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.*;

public class Solution {

	static int SIZE = 100000;
	static Unit[] mmTree = new Unit[SIZE * 2 + 10];
	static int tt = 0;
	static int[] v;

	static class Unit {
		int lson, rson;
		int l, r;
		int min, max;
		int dpmin;
	}

	static int Build(int l, int r) {
		int nt = tt++;
		Unit u = new Unit();
		u.l = l;
		u.r = r;
		u.min = -1;
		u.max = -1;
		u.dpmin = Integer.MAX_VALUE;
		mmTree[nt] = u;
		if (l == r)
			return nt;

		int m = (l + r) >> 1;
		u.lson = Build(l, m);
		u.rson = Build(m + 1, r);
		return nt;
	}

	static int FindMax(int indx, int l, int r) {
		if (mmTree[indx].l == l && r == mmTree[indx].r) {
			return mmTree[indx].max;
		}
		int m = (mmTree[indx].l + mmTree[indx].r) >> 1;
		if (r <= m) {
			return FindMax(mmTree[indx].lson, l, r);
		} else if (l > m) {
			return FindMax(mmTree[indx].rson, l, r);
		} else {
			int m1 = FindMax(mmTree[indx].lson, l, m);
			int m2 = FindMax(mmTree[indx].rson, m + 1, r);
			if (m1 == -1 && m2 == -1)
				return -1;
			if (m1 == -1)
				return m2;
			if (m2 == -1)
				return m1;

			if (v[m1] > v[m2])
				return m1;
			return m2;
		}
	}

	static int FindMin(int indx, int l, int r) {
		if (mmTree[indx].l == l && r == mmTree[indx].r) {
			return mmTree[indx].min;
		}
		int m = (mmTree[indx].l + mmTree[indx].r) >> 1;
		if (r <= m) {
			return FindMin(mmTree[indx].lson, l, r);
		} else if (l > m) {
			return FindMin(mmTree[indx].rson, l, r);
		} else {
			int m1 = FindMin(mmTree[indx].lson, l, m);
			int m2 = FindMin(mmTree[indx].rson, m + 1, r);

			if (m1 == -1 && m2 == -1)
				return -1;
			if (m1 == -1)
				return m2;
			if (m2 == -1)
				return m1;

			if (v[m1] < v[m2])
				return m1;
			return m2;
		}
	}

	static int FindDP(int indx, int l, int r) {
		if (mmTree[indx].l == l && r == mmTree[indx].r) {
			return mmTree[indx].dpmin;
		}
		int m = (mmTree[indx].l + mmTree[indx].r) >> 1;
		if (r <= m) {
			return FindDP(mmTree[indx].lson, l, r);
		} else if (l > m) {
			return FindDP(mmTree[indx].rson, l, r);
		} else {
			int m1 = FindDP(mmTree[indx].lson, l, m);
			int m2 = FindDP(mmTree[indx].rson, m + 1, r);

			if (m1 < m2)
				return m1;
			return m2;
		}
	}

	static void insertValue(int indx, int ii) {
		Unit u = mmTree[indx];
		if (u.min == -1 || v[u.min] > v[ii])
			u.min = ii;
		if (u.max == -1 || v[u.max] < v[ii])
			u.max = ii;

		if (u.l == u.r)
			return;
		int m = (u.l + u.r) >> 1;
		if (ii <= m)
			insertValue(u.lson, ii);
		else
			insertValue(u.rson, ii);
	}

	static void insertDP(int indx, int ii, int vi) {
		Unit u = mmTree[indx];
		if (u.dpmin > vi)
			u.dpmin = vi;
		if (u.l == u.r)
			return;
		int m = (u.l + u.r) >> 1;
		if (ii <= m)
			insertDP(u.lson, ii, vi);
		else
			insertDP(u.rson, ii, vi);
	}

	public static void main(String[] args) throws Exception {
		Reader.init(System.in);
		int n = Reader.nextInt();
		int s = Reader.nextInt();
		int l = Reader.nextInt();

		v = new int[n];
		Build(0, n);

		int fdp = -1;
		for (int i = 0; i < n; i++) {
			int vi = Reader.nextInt();
			v[i] = vi;
			insertValue(0, i);

			int vv;
			{
				int a = 0, b = i;
				while (b - a > 0) {
					int m = (a + b) >> 1;
					int maxi = FindMax(0, m, i);
					int mini = FindMin(0, m, i);
					if (v[maxi] - v[mini] <= s) {
						b = m;
					} else {
						a = m + 1;
					}
				}
				vv = a;
			}

			if (i - vv + 1 < l)
				continue;

			int bestDP = (vv == 0 ? 0 : FindDP(0, vv - 1, i - l));
			if (bestDP != Integer.MAX_VALUE) {
				insertDP(0, i, bestDP + 1);
				if (i == n - 1)
					fdp = bestDP + 1;
			}
		}
		System.out.println(fdp);
	}
}

class Reader {
	static BufferedReader reader;
	static StringTokenizer tokenizer;

	/** call this method to initialize reader for InputStream */
	static void init(InputStream input) {
		reader = new BufferedReader(new InputStreamReader(input));
		tokenizer = new StringTokenizer("");
	}

	/** get next word */
	static String next() throws IOException {
		while (!tokenizer.hasMoreTokens()) {
			// TODO add check for eof if necessary
			tokenizer = new StringTokenizer(reader.readLine());
		}
		return tokenizer.nextToken();
	}

	static int nextInt() throws IOException {
		return Integer.parseInt(next());
	}

	static double nextDouble() throws IOException {
		return Double.parseDouble(next());
	}
}