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.*;

public class B {

    BufferedReader br;
    PrintWriter out;
    StringTokenizer st;
    boolean eof;

    static class MultiTreeSet {
        private TreeMap<Integer, Integer> map = new TreeMap<>();

        int count(int x) {
            Integer ret = map.get(x);
            return ret == null ? 0 : ret;
        }

        void put(int x) {
            map.put(x, count(x) + 1);
        }
        
        void remove(int x) {
            int c = count(x);
            if (c == 1) {
                map.remove(x);
            } else {
                map.put(x, c - 1);
            }
        }
        
        int first() {
            return map.isEmpty() ? 1_000_000_001 : map.firstKey();
        }
        
        int last() {
            return map.isEmpty() ? -1 : map.lastKey();
        }
    }
    
    static final int INF = Integer.MAX_VALUE / 3;
    
    static class Node {
        int l, r;
        Node left, right;
        int min;
        public Node(int l, int r) {
            this.l = l;
            this.r = r;
            min = INF;
            if (r - l > 1) {
                int mid = (l + r) >> 1;
                left = new Node(l, mid);
                right = new Node(mid, r);
            }
        }
        
        int get(int ql, int qr) {
            if (l >= qr || ql >= r) {
                return INF;
            }
            if (ql <= l && r <= qr) {
                return min;
            }
            return Math.min(left.get(ql, qr), right.get(ql, qr));
        }
        
        void set(int ind, int val) {
            if (l == ind && ind + 1 == r){ 
                min = val;
                return;
            }
            (ind < left.r ? left : right).set(ind, val);
            min = Math.min(left.min, right.min);
        }
        
    }

    void solve() throws IOException {
        int n = nextInt();
        int s = nextInt();
        int l = nextInt();
        int[] a = new int[n];
        for (int i = 0; i < n; i++) {
            a[i] = nextInt();
        }
        
        int[] to = new int[n];
        
        MultiTreeSet set = new MultiTreeSet();
        for (int i = 0, j = 0; i < n; i++) {
            while (j < n) {
                set.put(a[j]);
                if (set.last() - set.first() <= s) {
                    j++;
                } else {
                    set.remove(a[j]);
                    break;
                }
            }
            to[i] = j;
            set.remove(a[i]);
        }
        
        Node ans = new Node(0, n + 1);
        ans.set(n, 0);
        for (int i = n - 1; i >= 0; i--) {
            int from = i + l;
            int toQ = Math.min(to[i] + 1, n + 1);
//          System.err.println(i + " " + from + " " + toQ);
            
            if (from < toQ) {
//              System.err.println(ans.get(from, toQ));
                ans.set(i, ans.get(from, toQ) + 1);
            }
        }
        int ret = ans.get(0, 1);
        if (ret >= INF) {
            ret = -1;
        }
        out.println(ret);
    }

    B() throws IOException {
        br = new BufferedReader(new InputStreamReader(System.in));
        out = new PrintWriter(System.out);
        solve();
        out.close();
    }

    public static void main(String[] args) throws IOException {
        new B();
    }

    String nextToken() {
        while (st == null || !st.hasMoreTokens()) {
            try {
                st = new StringTokenizer(br.readLine());
            } catch (Exception e) {
                eof = true;
                return null;
            }
        }
        return st.nextToken();
    }

    String nextString() {
        try {
            return br.readLine();
        } catch (IOException e) {
            eof = true;
            return null;
        }
    }

    int nextInt() throws IOException {
        return Integer.parseInt(nextToken());
    }

    long nextLong() throws IOException {
        return Long.parseLong(nextToken());
    }

    double nextDouble() throws IOException {
        return Double.parseDouble(nextToken());
    }
}