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.*;
import java.math.*;

public class B implements Runnable {
	static BufferedReader in;
	static PrintWriter out;
	static StringTokenizer st;
	static Random rnd;

	static class Pair {
		int index, value;

		public Pair(int index, int value) {
			this.index = index;
			this.value = value;
		}

	}

	static class SmartSet {
		Deque<Pair> max, min;

		public SmartSet() {
			this.max = new ArrayDeque<B.Pair>();
			this.min = new ArrayDeque<B.Pair>();
		}

		public boolean isEmpty() {
			return max.isEmpty();
		}

		public int getMax() {
			return (max.peekFirst().value);
		}

		public int getMin() {
			return (min.peekFirst().value);
		}

		public void remove(int index) {
			if (!max.isEmpty() && max.peekFirst().index == index) {
				max.pollFirst();
			}
			if (!min.isEmpty() && min.peekFirst().index == index) {
				min.pollFirst();
			}
		}

		public void add(int index, int value) {
			Pair pair = new Pair(index, value);
			while (!max.isEmpty() && max.peekLast().value < value) {
				max.pollLast();
			}
			max.add(pair);
			while (!min.isEmpty() && min.peekLast().value > value) {
				min.pollLast();
			}
			min.add(pair);
		}
	}

	static class SegmentTree {
		int size;
		int[] values;

		public SegmentTree(int size) {
			this.size = size;
			this.values = new int[4 * size];
			Arrays.fill(this.values, Integer.MAX_VALUE);
		}

		public static final int left(int v) {
			return (v << 1);
		}

		public static final int right(int v) {
			return (v << 1) | 1;
		}

		public static final int middle(int l, int r) {
			return (l + r) >> 1;
		}

		public void set(int v, int l, int r, int index, int value) {
			if (l == r) {
				values[v] = value;
			} else {
				int m = middle(l, r);
				if (index <= m)
					set(left(v), l, m, index, value);
				else
					set(right(v), m + 1, r, index, value);
				values[v] = Math.min(values[left(v)], values[right(v)]);
			}
		}

		public int get(int v, int l, int r, int tl, int tr) {
			if (l == tl && r == tr) {
				return values[v];
			} else {
				int m = middle(l, r), result = Integer.MAX_VALUE;
				if (tl <= m)
					result = get(left(v), l, m, tl, Math.min(tr, m));
				if (tr > m)
					result = Math.min(result,
							get(right(v), m + 1, r, Math.max(m + 1, tl), tr));
				return result;
			}
		}

		public void set(int index, int value) {
			set(1, 0, size - 1, index, value);
		}

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

	private void solve() throws IOException {
		int numbersCount = nextInt(), maxAbs = nextInt(), minSize = nextInt();
		int[] numbers = new int[numbersCount];
		for (int i = 0; i < numbersCount; i++) {
			numbers[i] = nextInt();
		}
		int[] maxLeftBorder = new int[numbersCount];
		int cursor = numbersCount - 1;
		SmartSet smartSet = new SmartSet();
		for (int i = numbersCount - 1; i >= 0; i--) {
			while (cursor >= 0 && stayGood(smartSet, numbers[cursor], maxAbs)) {
				smartSet.add(cursor, numbers[cursor]);
				--cursor;
			}
			maxLeftBorder[i] = cursor + 1;
			smartSet.remove(i);
		}
		SegmentTree segTree = new SegmentTree(numbersCount + 1);
		segTree.set(0, 0);
		for (int i = 1; i <= numbersCount; i++) {
			int leftBorder = maxLeftBorder[i - 1];
			int rightBorder = i - minSize;
			if (leftBorder <= rightBorder) {
				int currentResult = segTree.get(leftBorder, rightBorder);
				//out.println(i + " " + currentResult);
				if (currentResult < Integer.MAX_VALUE) {
					segTree.set(i, currentResult + 1);
				}
			}
		}
		int result = segTree.get(numbersCount, numbersCount);
		if (result > numbersCount) {
			out.println("-1");
		} else {
			out.println(result);
		}
	}

	private boolean stayGood(SmartSet smartSet, int value, int maxAbs) {
		if (smartSet.isEmpty())
			return true;
		int min = Math.min(smartSet.getMin(), value);
		int max = Math.max(smartSet.getMax(), value);
		return (max - min) <= maxAbs;
	}

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

	public void run() {
		try {
			final String className = this.getClass().getName().toLowerCase();

			try {
				in = new BufferedReader(new FileReader(className + ".in"));
				out = new PrintWriter(new FileWriter(className + ".out"));
				// in = new BufferedReader(new FileReader("input.txt"));
				// out = new PrintWriter(new FileWriter("output.txt"));
			} catch (FileNotFoundException e) {
				in = new BufferedReader(new InputStreamReader(System.in));
				out = new PrintWriter(System.out);
			}

			rnd = new Random();

			solve();

			out.close();
		} catch (IOException e) {
			e.printStackTrace();
			System.exit(1);
		}
	}

	private String nextToken() throws IOException {
		while (st == null || !st.hasMoreTokens()) {
			String line = in.readLine();

			if (line == null)
				return null;

			st = new StringTokenizer(line);
		}

		return st.nextToken();
	}

	private int nextInt() throws IOException {
		return Integer.parseInt(nextToken());
	}

	private long nextLong() throws IOException {
		return Long.parseLong(nextToken());
	}

	private double nextDouble() throws IOException {
		return Double.parseDouble(nextToken());
	}
}