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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.StringTokenizer;

public class Round278_B {
    final int MAX = 1000000000+1000;
    final int MIN = -MAX;
    int M;
    int S;

    public int getMin(int[] arr, int index, int max_left, int max_right,
        int queryLeft, int queryRight) {
    if (queryLeft <= max_left && queryRight >= max_right) {
        return arr[index];
    }
    int leftChild = index << 1;
    int rightChild = leftChild + 1;
    int mid = max_left + (max_right - max_left) / 2;
    int leftAns = MAX;
    int rightAns = MAX;

    if (queryRight > mid) {
        // go right
        rightAns = getMin(arr, rightChild, mid + 1, max_right, queryLeft,
            queryRight);
    }

    if (queryLeft <= mid) {
        // go left
        leftAns = getMin(arr, leftChild, max_left, mid, queryLeft,
            queryRight);
    }
    return Math.min(leftAns, rightAns);
    }

    public int getMax(int[] arr, int index, int max_left, int max_right,
        int queryLeft, int queryRight) {
    if (queryLeft <= max_left && queryRight >= max_right) {
        return arr[index];
    }
    int leftChild = index << 1;
    int rightChild = leftChild + 1;
    int mid = max_left + (max_right - max_left) / 2;
    int leftAns = MIN;
    int rightAns = MIN;

    if (queryRight > mid) {
        // go right
        rightAns = getMax(arr, rightChild, mid + 1, max_right, queryLeft,
            queryRight);
    }

    if (queryLeft <= mid) {
        // go left
        leftAns = getMax(arr, leftChild, max_left, mid, queryLeft,
            queryRight);
    }
    return Math.max(leftAns, rightAns);
    }

    public void update(int[] arr, int index, int val) {
    arr[index] = val;
    index >>=1;
    while (index != 0) {
        arr[index] = Math.min(arr[index<<1], arr[(index<<1)+1]);
        index >>= 1;
    }
    }

    int[] data;
    int[] mins, maxs;

    public boolean check(int from, int to) {
    int min = getMin(mins, 1, M, 2 * M-1, M + from, M + to);
    int max = getMax(maxs, 1, M, 2 * M-1, M + from, M + to);
    return (max - min) <= S;
    }

    public int getRightQuery(int start, int from, int to) {
    int low = from;
    int high = to;
    int ret = -1;
    while (low <= high) {
        if (high - low <= 1) {
        if (check(start, high)) {
            ret = Math.max(ret, high);
        } else if (check(start, low)) {
            ret = Math.max(ret, low);
        }
        break;
        }

        int mid = low + (high - low) / 2;
        if (check(start, mid)) {
        ret = mid;
        low = mid + 1;
        } else {
        high = mid - 1;
        }
    }
    return ret;
    }

    public void solve() throws Exception {
    InputReader in = new InputReader();

    int n = in.nextInt();
    S = in.nextInt();
    int l = in.nextInt();
    int[] data = new int[n];
    for (int i = 0; i < n; i++) {
        data[i] = in.nextInt();
    }
    M = n + 1;
    for (int i = 0; i < 30; i++) {
        if ((1 << i) >= M) {
        M = (1 << i);
        break;
        }
    }

    // build mins and max
    mins = new int[2 * M + 2];
    maxs = new int[2 * M + 2];
    for (int i = 0; i < n; i++) {
        mins[M + i] = maxs[M + i] = data[i];
    }
    for (int i = M - 1; i > -1; i--) {
        mins[i] = Math.min(mins[2 * i], mins[2 * i + 1]);
        maxs[i] = Math.max(maxs[2 * i], maxs[2 * i + 1]);
    }
    // build memo
    int[] memo = new int[2 * M + 2];
    for (int i = 0; i < 2 * M; i++) {
        memo[i] = MAX;
    }

    update(memo, M + n, 0);

    for (int i = n - 1; i > -1; i--) {
        // search in the range of index i i+l to ..
        int qLeft = i + l - 1;
//      System.out.println(i+"..");
//      System.out.println("left " + qLeft);
        if (qLeft >= n)
        continue;
        int qRight = getRightQuery(i, qLeft, n - 1);
//      System.out.println("right " + qRight);
        if (qRight == -1)
        continue;
        ++qLeft;
        ++qRight;
//      System.out.println(i + " " + qLeft + " " + qRight);

        int minInRange = getMin(memo, 1, M, 2 * M - 1, M + qLeft, M
            + qRight);
        minInRange = Math.min(MAX, minInRange+1);
//      System.out.println(minInRange);
        update(memo, M + i, minInRange);
    }
//  System.out.println(Arrays.toString(memo));
    System.out.println((memo[M] == MAX) ? -1 : memo[M]);
    }

    public static void main(String[] args) throws Exception {
    new Round278_B().solve();
    }

    static class InputReader {
    BufferedReader in;
    StringTokenizer st;

    public InputReader() throws IOException {
        in = new BufferedReader(new InputStreamReader(System.in));
        st = new StringTokenizer(in.readLine());

    }

    public String next() throws IOException {

        while (!st.hasMoreElements())
        st = new StringTokenizer(in.readLine());
        return st.nextToken();
    }

    public int nextInt() throws NumberFormatException, IOException {
        return Integer.parseInt(next());
    }

    public long nextLong() throws NumberFormatException, IOException {
        return Long.parseLong(next());
    }
    }
}
