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.util.*;
import java.io.*;


public class Main implements Runnable {
        static int INF = (int)1e9 + 10;
        
        class SegmentTree{
            int n;
            int[] a;
            SegmentTree(int _n){
                n = _n;
                a = new int[4 * n + 10];
                Arrays.fill(a, INF);
            }
            
            void update(int x, int v){
                set(0, 0, n-1, x, v);
            }
            
            void set(int at, int l, int r, int need, int v){
                if(l == r){
                    a[at] = v;
                    return;
                }
                int m = (l + r) / 2;
                if(need <= m)
                    set(at * 2 + 1, l, m, need, v);
                else
                    set(at * 2 + 2, m+1, r, need, v);
                
                a[at] = Math.min(a[at * 2 + 1], a[at * 2 + 2]);
            }
            
            int get(int L, int R){
                return get(0, 0, n-1, L, R);
            }
            
            int get(int at, int l, int r, int L, int R){
                if(L > R)
                    return INF;
                if(l == L && R == r)
                    return a[at];
                
                int m = (l + r) / 2;
                int r1, r2;
                r1 = get(at * 2 + 1, l, m, L, Math.min(m, R));
                r2 = get(at * 2 + 2, m+1, r, Math.max(m+1, L), R);
                return Math.min(r1, r2);
            }
        }
    
	public void solve() throws IOException {
		int n = nextInt();
                int S = nextInt();
                int L = nextInt();
                
                int[] arr = new int[n];
                for(int i = 0; i < n; i++){
                    arr[i] = nextInt();
                }
                
                SegmentTree min = new SegmentTree(n);
                SegmentTree max = new SegmentTree(n);
                SegmentTree dpTree = new SegmentTree(n+1);
                for(int i = 0; i < n; i++){
                    min.update(i, arr[i]);
                    max.update(i, -arr[i]);
                }
                dpTree.update(0, 0);
                
                int[] dp = new int[n+1];
                Arrays.fill(dp, INF);
                dp[0] = 0;
                
                int left = 0;
                for(int right = 0; right < n; right++){
                    while(-max.get(left, right) - min.get(left, right) > S) left++;
                    int validL = left;
                    int validR = right - L + 1;
                    if(validL <= validR){
                        int v = dpTree.get(validL, validR);
                        dp[right+1] = v + 1;
                    }
                    
                    dpTree.update(right+1, dp[right+1]);
                }
                
                if(dp[n] >= INF)
                    out.println(-1);
                else
                    out.println(dp[n]);
	}
        

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

        public void debug(Object... arr){
            System.out.println(Arrays.deepToString(arr));
        }

        public void print1Int(int[] a){
                for(int i = 0; i < a.length; i++)
                        System.out.print(a[i] + " ");
                System.out.println();
        }
        
        public void print2Int(int[][] a){
                for(int i = 0; i < a.length; i++){
                        for(int j = 0; j < a[0].length; j++){
                                System.out.print(a[i][j] + " ");
                        }
                        System.out.println();
                }
        }
        
	public void run() {
		try {
			in = new BufferedReader(new InputStreamReader(System.in));
                        out = new PrintWriter(System.out);
			tok = null;
			solve();
			in.close();
                        out.close();
		} catch (IOException e) {
			System.exit(0);
		}
	}

	public String nextToken() throws IOException {
		while (tok == null || !tok.hasMoreTokens()) {
			tok = new StringTokenizer(in.readLine());
		}
		return tok.nextToken();
	}

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

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

	public double nextDouble() throws IOException {
		return Double.parseDouble(nextToken());
	}
        PrintWriter out;
	BufferedReader in;
	StringTokenizer tok;
}