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 B
{
	public static final int INF = 100000000;
	
	public static void main(String[] args) throws Exception
	{
		FastScanner in = new FastScanner(System.in);
		
		int n = in.nextInt();
		int s = in.nextInt();
		int l = in.nextInt();
		
		IntervalTree it = new IntervalTree(n + 1);
		it.inc(0, 0, 0);
		
		ArrayList<Integer> low = new ArrayList<Integer>();
		ArrayList<Integer> lowIndex = new ArrayList<Integer>();
		ArrayList<Integer> high = new ArrayList<Integer>();
		ArrayList<Integer> highIndex = new ArrayList<Integer>();
		low.add(Integer.MIN_VALUE);
		lowIndex.add(0);
		high.add(Integer.MAX_VALUE);
		highIndex.add(0);
		
		Compare compare = new Compare();
		
		int left = 0;
		for(int x = 1; x <= n; x++)
		{
			int val = in.nextInt();
			
			int index = Collections.binarySearch(low, val - s);
			if(index < 0)
			{
				index = -(index + 1);
			}
			
			index--;
			
			left = Math.max(left, lowIndex.get(index));
			
			index = Collections.binarySearch(high, val + s, compare);
			if(index < 0)
			{
				index = -(index + 1);
			}
			
			index--;
			
			left = Math.max(left, highIndex.get(index));
			
			if(left > x - l)
			{
				it.inc(x, x, INF);
			}
			else
			{
				it.inc(x, x, it.query(left, x - l) + 1);
			}
			
			while(low.get(low.size() - 1) >= val)
			{
				low.remove(low.size() - 1);
				lowIndex.remove(lowIndex.size() - 1);
			}
			
			low.add(val);
			lowIndex.add(x);
			
			while(high.get(high.size() - 1) <= val)
			{
				high.remove(high.size() - 1);
				highIndex.remove(highIndex.size() - 1);
			}
			
			high.add(val);
			highIndex.add(x);
		}
		
		int result = it.query(n, n);
		if(result >= INF)
		{
			System.out.println(-1);
		}
		else
		{
			System.out.println(result);
		}
	}
	
	static class IntervalTree
	{
		public static final int INFINITY = 1000000000;
		
		int n;
		int[] tree;
		int[] delta;
		
		public IntervalTree(int n)
		{
			this.n = n;
			tree = new int[4 * n];
			delta = new int[4 * n];
		}
		
		public void inc(int left, int right, int x)
		{
			inc(left, right, x, 1, 0, n - 1);
		}
		
		public void inc(int left, int right, int x, int i, int l, int r)
		{
			if(r < left || l > right)
			{
				return;
			}
			else if(l >= left && r <= right)
			{
				delta[i] += x;
				return;
			}
			else
			{
				prop(i);
				
				int m = (l + r) / 2;
				inc(left, right, x, 2 * i, l, m);
				inc(left, right, x, 2 * i + 1, m + 1, r);
				
				update(i);
			}
		}
		
		public int query(int left, int right)
		{
			return query(left, right, 1, 0, n - 1);
		}
		
		public int query(int left, int right, int i, int l, int r)
		{
			if(r < left || l > right)
			{
				return INFINITY;
			}
			else if(l >= left && r <= right)
			{
				return tree[i] + delta[i];
			}
			else
			{
				prop(i);
				
				int m = (l + r) / 2;
				int ret = Math.min(query(left, right, 2 * i, l, m), query(left, right, 2 * i + 1, m + 1, r));
				
				update(i);
				
				return ret;
			}
		}
		
		public void prop(int i)
		{
			delta[2 * i] += delta[i];
			delta[2 * i + 1] += delta[i];
			delta[i] = 0;
		}
		
		public void update(int i)
		{
			tree[i] = Math.min(tree[2 * i] + delta[2 * i], tree[2 * i + 1] + delta[2 * i + 1]);
		}
	}
	
	static class Compare implements Comparator<Integer>
	{
		public int compare(Integer o1, Integer o2)
		{
			if((int)o2 > (int)o1)
			{
				return 1;
			}
			else if((int)o2 < (int)o1)
			{
				return -1;
			}
			else
			{
				return 0;
			}
		}
	}
	
	static class FastScanner
	{
		BufferedReader br;
		StringTokenizer st;
		
		public FastScanner(InputStream input)
		{
			br = new BufferedReader(new InputStreamReader(input));
			st = new StringTokenizer("");
		}
		
		public String next() throws IOException
		{
			if(st.hasMoreTokens())
			{
				return st.nextToken();
			}
			else
			{
				st = new StringTokenizer(br.readLine());
				return next();
			}
		}
		
		public int nextInt() throws IOException
		{
			return Integer.parseInt(next());
		}
	}
}
