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 B implements Runnable{
	public static void main (String[] args) {new Thread(null, new B(), "_cf", 1 << 28).start();}

	public void run() {
		FastScanner fs = new FastScanner();
		PrintWriter out = new PrintWriter(System.out);
		System.err.println("Go!");

		int n = fs.nextInt();
		int s = fs.nextInt();
		int k = fs.nextInt();
		int log = Integer.numberOfTrailingZeros(Integer.highestOneBit(n)*2);
		int[] best = new int[n + 1]; Arrays.fill(best, -1);
		best[n] = 0;
		ArrayDeque<Integer> dq = new ArrayDeque<>();
		dq.add(n);
		
		int[] a = fs.nextIntArray(n);
		int[][] max = new int[log][n];
		int[][] min = new int[log][n];
		for(int i = 0; i < n; i++) {
			max[0][i] = a[i];
			min[0][i] = a[i];
		}
		int lastRange = 1;
		for(int p = 1; p < log; p++) {
			for(int i = 0; i < n; i++) {
				max[p][i] = Math.max(max[p-1][i], max[p-1][Math.min(i+lastRange, n-1)]);
				min[p][i] = Math.min(min[p-1][i], min[p-1][Math.min(i+lastRange, n-1)]);
			}
			lastRange *= 2;
		}
		
		for(int i = n - 1; i >= 0 && !dq.isEmpty(); i--) {
			if(dq.peekFirst() - i < k) continue;
			int mn = query(i, dq.peekFirst()-1, min, true);
			int mx = query(i, dq.peekFirst()-1, max, false);
			if(mx-mn <= s) {
				best[i] = 1 + best[dq.peekFirst()];
				dq.addLast(i);
				continue;
			}
			dq.pollFirst();
			while(mx-mn > s && !dq.isEmpty() && dq.peekFirst() - i >= k) {
				mn = query(i, dq.peekFirst()-1, min, true);
				mx = query(i, dq.peekFirst()-1, max, false);
				if(mx-mn <= s) {
					best[i] = 1 + best[dq.peekFirst()];
					dq.addLast(i);
					break;
				}
				dq.pollFirst();
			}
		}

		out.println(best[0]);
		out.close();
	}
	
	int query(int left, int right, int[][] lift, boolean min) {
		int range = right - left + 1;
		int exp = Integer.highestOneBit(range);
		int lg = Integer.numberOfTrailingZeros(exp);
		if(min)
			return Math.min(lift[lg][left], lift[lg][right-exp+1]);
		else
			return Math.max(lift[lg][left], lift[lg][right-exp+1]);
	}

	void sort (int[] a) {
		int n = a.length;
		for(int i = 0; i < 50; i++) {
			Random r = new Random();
			int x = r.nextInt(n), y = r.nextInt(n);
			int temp = a[x];
			a[x] = a[y];
			a[y] = temp;
		}
		Arrays.sort(a);
	}

	class FastScanner {
		public int BS = 1<<16;
		public char NC = (char)0;
		byte[] buf = new byte[BS];
		int bId = 0, size = 0;
		char c = NC;
		double num = 1;
		BufferedInputStream in;

		public FastScanner() {
			in = new BufferedInputStream(System.in, BS);
		}

		public FastScanner(String s) throws FileNotFoundException {
			in = new BufferedInputStream(new FileInputStream(new File(s)), BS);
		}

		public char nextChar(){
			while(bId==size) {
				try {
					size = in.read(buf);
				}catch(Exception e) {
					return NC;
				}                
				if(size==-1)return NC;
				bId=0;
			}
			return (char)buf[bId++];
		}

		public int nextInt() {
			return (int)nextLong();
		}

		public long nextLong() {
			num=1;
			boolean neg = false;
			if(c==NC)c=nextChar();
			for(;(c<'0' || c>'9'); c = nextChar()) {
				if(c=='-')neg=true;
			}
			long res = 0;
			for(; c>='0' && c <='9'; c=nextChar()) {
				res = (res<<3)+(res<<1)+c-'0';
				num*=10;
			}
			return neg?-res:res;
		}

		public double nextDouble() {
			double cur = nextLong();
			return c!='.' ? cur:cur+nextLong()/num;
		}

		public String next() {
			StringBuilder res = new StringBuilder();
			while(c<=32)c=nextChar();
			while(c>32) {
				res.append(c);
				c=nextChar();
			}
			return res.toString();
		}

		public String nextLine() {
			StringBuilder res = new StringBuilder();
			while(c<=32)c=nextChar();
			while(c!='\n') {
				res.append(c);
				c=nextChar();
			}
			return res.toString();
		}

		public boolean hasNext() {
			if(c>32)return true;
			while(true) {
				c=nextChar();
				if(c==NC)return false;
				else if(c>32)return true;
			}
		}
		
		public int[] nextIntArray(int n) {
			int[] res = new int[n];
			for(int i = 0; i < n; i++) res[i] = nextInt();
			return res;
		}
		
	}

}