("ONLINE_JUDGE") != null;
    BufferedReader in;
    PrintWriter out;
    StringTokenizer tok = new StringTokenizer("");

	Random rg = new Random(322);

	class Treap {
		class Node {
			Node left, right;
			long prior;
			int key;
			int value;
			int minValue;

			Node(int key, int value) {
				this.key = key;
				this.value = value;
				this.minValue = value;
				prior = rg.nextLong();
			}
		}

		Node root;

		void update(Node node){
			if(node != null) {
				node.minValue = Math.min(node.value, Math.min(getValue(node.left), getValue(node.right)));
			}
		}

		int getValue(Node node) {
			return node == null ? 1000000 : node.minValue;
		}



		Node merge(Node left, Node right) {
			if(left == null) {
				return right;
			}
			if(right == null) {
				return left;
			}
			Node res;
			if(left.prior > right.prior) {
				res = merge(left.right, right);
				left.right = res;
				res = left;
			} else {
				res = merge(left, right.left);
				right.left = res;
				res = right;
			}
			update(res);
			return res;
		}

		Node[] split(Node t, int key) {
			if(t == null) {
				return new Node[2];
			}
			Node[] res;
			if(key < t.key) {
				res = split(t.left, key);
				t.left = res[1];
				res[1] = t;
			} else {
				res = split(t.right, key);
				t.right = res[0];
				res[0] = t;
			}
			update(res[0]);
			update(res[1]);
			return res;
		}

		void add(int index, int value) {
			root = merge(root, new Node(index, value));
		}

		int getMinValueOnInterval(int left, int right) {
			Node[] parts = split(root, right);
			Node r = parts[1];
			parts = split(parts[0], left-1);
			int res = getValue(parts[1]);
			root = merge(parts[0], merge(parts[1], r));
			return res;
		}

	}

	void solve() throws IOException {
		int n = readInt();
		int s = readInt();
		int l = readInt();
		int[] a = readArr(n);
		int[] left = new int[n];
		int j = 0;
		TreeMap<Integer, Integer> map = new TreeMap<Integer, Integer>();
		for(int i = 0; i < n; i++) {
			Integer cur = map.get(a[i]);
			map.put(a[i], cur == null ? 1 : cur + 1);
			while (true) {
				int min = map.firstKey();
				int max = map.lastKey();
				int d = max - min;
				if(d <= s) break;
				int z = map.get(a[j])-1;
				if(z == 0) {
					map.remove(a[j]);
				} else {
					map.put(a[j], z);
				}
				j++;
			}
			left[i] = j;
		}
		Treap treap = new Treap();
		int[] mins = new int[n];
		for(int i = 0; i < n; i++) {
			int x = left[i];
			int y = i - l + 1;
			if(x > y) {
				mins[i] = Integer.MAX_VALUE / 2;
				treap.add(i, mins[i]);
				continue;
			}
			if(x == 0) {
				mins[i] = 1;
				treap.add(i, 1);
				continue;
			}
			int min = treap.getMinValueOnInterval(x-1, y-1);
			mins[i] = min + 1;
			treap.add(i, mins[i]);
		}
		out.print(mins[n-1] > n ? -1 : mins[n-1]);
	}


    void init() throws FileNotFoundException {
        if (ONLINE_JUDGE) {
            in = new BufferedReader(new InputStreamReader(System.in));
            out = new PrintWriter(System.out);
        } else {
            in = new BufferedReader(new FileReader("input.txt"));
            out = new PrintWriter("output.txt");
        }
    }

    String readString() throws IOException {
        while (!tok.hasMoreTokens()) {
            tok = new StringTokenizer(in.readLine());
        }
        return tok.nextToken();
    }

    int readInt() throws IOException {
        return Integer.parseInt(readString());
    }

    long readLong() throws IOException {
        return Long.parseLong(readString());
    }

    double readDouble() throws IOException {
        return Double.parseDouble(readString());
    }

    int[] readArr(int n) throws IOException {
        int[] res = new int[n];
        for (int i = 0; i < n; i++) {
            res[i] = readInt();
        }
        return res;
    }

    long[] readArrL(int n) throws IOException {
        long[] res = new long[n];
        for (int i = 0; i < n; i++) {
            res[i] = readLong();
        }
        return res;
    }

    public static void main(String[] args) {
        new B().run();
    }

    public void run() {
        try {
            long t1 = System.currentTimeMillis();
            init();
            solve();
            out.close();
            long t2 = System.currentTimeMillis();
            System.err.println("Time = " + (t2 - t1));
        } catch (Exception e) {
            e.printStackTrace(System.err);
            System.exit(-1);
        }
    }
}