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.*;
import java.math.BigInteger;
/*
8 6

46
 */
public class b
{
	public static void main(String[] arg) throws Exception
	{
		new b();
	}
	int oo = Integer.MAX_VALUE/10;
	public b() throws Exception
	{
		FastScanner in = new FastScanner(System.in);
		PrintWriter out = new PrintWriter(System.out);
		int n = in.nextInt();
		int s = in.nextInt();
		int l = in.nextInt();
		if(l > n)
		{
			System.out.println(-1);
			return;
		}
		int[] dp = new int[n];
		int[] vs = new int[n];
		ST minst = new ST(n);
		ST maxst = new ST(n);
		for(int i = 0; i < n; i++)
		{
			vs[i] = in.nextInt();
			minst.update(i, i, vs[i]);
			maxst.update(i, i, vs[i]);
		}
		Arrays.fill(dp, oo);
		int min = vs[0];
		int max = vs[0];
		for(int i = 0; i < l; i++)
		{
			min = Math.min(min, vs[i]);
			max = Math.max(max, vs[i]);
		}
		if(max-min <= s) dp[l-1] = 1;
		ArrayDeque<Integer> q = new ArrayDeque<Integer>();
		if(dp[0] == 1)
		{
			q.add(dp[0]);
			q.add(0);
		}
		//System.out.println(Arrays.toString(dp));
		for(int i = l; i < n; i++)
		{
			min = minst.min(0, i);
			max = maxst.max(0, i);
			//System.out.println(min + " " + max);
			if(max-min <= s)
			{
				dp[i] = 1;
			}
			else
			{
				while(q.size() > 0)
				{
					int val = q.poll();
					int idx = q.poll();
					min = Math.min(vs[i], minst.min(idx+1, i));
					max = Math.max(vs[i], maxst.max(idx+1, i));
					if(max-min <= s)
					{
						dp[i] = Math.min(dp[i], val+1);
						q.addFirst(idx);
						q.addFirst(val);
						break;
					}
				}
			}
			if(i-l+1 < n && dp[i-l+1] != oo)
			{
				while(q.size() > 0)
				{
					int idx = q.pollLast();
					int val = q.pollLast();
					if(val < dp[i-l+1])
					{
						q.add(val);
						q.add(idx);
						break;
					}
				}
				q.add(dp[i-l+1]);
				q.add(i-l+1);
			}
//			for(int j = i; j >= 0; j--)
//			{
//				min = Math.min(min, vs[j]);
//				max = Math.max(max, vs[j]);
//				if(i-j+1 >= l && max-min <= s)
//				{
//					if(j-1 >= 0)
//						dp[i] = Math.min(dp[i], dp[j-1]+1);
//					else
//						dp[i] = Math.min(dp[i], 1);
//				}
//			}
		}
		//System.out.println(Arrays.toString(dp));
		if(dp[n-1] == oo) System.out.println(-1);
		else System.out.println(dp[n-1]);
		in.close(); out.close();
	}
	class ST
	{
		int[] min;
		int[] max;
		int s;
		public ST(int s)
		{
			this.s = s;
			min = new int[4*(s+1)+1];
			max = new int[4*(s+1)+1];
		}
		void update(int l, int r, int v)
		{
			update(l, r, v, 0, s-1, 1);
		}
		void update(int lq, int rq, int v, int li, int ri, int c)
		{
			if(rq < li || ri < lq) return;
			if(lq <= li && ri <= rq)
			{
				min[c] = v;
				max[c] = v;
				return;
			}
			int m = li+(ri-li)/2;
			update(lq, rq, v, li, m, 2*c);
			update(lq, rq, v, m+1, ri, 2*c+1);
			min[c] = Math.min(min[2*c], min[2*c+1]);
			max[c] = Math.max(max[2*c], max[2*c+1]);
		}
		int min(int l, int r)
		{
			return min(l, r, 0, s-1, 1);
		}
		int min(int lq, int rq, int li, int ri, int c)
		{
			if(rq < li || ri < lq) return Integer.MAX_VALUE;
			if(lq <= li && ri <= rq) return min[c];
			int m = li+(ri-li)/2;
			return Math.min(min(lq, rq, li, m, 2*c), min(lq, rq, m+1, ri, 2*c+1));
		}
		int max(int l, int r)
		{
			return max(l, r, 0, s-1, 1);
		}
		int max(int lq, int rq, int li, int ri, int c)
		{
			if(rq < li || ri < lq) return Integer.MIN_VALUE;
			if(lq <= li && ri <= rq) return max[c];
			int m = li+(ri-li)/2;
			return Math.max(max(lq, rq, li, m, 2*c), max(lq, rq, m+1, ri, 2*c+1));
		}
	}
	class FastScanner
	{
		BufferedReader br;
		StringTokenizer st;
		public FastScanner(InputStream in)
		{
			br = new BufferedReader(new InputStreamReader(in));
			st = new StringTokenizer("");
		}
		public String next() throws IOException
		{
			while(!st.hasMoreTokens()) st = new StringTokenizer(br.readLine());
			return st.nextToken();
		}
		public int nextInt() throws IOException
		{
			return Integer.parseInt(next());
		}
		public void close() throws IOException
		{
			br.close();
		}
		public long nextLong() throws IOException
		{
			return Long.parseLong(next());
		}
		public double nextDouble() throws IOException
		{
			return Double.parseDouble(next());
		}
	}
}