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.
// package Div2;

import java.util.ArrayList;
import java.util.HashMap;
import java.util.LinkedList;
import java.util.List;
import java.util.Random;
import java.util.Scanner;
import java.util.Stack;

public class Sketch {
	private static class Segtree {
		public int[] nodes;
		
		private void build(int[] nums, int pos, int head, int tail){
			if(head == tail){
				if(nums[head] != -1) nodes[pos] = head;
				else nodes[pos] = -1;
				return;
			}
			int mid = (head+tail)/2;
			build(nums, (pos<<1) + 1, head, mid);
			build(nums, (pos<<1) + 2, mid+1, tail);
			if(nodes[(pos<<1) + 1] != -1) nodes[pos] = nodes[(pos<<1) + 1];
			else nodes[pos] = nodes[(pos<<1) + 2];
		}
		
		public Segtree(int[] nums){
			nodes = new int[nums.length << 2];
			build(nums, 0, 0, nums.length-1);
		}
		
		public int find(int[] nums, int l, int r, int pos, int head, int tail){
			if(tail < l || head > r) return -1;
			if(head >= l && tail <= r) return nodes[pos];
			int mid = (head+tail)/2;
			int ret0 = find(nums, l, r, 2*pos+1, head, mid);
			int ret1 = find(nums, l, r, 2*pos+2, mid+1, tail);
			if(ret0 != -1) return ret0;
			else return ret1;
		}
		
		public void update(int[] nums, int idx, int pos, int head, int tail){
			if(head == tail && head == idx){
				if(nums[idx] != -1) nodes[pos] = idx;
				return;
			}
			if(idx < head || idx > tail) return;
			int mid = (head+tail)/2;
			if(idx <= mid) update(nums, idx, 2*pos+1, head, mid);
			else update(nums, idx, 2*pos+2, mid+1, tail);
			int new0 = nodes[2*pos+1]; int new1 = nodes[2*pos+2];
			if(new0 != -1) nodes[pos] = new0;
			else nodes[pos] = new1;
		}
	}
	
	public static void main(String[] args){
		Scanner input = new Scanner(System.in);
		int n = input.nextInt(); int s = input.nextInt(); int l = input.nextInt();
		int[] nums = new int[n];
		for(int i=0; i<n; i++) nums[i] = input.nextInt();
		input.close();
		
		if(l > n){
			System.out.println(-1); return;
		}
		
		int[][] rmqmax = new int[n][20];
		int[][] rmqmin = new int[n][20];
		for(int i=0; i<n; i++){
			for(int j=0; j<20; j++){
				rmqmax[i][j] = Integer.MIN_VALUE;
				rmqmin[i][j] = Integer.MAX_VALUE;
			}
		}
		int offset = 1;
		for(int i=0; i<n; i++){
			rmqmax[i][0] = nums[i];
			rmqmin[i][0] = nums[i];
		}
		for(int i=1; i<20; i++){
			for(int j=0; j<n-offset; j++){
				rmqmax[j][i] = Math.max(rmqmax[j][i-1], rmqmax[j+offset][i-1]);
				rmqmin[j][i] = Math.min(rmqmin[j][i-1], rmqmin[j+offset][i-1]);
			}
			offset = offset << 1;
		}
		
		int[] dps = new int[n];
		for(int i=0; i<n; i++) dps[i] = -1;
		Segtree seg = new Segtree(dps);
		for(int i=l-1; i<n; i++){
			int hd = 0; int tl = i-l+1;
			boolean flag = false;
			do{
				boolean quit = hd == tl;
				int mid = (hd+tl)/2;
				int pow = 1; int idx = 0;
				while(pow<<1 <= i-mid){
					pow = pow << 1; idx++;
				}
				int maxi = Math.max(rmqmax[mid][idx], rmqmax[i-pow+1][idx]);
				int mini = Math.min(rmqmin[mid][idx], rmqmin[i-pow+1][idx]);
				if(maxi-mini <= s){
					flag = true;
					tl = mid;
				}
				else hd = mid+1;
				if(quit) break;
			}while(true);
			if(!flag) continue;
			if(hd == 0) dps[i] = 1;
			else {
				int first = seg.find(dps, hd-1, i-l, 0, 0, n-1);
				if(first == -1) continue;
				dps[i] = dps[first] + 1;
			}
			seg.update(dps, i, 0, 0, n-1);
		}
		
		System.out.println(dps[n-1]);
	}
}