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.
//package codeforces;

import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.*;

public class D {
    BufferedReader reader = new BufferedReader(new InputStreamReader(System.in));
    PrintWriter writer = new PrintWriter(System.out);
    StringTokenizer stringTokenizer;

    String next() throws IOException {
        while (stringTokenizer == null || !stringTokenizer.hasMoreTokens()) {
            stringTokenizer = new StringTokenizer(reader.readLine());
        }
        return stringTokenizer.nextToken();
    }

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

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

    int MOD = 1000 * 1000 * 1000 + 7;

    int sum(int a, int b) {
        a += b;
        return a >= MOD ? a - MOD : a;
    }

    int product(int a, int b) {
        return (int) (1l * a * b % MOD);
    }

    @SuppressWarnings("unchecked")
    void solve() throws IOException {
        int n = nextInt(), s = nextInt(), l = nextInt();
        class SegmentTree {
            int INF = 1 << 20;
            int n;
            int q;
            int[] a;

            SegmentTree(int n) {
                this.n = n;
                q = 1;
                while(q <= n) q *= 2;
                a = new int[2 * q];
                Arrays.fill(a, INF);
            }

            void set(int i, int x) {
                for(i += q; i > 0; i /= 2) {
                    a[i] = Math.min(a[i], x);
                }
            }

            int getMin(int l, int r) {
                int result = INF;
                for(l += q, r += q; l < r; l /= 2, r /= 2) {
                    if(l % 2 == 1) {
                        result = Math.min(result, a[l++]);
                    }
                    if(r % 2 == 1) {
                        result = Math.min(result, a[--r]);
                    }
                }
                return result;
            }
        }
        int[] a = new int[n];
        for(int i = 0; i < n; i++) {
            a[i] = nextInt();
        }
        TreeSet<Integer> set = new TreeSet<>();
        for (int x : a) {
            set.add(x);
        }
        Map<Integer, Integer> index = new HashMap<>(2 * n);
        for (Integer x : set) {
            index.put(x, index.size());
        }
        SegmentTree minPosition = new SegmentTree(n);
        SegmentTree re = new SegmentTree(n);
        SegmentTree dp = new SegmentTree(n + 1);
        dp.set(n, 0);
        for(int i = n - 1; i >= 0; i--) {
            minPosition.set(index.get(a[i]), i);
            Integer upperBad = set.ceiling(a[i] + s + 1);
            Integer lowerBad = set.floor(a[i] - s - 1);
            int rightEnd = n;
            if(lowerBad != null) {
                int ix = index.get(lowerBad);
                rightEnd = Math.min(rightEnd, minPosition.getMin(0, ix + 1));
            }
            if(upperBad != null) {
                int ix = index.get(upperBad);
                rightEnd = Math.min(rightEnd, minPosition.getMin(ix, n));
            }
            rightEnd = Math.min(rightEnd, re.getMin(i + 1, rightEnd));
            re.set(i, rightEnd);
            int leftEnd = i + l;
            dp.set(i, 1 + dp.getMin(leftEnd, rightEnd + 1));
        }
        int ans = dp.getMin(0, 1);
        if(ans == dp.INF) {
            ans = -1;
        }
        writer.println(ans);
        writer.close();
    }

    public static void main(String[] args) throws IOException {
//        new D().test();
        new D().solve();
    }
}
