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 b487 {
	
	public static void main(String[] args) {
		JoltyScanner in = new JoltyScanner(System.in);
		int n = in.nextInt();
		int s = in.nextInt();
		int l = in.nextInt();
		
		int ar[] = new int[n];
		for(int i =0; i < n; i++)
			ar[i]=in.nextInt();
		
		int leftMost[] = new int[n];
		Arrays.fill(leftMost, -1);
		
		int left = 0;
		MinQueue<Integer> mnq= new MinQueue<>();
		MaxQueue<Integer> mxq= new MaxQueue<>();
		
		
		for(int i = 0; i < l - 1; i++) {
			if(i >= n) break;
			mnq.add(ar[i]);
			mxq.add(ar[i]);
		}
		
		for(int i = l - 1; i < n; i++) {
			mnq.add(ar[i]);
			mxq.add(ar[i]);
			while(mxq.max() - mnq.min() > s) {
				left++;
				mnq.poll();
				mxq.poll();
			}
			if(i - left + 1 >= l)leftMost[i] =  i - left;
		}
		
		int dp[] = new int[n + 1];
		Arrays.fill(dp, Integer.MAX_VALUE/2);
		dp[0] = 0;
		int lp = 0, rp = 1;
		MinQueue<Integer> ans = new MinQueue<>();
		ans.add(0);
		for(int i = 0; i < n; i++) {
			if(leftMost[i] == -1) continue;
			int nl = i - leftMost[i];
			int nr = i - l + 1;
			while(nr >= rp) {
				ans.add(dp[rp++]);
			}
			while(nl > lp) {
				ans.poll();
				lp++;
			}
			dp[i+1] = ans.min() + 1;
		}
		if(dp[n] >= Integer.MAX_VALUE/2) {
			System.out.println(-1);
		} else {
			System.out.println(dp[n]);
		}
		
	}
	
	static class MinQueue<T extends Comparable<T>> {
		ArrayDeque<T> q, min;  MinQueue() { q = new ArrayDeque<T>(); min  = new ArrayDeque<T>(); }
		void add(T val) {  q.add(val);
			while(!min.isEmpty() && min.peekLast().compareTo(val) > 0)  min.pollLast();
			min.add(val);  }
		int size() { return q.size(); }
		T poll() {  T val = q.poll();
			if(min.peek().compareTo(val) == 0)  min.poll();
			return val;  }
		T min() { return min.peek(); }
	}
	
	static class MaxQueue<T extends Comparable<T>> {
		ArrayDeque<T> q, min;  MaxQueue() { q = new ArrayDeque<T>(); min  = new ArrayDeque<T>(); }
		void add(T val) {  q.add(val);
			while(!min.isEmpty() && min.peekLast().compareTo(val) < 0)  min.pollLast();
			min.add(val);  }
		int size() { return q.size(); }
		T poll() {  T val = q.poll();
			if(min.peek().compareTo(val) == 0)  min.poll();
			return val;  }
		T max() { return min.peek(); }
	}
	
	static class JoltyScanner 
	{
		public static final int BUFFER_SIZE = 1 << 16;
		public static final char NULL_CHAR = (char) -1;
		byte[] buffer = new byte[BUFFER_SIZE];
		boolean EOF_FLAG = false;
		int bufferIdx = 0, size = 0;
		char c = NULL_CHAR;
		BufferedInputStream in;
		public JoltyScanner(InputStream in) 
		{
			this.in = new BufferedInputStream(in, BUFFER_SIZE);
		}
		public int nextInt() 
		{
			long x = nextLong();
			if (x > Integer.MAX_VALUE || x < Integer.MIN_VALUE) 
			{
				throw new ArithmeticException("Scanned value overflows integer");
			}
			return (int) x;
		}
		public long nextLong() 
		{
			boolean negative = false;
			if (c == NULL_CHAR) 
			{
				c = nextChar();
			}
			for (; !EOF_FLAG && (c < '0' || c > '9'); c = nextChar()) 
			{
				if (c == '-') 
				{
					negative = true;
				}				
			}
			checkEOF();
			long res = 0;
			for (; c >= '0' && c <= '9'; c = nextChar()) 
			{
				res = (res << 3) + (res << 1) + c - '0';
			}
			return negative ? -res : res;
		}
		public char nextChar() 
		{
			if (EOF_FLAG) 
			{
				return NULL_CHAR;
			}
			while (bufferIdx == size) 
			{
				try 
				{
					size = in.read(buffer);
					if (size == -1) 
					{
						throw new Exception();
					}
				} 
				catch (Exception e) 
				{
					EOF_FLAG = true;
					return NULL_CHAR;
				}
				if (size == -1) 
				{
					size = BUFFER_SIZE;
				}
				bufferIdx = 0;
			}
			return (char) buffer[bufferIdx++];
		}
		public void checkEOF() 
		{
			if (EOF_FLAG) 
			{
				throw new EndOfFileException();
			}
		}
		public class EndOfFileException extends RuntimeException 
		{
		}
	}
}
