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.InputStream;
import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.BufferedReader;
import java.io.PrintWriter;
import java.util.StringTokenizer;
import java.util.Arrays;
import java.io.InputStreamReader;

/**
 * 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);
        TaskB solver = new TaskB();
        solver.solve(1, in, out);
        out.close();
    }

    static class TaskB {
        public void solve(int testNumber, InputReader in, PrintWriter out) {
            int n = in.nextInt();
            int s = in.nextInt();
            int l = in.nextInt();

            int[] a = new int[n];
            for (int i = 0; i < n; ++i) {
                a[i] = in.nextInt();
            }

            int[] b = a.clone();
            for (int i = 0; i < n; ++i) {
                b[i] = -a[i];
            }

            RMQ rmq1 = new SparseTable(a);
            RMQ rmq2 = new SparseTable(b);

            IntervalTree tree = new IntervalTree(n + 1);

            int[] dp = new int[n + 1];
            dp[0] = 0;
            tree.insert(0, 0);
            for (int i = 1; i <= n; ++i) {
                int left = 0, right = i - l;
                while (left < right) {
                    int mid = (left + right) >> 1;
                    if (-rmq1.getMinValue(mid, i - 1) - rmq2.getMinValue(mid, i - 1) <= s) {
                        right = mid;
                    } else {
                        left = mid + 1;
                    }
                }
                if (right < 0 || -rmq1.getMinValue(left, i - 1) - rmq2.getMinValue(left, i - 1) > s) {
                    dp[i] = 0x3F3F3F3F;
                } else {
                    dp[i] = -tree.getMaxValue(left, i - l) + 1;
                }
                tree.insert(i, -dp[i]);
            }

            if (dp[n] >= 0x3F3F3F3F) {
                dp[n] = -1;
            }

            out.println(dp[n]);

        }

        interface RMQ {
            int getMinValue(int left, int right);

        }

        static class SparseTable implements RMQ {
            int[][] min;
            int[] orig;
            int[] log;
            int size;
            int maxPw;

            SparseTable(int[] seq) {
                this.orig = seq;
                this.size = seq.length;
                construct();
            }

            void construct() {
                int power = 1;
                while ((1 << power) < size) {
                    ++power;
                }
                maxPw = power + 1;
                min = new int[maxPw][size];
                log = new int[size + 1];
                log[0] = 0;
                for (int i = 1; i <= size; ++i) {
                    log[i] = 0;
                    while ((1 << (log[i] + 1)) < i) {
                        ++log[i];
                    }
                }

                for (int i = 0; i < size; ++i) {
                    min[0][i] = orig[i];
                }

                for (int i = 1; i < maxPw; ++i) {
                    for (int j = 0; j < size; ++j) {
                        min[i][j] = min[i - 1][j];
                        if (j + (1 << (i - 1)) < size) {
                            min[i][j] = Math.min(min[i][j], min[i - 1][j + (1 << (i - 1))]);
                        }
                    }
                }
            }


            public int getMinValue(int left, int right) {
                if (right < left) {
                    return Integer.MAX_VALUE;
                }
                int step = log[right - left + 1];
                return Math.min(min[step][left], min[step][right - (1 << step) + 1]);
            }

        }

        class IntervalTree {
            int size;
            int[] val;

            IntervalTree(int length) {
                this.size = length;
                val = new int[length * 4 + 100];
                Arrays.fill(val, -0x3F3F3F3F);
            }

            int getMaxValue(int left, int right, int l, int r, int x) {
                if (l <= left && r >= right) {
                    return val[x];
                }
                int mid = (left + right) >> 1;
                int ret = Integer.MIN_VALUE;
                if (l <= mid) ret = getMaxValue(left, mid, l, r, x * 2);
                if (r > mid) ret = Math.max(ret, getMaxValue(mid + 1, right, l, r, x * 2 + 1));
                return ret;
            }

            int getMaxValue(int left, int right) {
                return getMaxValue(0, size - 1, left, right, 1);
            }

            void insert(int left, int right, int pos, int x, int value) {
                if (left == right) {
                    val[x] = Math.max(val[x], value);
                    return;
                }

                int mid = (left + right) >> 1;
                if (pos <= mid) {
                    insert(left, mid, pos, x * 2, value);
                } else {
                    insert(mid + 1, right, pos, x * 2 + 1, value);
                }

                val[x] = Math.max(val[x * 2], val[x * 2 + 1]);
            }

            void insert(int pos, int value) {
                insert(0, size - 1, pos, 1, value);
            }

        }

    }

    static class InputReader {
        BufferedReader reader;
        StringTokenizer tokenizer;

        public InputReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream));
            tokenizer = null;
        }

        public String next() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (Exception e) {
                    throw new UnknownError();
                }
            }
            return tokenizer.nextToken();
        }

        public int nextInt() {
            return Integer.parseInt(next());
        }

    }
}

