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 Task {
		
	public static void main(String[] args) throws IOException {
		new Task().solve();
	}
	
	PrintWriter out;
	int cnt = 0;
	int n;
	boolean[] used;
	int[] use;
	ArrayList<Integer>[] rg;
	ArrayList<Integer> tsort = new ArrayList<Integer>();
	int[] comp;
	int[] compsize;
	int[] mt;
	int[] a;
	int k;
	boolean[][] g;
	int dp[];
	int m;
	int[] list;
	void solve() throws IOException{
		Reader in = new Reader("output.txt");
		out = new PrintWriter( new BufferedWriter(new OutputStreamWriter(System.out)) );
		//out = new PrintWriter(new FileWriter(new File("output.txt"))); 
		
		
		int n = in.nextInt();
		int s = in.nextInt();
		int l = in.nextInt();
		
		int[] a = new int[n+1];
		int[] g = new int[n+1];
		
		for (int i = 0; i < n; i++)
			a[i] = in.nextInt();
		
		Deque<Pair> deq_min = new LinkedList<Pair>();
		Deque<Pair> deq_max = new LinkedList<Pair>();
		
		int[] f = new int[n];
		int inf = Integer.MAX_VALUE;
		int w = 0;
		int pos = 0;
		
		for (int i = 0; i < n; i++) {
			
			Pair p = new Pair(a[i], i);
			
			while (!deq_min.isEmpty() && a[i] < deq_min.getLast().v)
				deq_min.removeLast();
			deq_min.addLast(p);
			
			while (!deq_max.isEmpty() && a[i] > deq_max.getLast().v)
				deq_max.removeLast();
			deq_max.addLast(p);
			
			w++;
			
			while (deq_max.getFirst().v-deq_min.getFirst().v > s) {
				pos++;
				while (deq_max.getFirst().i < pos)
					deq_max.removeFirst();
				while (deq_min.getFirst().i < pos)
					deq_min.removeFirst();
			}
			
			g[i] = i-pos+1;
			//if (g[i] < l)
				//g[i] = inf;
		}
		
		//for (int i = 0; i < n; i++)
			//out.print(g[i]+" ");
		//out.println();
		SegmentTree st = new SegmentTree(n);
		//st.build(1, g, 0, n-1);
		//out.println(st.getmin(4, 4));
		Arrays.fill(f, 2000000000);
		inf = 2000000000;
		
		if (l-1 < n) {
		if (g[l-1] == l)
			f[l-1] = 1;
		else
			f[l-1] = inf;
		}
		
		for (int i = 0; i <= Math.min(l-1, n-1); i++) {
			st.update(f[i], i, 0, n-1, 1);
		}
		
		for (int i = l; i < n; i++) {
			
			if (g[i-1]+1 == g[i])
				f[i] = f[i-1];
			
			int min = inf;
			if (Math.max(0, i-g[i]) <= i-l)
				min = st.getmin(Math.max(0, i-g[i]), i-l);
			
			//for (int j = Math.max(0, i-g[i]); j <= i-l; j++)
				//if (f[j] != inf)
			//out.println(min+" "+Math.max(0, i-g[i])+" "+(i-l));
			if (min != inf)
				f[i] = Math.min(f[i], min+1);
			st.update(f[i], i, 0, n-1, 1);
		}
		
		//for (int i = 0; i < n; i++)
			//System.out.print(f[i]+" ");
		
		if (f[n-1] == 2000000000)
			f[n-1] = -1;
		
		out.print(f[n-1]);
		out.flush();
		out.close();
		
	}
	
	class SegmentTree {
		
		int n;
		int[] t;
		int inf = 2_000_000_000;
		
		SegmentTree(int n) {
			this.n = n;
			t = new int[4*n];
			Arrays.fill(t, inf);
		}
		
		int getmin(int l, int r) {
			//System.out.println(l+" "+r);
			return get(l, r, 0, n-1, 1);
		}
		
		int get(int l, int r, int tl, int tr, int v) {
			
			//System.out.println(tl+" "+tr+" "+v);
			
			if (l > r)
				return inf;
			
			if (tl == l && tr == r)
				return t[v];
			
			int tm = (tl+tr)/2;
			
			return Math.min(get(l, Math.min(tm, r), tl, tm, v*2), get(Math.max(tm+1, l), r, tm+1, tr, v*2+1));
			
		}
		
		void build(int v, int[] a, int tl, int tr) {
			
			if (tl == tr) {
				t[v] = a[tl];
				return;
			}
			
			int tm = (tl+tr)/2;
			
			build(v*2, a, tl, tm);
			build(v*2+1, a, tm+1, tr);
			t[v] = Math.min(t[v*2], t[v*2+1]);
			
		}
		
		void update(int val, int ind, int tl, int tr, int v) {
			
			if (tl == tr) {
				t[v] = val;
				return;
			}
			
			int tm = (tl+tr)/2;
			
			if (ind <= tm)
				update(val, ind, tl, tm, v*2);
			else
				update(val, ind, tm+1, tr, v*2+1);
			
			t[v] = Math.min(t[v*2], t[v*2+1]);			
		}
		
	}
	
	long pow(int x, int m) {
		if (m == 0)
			return 1;
		return x*pow(x, m-1);
	}

}
	
	class Pair implements Comparable<Pair> {
		
		int v;
		int i;
		
		Pair (int v, int i) {
			this.v = v;
			this.i = i;
		}

		@Override
		public int compareTo(Pair p) {
			if (v > p.v)
				return 1;
			if (v < p.v)
				return -1;
			return 0;
		}
		
	}

	class Item implements Comparable<Item> {

		int v;
		int l;
		int z;
		
		Item(int v, int l, int z) {
			this.v = v;
			this.l = l;
			this.z = z;
		}
		
		@Override
		public int compareTo(Item item) {
			
			if (l > item.l)
				return 1;
			else
			if (l < item.l)
				return -1;
			else {
				if (z > item.z)
					return 1;
				else
				if (z < item.z)
					return -1;
				return 0;
			}
						
		}
		
	}
	
	class Reader {
	    
	    StringTokenizer token;
	    BufferedReader in;
	    
	    public Reader(String file) throws IOException {
	        //in = new BufferedReader( new FileReader( file ) );
	        in = new BufferedReader( new InputStreamReader( System.in ) );
	    }
	    
	    public byte nextByte() throws IOException {
	        return Byte.parseByte(Next());
	    }
	    
	    public int nextInt() throws IOException {
	        return Integer.parseInt(Next());
	    }
	    
	    public long nextLong() throws IOException {
	        return Long.parseLong(Next());
	    }
	    
	    public String nextString() throws IOException {
	        return in.readLine();
	    }
	    
	    public String Next() throws IOException {
	        while (token == null || !token.hasMoreTokens()) {
	            token = new StringTokenizer(in.readLine());
	        }
	        return token.nextToken();
	    }

	    
	}

	
