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.io.PrintWriter;
import java.util.Arrays;
import java.util.StringTokenizer;
import java.util.function.BiFunction;

import static java.lang.Math.abs;

public class Main {

    static class Queue {
        BiFunction<Integer, Integer, Integer> f;
        int indentity;
        int size;
        class Stack {
            int size;
            int[][] s;
            Stack(int c) {
                s = new int[c][2];
            }
            void push(int item) {
                s[size][1] = size == 0 ? item : f.apply(item, s[size - 1][1]);
                s[size++][0] = item;
            }
            int f() {return size == 0 ? indentity : s[size - 1][1]; }
            int pop() { return s[--size][0]; }
        }
        Stack st1;
        Stack st2;
        Queue(int c, BiFunction<Integer, Integer, Integer> f, int indentity) {
            this.f = f;
            this.indentity = indentity;
            st1 = new Stack(c);
            st2 = new Stack(c);
        }
        void enq(int elem) { st1.push(elem); size++; }
        int deq() {
            if(st2.size == 0) {
                while (st1.size != 0) {
                    st2.push(st1.pop());
                }
            }
            size--;
            return st2.pop();
        }
        int f() { return f.apply(st1.f(), st2.f());}
    }

    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();
        }
        Queue q1 = new Queue(n, Math::min, Integer.MAX_VALUE);
        Queue q2 = new Queue(n, Math::max, Integer.MIN_VALUE);
        int[] g = new int[n];
        for (int i = 0; i < n; i++) {
            q1.enq(a[i]);
            q2.enq(a[i]);
            if(abs(q1.f() - q2.f()) <= s && q1.size >= l) {
                g[i] = Math.max(g[i], q1.size);
            }
            while (abs(q1.f() - q2.f()) > s && q1.size > 0) {
                q1.deq();
                q2.deq();
            }
            if(abs(q1.f() - q2.f()) <= s && q1.size >= l) {
                g[i] = Math.max(g[i], q1.size);
            }
        }
        int[] dp = new int[n + 1];
        Arrays.fill(dp, Integer.MAX_VALUE / 2);
        dp[0] = 0;
        Queue q3 = new Queue(n + 1, Math::min, Integer.MAX_VALUE / 2);
        int st = -1;
        int end = 0;
        for (int i = 1; i <= n; i++) {
            if(g[i - 1] == 0) continue;

            while (st <= i - g[i - 1]) {
                if(q3.size > 0) q3.deq();
                st++;
                end = Math.max(i - g[i - 1], end);
            }

            for (int j = end; j <= i - l; j++) {
                q3.enq(dp[j] + 1);
                end = i - l + 1;
            }
            dp[i] = Math.min(dp[i], q3.f());
        }

//        for (int i = 1; i <= n; i++) {
//            if(g[i - 1] == 0) continue;
//            for (int j = i - g[i - 1]; j <= i - l; j++) {
//                dp[i] = Math.min(dp[i], dp[j] + 1);
//            }
//        }
        if (dp[n] == 0 || dp[n] >= Integer.MAX_VALUE / 2) System.out.println("-1");
        else System.out.println(dp[n]);
    }

    public void run() {
        try {
            br = new BufferedReader(new InputStreamReader(System.in));
            out = new PrintWriter(System.out);
            solve();
            out.close();
            br.close();
        } catch (Exception e) {
            e.printStackTrace();
            System.exit(239);
        }
    }

    BufferedReader br;
    StringTokenizer st;
    PrintWriter out;

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

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

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

    String nextToken() throws IOException {
        while (st == null || !st.hasMoreTokens()) {
            String line = br.readLine();
            if (line == null) {
                return null;
            }
            st = new StringTokenizer(line);
        }
        return st.nextToken();
    }

    public static void main(String[] args) {
        new Main().run();
    }
}