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.util.stream.Stream;

public class Main implements Runnable {
    static final int MOD = (int) 1e9 + 7;
    static final int MI = (int) 1e9;
    static final long ML = (long) 1e18;
    static final Reader in = new Reader();
    static final PrintWriter out = new PrintWriter(System.out);
    StringBuilder answer = new StringBuilder();

    public static void main(String[] args) {
        new Thread(null, new Main(), "persefone", 1 << 32).start();
    }

    @Override
    public void run() {
        solve();
        printf();
        flush();
    }

    void solve() {
        int n = in.nextInt();
        int s = in.nextInt();
        int l = in.nextInt();
        int[] a = in.nextIntArray(n);
        SparseTable rmq = new SparseTable(a, n);
        int[] dp = new int[n];
        Arrays.fill(dp, n + 10);
        SegmentTreeMin segMins = new SegmentTreeMin(dp, n);
        for (int i = l - 1; i < n; i++) {
            int leftBound = rmq.get(i, s);
            if (leftBound > i - l + 1) continue;
            int min = leftBound == 0 ? 0 : segMins.get(leftBound - 1, i - l);
            if (min > n) continue;
            segMins.update(i, min + 1);
        }
        printf(dp[n - 1] > n ? -1 : dp[n - 1]);
    }

    static class SparseTable {
        private int n, MAX_BLOCK_LENGTH;
        private int[] a, log;
        private int[][] min, max;

        public SparseTable(int[] a, int n) {
            this.n = n;
            this.a = a;
            this.log = new int[n + 1];
            for (int i = 2; i <= n; i++) log[i] = log[i >> 1] + 1;
            this.MAX_BLOCK_LENGTH = log[n];
            this.max = new int[n][MAX_BLOCK_LENGTH + 1];
            this.min = new int[n][MAX_BLOCK_LENGTH + 1];
            build();
        }

        void build() {
            for (int i = 0; i < n; i++) max[i][0] = min[i][0] = a[i];
            for (int j = 1; j <= MAX_BLOCK_LENGTH; j++) {
                for (int i = 0; i + (1 << j) <= n; i++) {
                    int k = i + (1 << j - 1);
                    max[i][j] = Math.max(max[i][j - 1], max[k][j - 1]);
                    min[i][j] = Math.min(min[i][j - 1], min[k][j - 1]);
                }
            }
        }

        int getMax(int l, int r) {
            int k = log[r - l + 1];
            return Math.max(max[l][k], max[r - (1 << k) + 1][k]);
        }

        int getMin(int l, int r) {
            int k = log[r - l + 1];
            return Math.min(min[l][k], min[r - (1 << k) + 1][k]);
        }

        int[] getMinMax(int l, int r) {
            int k = log[r - l + 1];
            int m = r - (1 << k) + 1;
            return new int[]{Math.min(min[l][k], min[m][k]), Math.max(max[l][k], max[m][k])};
        }

        int get(int r, int k) {
            int l = 0, m = 0, R = r, ans = r;
            while (l < r) {
                int[] cur = getMinMax(m = l + r >> 1, R);
                if (cur[1] - cur[0] <= k) ans = r = m; else l = m + 1;
            }
            return ans;
        }
    }

    static class SegmentTreeMin {
        private int n;
        private int[] a, min;

        public SegmentTreeMin(int[] a, int n) {
            this.n = n;
            this.a = a;
            this.min = new int[4 * n + 4];
            build(1, 0, n - 1);
        }

        void build(int currentVertex, int currentLeft, int currentRight) {
            if (currentLeft == currentRight) min[currentVertex] = a[currentLeft];
            else {
                int middle = currentLeft + currentRight >> 1, doubleVex = currentVertex << 1;
                build(doubleVex, currentLeft, middle);
                build(doubleVex + 1, middle + 1, currentRight);
                min[currentVertex] = Math.min(min[doubleVex], min[doubleVex + 1]);
            }
        }

        void update(int currentVertex, int currentLeft, int currentRight, int pos, int value) {
            if (currentLeft == currentRight) min[currentVertex] = a[pos] = value;
            else {
                int middle = currentLeft + currentRight >> 1, doubleVex = currentVertex << 1;
                if (pos <= middle)
                    update(doubleVex, currentLeft, middle, pos, value);
                else
                    update(doubleVex + 1, middle + 1, currentRight, pos, value);
                min[currentVertex] = Math.min(min[doubleVex], min[doubleVex + 1]);
            }
        }

        void update(int pos, int value) {
            update(1, 0, n - 1, pos, value);
        }

        int get(int currentVertex, int currentLeft, int currentRight, int left, int right) {
            if (currentLeft > right || currentRight < left) return Integer.MAX_VALUE;
            else if (currentLeft >= left && currentRight <= right) return min[currentVertex];
            else {
                int middle = currentLeft + currentRight >> 1, doubleVex = currentVertex << 1;
                return Math.min(get(doubleVex, currentLeft, middle, left, right),
                        get(doubleVex + 1, middle + 1, currentRight, left, right));
            }
        }

        int get(int left, int right) {
            return get(1, 0, n - 1, left, right);
        }
    }

    void printf() {
        out.print(answer);
    }

    void close() {
        out.close();
    }

    void flush() {
        out.flush();
    }

    void printf(Stream<?> str) {
        str.forEach(o -> add(o, " "));
        add("\n");
    }


    void printf(Object... obj) {
        printf(false, obj);
    }

    void printfWithDescription(Object... obj) {
        printf(true, obj);
    }


    private void printf(boolean b, Object... obj) {

        if (obj.length > 1) {
            for (int i = 0; i < obj.length; i++) {
                if (b) add(obj[i].getClass().getSimpleName(), " - ");
                if (obj[i] instanceof Collection<?>) {
                    printf((Collection<?>) obj[i]);
                } else if (obj[i] instanceof int[][]) {
                    printf((int[][]) obj[i]);
                } else if (obj[i] instanceof long[][]) {
                    printf((long[][]) obj[i]);
                } else if (obj[i] instanceof double[][]) {
                    printf((double[][]) obj[i]);
                } else printf(obj[i]);
            }
            return;
        }

        if (b) add(obj[0].getClass().getSimpleName(), " - ");
        printf(obj[0]);
    }

    void printf(Object o) {
        if (o instanceof int[])
            printf(Arrays.stream((int[]) o).boxed());
        else if (o instanceof char[])
            printf(new String((char[]) o));
        else if (o instanceof long[])
            printf(Arrays.stream((long[]) o).boxed());
        else if (o instanceof double[])
            printf(Arrays.stream((double[]) o).boxed());
        else if (o instanceof boolean[]) {
            for (boolean b : (boolean[]) o) add(b, " ");
            add("\n");
        } else
            add(o, "\n");
    }

    void printf(int[]... obj) {
        for (int i = 0; i < obj.length; i++) printf(obj[i]);
    }

    void printf(long[]... obj) {
        for (int i = 0; i < obj.length; i++) printf(obj[i]);
    }

    void printf(double[]... obj) {
        for (int i = 0; i < obj.length; i++) printf(obj[i]);
    }

    void printf(boolean[]... obj) {
        for (int i = 0; i < obj.length; i++) printf(obj[i]);
    }

    void printf(Collection<?> col) {
        printf(col.stream());
    }

    <T, K> void add(T t, K k) {
        if (t instanceof Collection<?>) {
            ((Collection<?>) t).forEach(i -> add(i, " "));
        } else if (t instanceof Object[]) {
            Arrays.stream((Object[]) t).forEach(i -> add(i, " "));
        } else
            add(t);
        add(k);
    }


    <T> void add(T t) {
        answer.append(t);
    }

    static class Reader {
        private BufferedReader br;
        private StringTokenizer st;

        Reader() {
            br = new BufferedReader(new InputStreamReader(System.in));
        }

        Reader(String fileName) throws FileNotFoundException {
            br = new BufferedReader(new FileReader(fileName));
        }

        boolean isReady() throws IOException {
            return br.ready();
        }

        String next() {
            try {
                while (st == null || !st.hasMoreTokens()) {
                    st = new StringTokenizer(br.readLine());
                }
            } catch (IOException e) {
                e.printStackTrace();
            }
            return st.nextToken();
        }

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

        int[] nextIntArray(int n) {
            int[] arr = new int[n];
            for (int i = 0; i < n; i++)
                arr[i] = nextInt();
            return arr;
        }

        long nextLong() {
            return Long.parseLong(next());
        }

        String nextLine() {
            String s = "";
            try {
                s = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return s;
        }
    }
}