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.BufferedWriter;
import java.util.InputMismatchException;
import java.util.NoSuchElementException;
import java.math.BigInteger;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.io.Writer;
import java.io.IOException;
import java.util.TreeSet;
import java.io.InputStream;
import java.io.OutputStreamWriter;
import java.util.Comparator;
import java.util.SortedSet;
import java.util.Set;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 * @author Nguyen Trung Hieu - vuondenthanhcong11@gmail.com
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        OutputWriter out = new OutputWriter(outputStream);
        TaskB solver = new TaskB();
        solver.solve(1, in, out);
        out.close();
    }
}

class TaskB {
    public void solve(int testNumber, InputReader in, OutputWriter out) {
        int count = in.readInt();
        int maxDelta = in.readInt();
        int minLength = in.readInt();
        final int[] A = IOUtils.readIntArray(in, count);

        IntervalTree minTree = new LongIntervalTree(count + 1) {
            protected long joinValue(long left, long right) {
                return Math.min(left, right);
            }

            protected long joinDelta(long was, long delta) {
                return Math.min(was, delta);
            }

            protected long accumulate(long value, long delta, int length) {
                return Math.min(value, delta);
            }

            protected long neutralValue() {
                return Integer.MAX_VALUE / 2;
            }

            protected long neutralDelta() {
                return Integer.MAX_VALUE / 2;
            }
        };

        NavigableSet<Integer> set = new TreeSet<Integer>(new Comparator<Integer>() {
            public int compare(Integer o1, Integer o2) {
                if (A[o1] != A[o2])
                    return A[o1] - A[o2];
                return o1 - o2;
            }
        });

        minTree.update(0, 0, 0);

        int i = 0;
        int start = 0;
        while (i < count) {
            set.add(i);
            while (!set.isEmpty() && A[set.last()] - A[set.first()] > maxDelta)
                set.remove(start++);
            if (i - start + 1 >= minLength)
                minTree.update(i + 1, i + 1, minTree.query(start, i - minLength + 1) + 1);
            i++;
        }

        if (minTree.query(count, count) >= Integer.MAX_VALUE / 2)
            out.printLine(-1);
        else
            out.printLine(minTree.query(count, count));
    }
}

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

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

    public int read() {
        if (numChars == -1)
            throw new InputMismatchException();
        if (curChar >= numChars) {
            curChar = 0;
            try {
                numChars = stream.read(buf);
            } catch (IOException e) {
                throw new InputMismatchException();
            }
            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();
        }
        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 boolean isSpaceChar(int c) {
        if (filter != null)
            return filter.isSpaceChar(c);
        return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
    }

    public interface SpaceCharFilter {
        public boolean isSpaceChar(int ch);
    }

}

class OutputWriter {
    private final PrintWriter writer;

    public OutputWriter(OutputStream outputStream) {
        writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(outputStream)));
    }

    public void print(Object...objects) {
        for (int i = 0; i < objects.length; i++) {
            if (i != 0)
                writer.print(' ');
            writer.print(objects[i]);
        }
    }

    public void printLine(Object...objects) {
        print(objects);
        writer.println();
    }

    public void close() {
        writer.close();
    }

}

class IOUtils {

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

}

abstract class IntervalTree {
    protected int size;

    public IntervalTree(int size, boolean shouldInit) {
        this.size = size;
        int nodeCount = Math.max(1, Integer.highestOneBit(size) << 2);
        initData(size, nodeCount);
        if (shouldInit)
            init();
    }

    protected abstract void initData(int size, int nodeCount);
    protected abstract void initAfter(int root, int left, int right, int middle);
    protected abstract void initBefore(int root, int left, int right, int middle);
    protected abstract void initLeaf(int root, int index);
    protected abstract void updatePostProcess(int root, int left, int right, int from, int to, long delta, int middle);
    protected abstract void updatePreProcess(int root, int left, int right, int from, int to, long delta, int middle);
    protected abstract void updateFull(int root, int left, int right, int from, int to, long delta);
    protected abstract long queryPostProcess(int root, int left, int right, int from, int to, int middle, long leftResult, long rightResult);
    protected abstract void queryPreProcess(int root, int left, int right, int from, int to, int middle);
    protected abstract long queryFull(int root, int left, int right, int from, int to);
    protected abstract long emptySegmentResult();

    public void init() {
        init(0, 0, size - 1);
    }

    private void init(int root, int left, int right) {
        if (left == right) {
            initLeaf(root, left);
        } else {
            int middle = (left + right) >> 1;
            initBefore(root, left, right, middle);
            init(2 * root + 1, left, middle);
            init(2 * root + 2, middle + 1, right);
            initAfter(root, left, right, middle);
        }
    }

    public void update(int from, int to, long delta) {
        update(0, 0, size - 1, from, to, delta);
    }

    protected void update(int root, int left, int right, int from, int to, long delta) {
        if (left > to || right < from)
            return;
        if (left >= from && right <= to) {
            updateFull(root, left, right, from, to, delta);
            return;
        }
        int middle = (left + right) >> 1;
        updatePreProcess(root, left, right, from, to, delta, middle);
        update(2 * root + 1, left, middle, from, to, delta);
        update(2 * root + 2, middle + 1, right, from, to, delta);
        updatePostProcess(root, left, right, from, to, delta, middle);
    }

    public long query(int from, int to) {
        return query(0, 0, size - 1, from, to);
    }

    protected long query(int root, int left, int right, int from, int to) {
        if (left > to || right < from)
            return emptySegmentResult();
        if (left >= from && right <= to)
            return queryFull(root, left, right, from, to);
        int middle = (left + right) >> 1;
        queryPreProcess(root, left, right, from, to, middle);
        long leftResult = query(2 * root + 1, left, middle, from, to);
        long rightResult = query(2 * root + 2, middle + 1, right, from, to);
        return queryPostProcess(root, left, right, from, to, middle, leftResult, rightResult);
    }
}

abstract class LongIntervalTree extends IntervalTree {
    protected long[] value;
    protected long[] delta;

    protected LongIntervalTree(int size) {
        this(size, true);
    }

    public LongIntervalTree(int size, boolean shouldInit) {
        super(size, shouldInit);
    }

    protected void initData(int size, int nodeCount) {
        value = new long[nodeCount];
        delta = new long[nodeCount];
    }

    protected abstract long joinValue(long left, long right);
    protected abstract long joinDelta(long was, long delta);
    protected abstract long accumulate(long value, long delta, int length);
    protected abstract long neutralValue();
    protected abstract long neutralDelta();

    protected long initValue(int index) {
        return neutralValue();
    }

    protected void initAfter(int root, int left, int right, int middle) {
        value[root] = joinValue(value[2 * root + 1], value[2 * root + 2]);
        delta[root] = neutralDelta();
    }

    protected void initBefore(int root, int left, int right, int middle) {
    }

    protected void initLeaf(int root, int index) {
        value[root] = initValue(index);
        delta[root] = neutralDelta();
    }

    protected void updatePostProcess(int root, int left, int right, int from, int to, long delta, int middle) {
        value[root] = joinValue(value[2 * root + 1], value[2 * root + 2]);
    }

    protected void updatePreProcess(int root, int left, int right, int from, int to, long delta, int middle) {
        pushDown(root, left, middle, right);
    }

    protected void pushDown(int root, int left, int middle, int right) {
        value[2 * root + 1] = accumulate(value[2 * root + 1], delta[root], middle - left + 1);
        value[2 * root + 2] = accumulate(value[2 * root + 2], delta[root], right - middle);
        delta[2 * root + 1] = joinDelta(delta[2 * root + 1], delta[root]);
        delta[2 * root + 2] = joinDelta(delta[2 * root + 2], delta[root]);
        delta[root] = neutralDelta();
    }

    protected void updateFull(int root, int left, int right, int from, int to, long delta) {
        value[root] = accumulate(value[root], delta, right - left + 1);
        this.delta[root] = joinDelta(this.delta[root], delta);
    }

    protected long queryPostProcess(int root, int left, int right, int from, int to, int middle, long leftResult, long rightResult) {
        return joinValue(leftResult, rightResult);
    }

    protected void queryPreProcess(int root, int left, int right, int from, int to, int middle) {
        pushDown(root, left, middle, right);
    }

    protected long queryFull(int root, int left, int right, int from, int to) {
        return value[root];
    }

    protected long emptySegmentResult() {
        return neutralValue();
    }
}
