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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.StringTokenizer;


public class E {
	static final int INF = (int)1e9+(int)1e6;
	public static void main(String[] args) throws NumberFormatException, IOException {
		Scanner sc = new Scanner();
		PrintWriter out = new PrintWriter(System.out);
		int n = sc.nextInt(), s = sc.nextInt(), l = sc.nextInt();
		int [] a = new int[n];
		int N = 1; while(N < n) N <<= 1; //padding
		MaxSegmentTree maxRange = new MaxSegmentTree(N);
		MinSegmentTree minRange = new MinSegmentTree(N);
		for (int i = 0; i < a.length; ++i) {
			a[i] = sc.nextInt();
			maxRange.update_point(i+1, a[i]);
			minRange.update_point(i+1, a[i]);
		}
		MinSegmentTree dp = new MinSegmentTree(N);
		for (int i = 0; i < a.length; ++i) {
			int lo = 0, hi = i, ans = -1;
			{// find left where diff at most
				while(lo <= hi) {
					int mid = (lo + hi)/2;
					if(maxRange.query(mid+1, i+1) - minRange.query(mid+1, i+1) <= s) {
						ans = mid;
						hi = mid-1;
					}
					else lo = mid+1;
				}
				if(ans == -1 || ans > i-l+1) 
					continue; // there is no index satisfying, no overlapping interval bet l, r
				//				ans, i-l+1
			}
			dp.update_point(i+1, 1 + (ans == 0?0:dp.query(ans-1+1, i-l+1))); // 1-indexed tree
		}
		int ans = dp.query(n, n);
		out.println(ans >= INF?-1:ans);
		out.close();
	}
	static class MaxSegmentTree {		// 1-based DS, OOP

		int N; 			//the number of elements in the array as a power of 2 (i.e. after padding)
		int[] sTree;

		MaxSegmentTree(int n)		
		{
			N = n;
			sTree = new int[N<<1];		//no. of nodes = 2*N - 1, we add one to cross out index zero
			Arrays.fill(sTree, -INF);
		}

		void update_point(int index, int val)			// O(log n)
		{
			index += N - 1;				
			sTree[index] = val;			
			while(index>1)				
			{
				index >>= 1;
			sTree[index] = Math.max(sTree[index<<1], sTree[index<<1|1]);		
			}
		}


		int query(int i, int j)
		{
			return query(1,1,N,i,j);
		}

		int query(int node, int b, int e, int i, int j)	// O(log n)
		{
			if(i>e || j <b)
				return -INF;		
			if(b>= i && e <= j)
				return sTree[node];
			int mid = b + e >> 1;
			int q1 = query(node<<1,b,mid,i,j);
			int q2 = query(node<<1|1,mid+1,e,i,j);
			return Math.max(q1, q2);	

		}

	}

	static class MinSegmentTree {		// 1-based DS, OOP

		int N; 			//the number of elements in the array as a power of 2 (i.e. after padding)
		int[] sTree;

		MinSegmentTree(int n)		
		{
			N = n;
			sTree = new int[N<<1];		//no. of nodes = 2*N - 1, we add one to cross out index zero
			Arrays.fill(sTree, INF);
		}

		void update_point(int index, int val)			// O(log n)
		{
			index += N - 1;				
			sTree[index] = val;			
			while(index>1)				
			{
				index >>= 1;
			sTree[index] = Math.min(sTree[index<<1], sTree[index<<1|1]);		
			}
		}


		int query(int i, int j)
		{
			return query(1,1,N,i,j);
		}

		int query(int node, int b, int e, int i, int j)	// O(log n)
		{
			if(i>e || j <b)
				return INF;		
			if(b>= i && e <= j)
				return sTree[node];
			int mid = b + e >> 1;
			int q1 = query(node<<1,b,mid,i,j);
			int q2 = query(node<<1|1,mid+1,e,i,j);
			return Math.min(q1, q2);	

		}

	}

	static class Scanner {
		BufferedReader br;
		StringTokenizer st;

		public Scanner() {
			br = new BufferedReader(new InputStreamReader(System.in));
		}

		public String next() throws IOException {
			while (st == null || !st.hasMoreTokens()) {
				st = new StringTokenizer(br.readLine());
			}
			return st.nextToken();
		}

		public int nextInt() throws NumberFormatException, IOException {
			return Integer.parseInt(next());
		}
		public long nextLong() throws NumberFormatException, IOException {
			return Long.parseLong(next());
		}
	}

}