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.NavigableSet;
import java.io.IOException;
import java.util.InputMismatchException;
import java.util.SortedSet;
import java.util.Set;
import java.util.Comparator;
import java.io.OutputStream;
import java.util.ArrayDeque;
import java.io.PrintWriter;
import java.util.TreeSet;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 */
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);
		TaskD solver = new TaskD();
		solver.solve(1, in, out);
		out.close();
	}
}

class TaskD {
    static class Entry {
        int value;
        int pos;
        public Entry(int value, int pos) {
            this.value = value;
            this.pos = pos;
        }
    };

    public void solve(int testNumber, InputReader in, PrintWriter out) {
        int n = in.readInt();
        int maxDelta = in.readInt();
        int minLen = in.readInt();
        final int[] array = IOUtils.readIntArray(in, n);
        if (minLen > n) {
            out.println(-1);
            return;
        }
        NavigableSet<Integer> set = new TreeSet<Integer>(new Comparator<Integer>() {
            public int compare(Integer o1, Integer o2) {
                if (array[o1] != array[o2]) {
                    return array[o1] - array[o2];
                }
                return o1 - o2;
            }
        });
        int[] maxLen = new int[n];
        int start = 0;
        for (int i = 0; i < n; ++i) {
            set.add(i);
            while (array[set.last()] - array[set.first()] > maxDelta) {
                set.remove(start++);
            }
            maxLen[i] = i - start + 1;
        }
        int[] dp = new int[n];
        ArrayDeque<Entry> q = new ArrayDeque<Entry>();
        dp[0] = 1;
        q.add(new Entry(array[0], 0));
        start = 0;
        int end = 0;
        for (int i = 1; i < n; i++) {
            int endRange = i - minLen + 1;
            int startRange = i - maxLen[i] + 1;

            if (endRange < startRange) {
                dp[i] = Integer.MAX_VALUE / 2;
                continue;
            }
            if (startRange == 0) {
                dp[i] = 1;
                continue;
            }

            while (end < endRange - 1) {
                end++;
                while (!q.isEmpty() && q.peekFirst().value >= dp[end]) {
                    q.pollFirst();
                }
                q.offerFirst(new Entry(dp[end], end));
            }
            while (!q.isEmpty() && q.peekLast().pos < startRange - 1) {
                q.pollLast();
            }
            dp[i] = 1 + dp[q.peekLast().pos];
        }
        if (dp[n - 1] >= Integer.MAX_VALUE / 2) {
            out.println(-1);
        } else {
            out.println(dp[n - 1]);
        }
    }
}

class InputReader {
    private InputStream stream;
    private byte[] buf = new byte[1024];
    private int curChar;
    private int numChars;

    public InputReader(InputStream stream) {
        this.stream = stream;
    }

    public int read() {
        // InputMismatchException -> UnknownError
        if (numChars == -1)
            throw new UnknownError();
        if (curChar >= numChars) {
            curChar = 0;
            try {
                numChars = stream.read(buf);
            } catch (IOException e) {
                throw new UnknownError();
            }
            if (numChars <= 0)
                return -1;
        }
        return buf[curChar++];
    }

    public int readInt() {
        int c = read();
        while (isSpaceChar(c))
            c = read();
        int sgn = 1;
        if (c == '-') {
            sgn = -1;
            c = read();
        } else if (c == '+') {
            c = read();
        }
        int res = 0;
        do {
            if (c < '0' || c > '9')
                throw new InputMismatchException();
            res *= 10;
            res += c - '0';
            c = read();
        } while (!isSpaceChar(c));
        return res * sgn;
    }

    public static boolean isSpaceChar(int c) {
        return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
    }

}

class IOUtils {

    public static int[] readIntArray(InputReader in, int size) {
        int[] res = new int[size];
        for (int i = 0; i < size; ++i) {
            res[i] = in.readInt();
        }
        return res;
    }

}

