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 Main {
        public static void main(String[] args) {
            InputStream inputStream = System.in;
            OutputStream outputStream = System.out;
            InputReader in = new InputReader(inputStream);
            PrintWriter out = new PrintWriter(outputStream);
            TaskE solver = new TaskE();
            solver.solve(1, in, out);
            out.flush();out.close();
        }
            static class TaskE {
              public void solve(int testNumber, InputReader in, PrintWriter out) {
                int n=in.nextInt(),s=in.nextInt(),l=in.nextInt();
                sp=new long[2][100001][21];       
                int a[]=new int[n+1];
                for(int i=0;i<=100000;i++)Arrays.fill(sp[0][i],MIN);
                for(int i=0;i<=100000;i++)Arrays.fill(sp[1][i],MAX);
                for(int i=1;i<=n;i++){
                 a[i]=in.nextInt();sp[0][i][0]=sp[1][i][0]=a[i];
                }
                 if(n<l){
                        out.print("-1");return;
                       }
                       build();
                       seg=new int[4*n];
                       Arrays.fill(seg,MAX);
                       upd(0,0,0,0,n);
                       int dp[]=new int[n+1];
                       Arrays.fill(dp,MAX);
                       dp[0]=0;
                       for(int i=1;i<=n;i++){
                        int min=spq(i,s),max=i-l;
                        if(min>max)continue;
                        int val=sgq(min,max,0,0,n);
                        if(val!=MAX){
                         dp[i]=val+1;upd(i,dp[i],0,0,n);
                        }
                       }
                       if(dp[n]==MAX)out.print("-1");else out.print(dp[n]);
                }
                int sgq(int ql,int qr,int n,int l,int r){
                 if(l>qr||r<ql)return MAX;
                 if(l>=ql&&r<=qr)return seg[n];
                 int m=(l+r)>>1;
                 return Math.min(sgq(ql,qr,2*n+1,l,m),sgq(ql,qr,2*n+2,m+1,r));
                }
                int spq(int id,int s){
                 long min=MAX,max=MIN;
                 for(int j=20;j>=0;j--){
                  long v1=Math.max(sp[1][id][j],max);
                  long v2=Math.min(sp[0][id][j],min);
                  if(v1-v2<=s){
                   max=v1;min=v2;
                   if(j!=0)id-=(1<<(j-1));
                  }
                 }return id-1;
                }
                void upd(int id,int val,int n,int l,int r){
                 if(id>r||id<l)return;
                 if(l==r){
                  seg[n]=val;return;
                 }
                 int m=(l+r)>>1;
                 upd(id,val,2*n+1,l,m);upd(id,val,2*n+2,m+1,r);
                 seg[n]=Math.min(seg[2*n+1],seg[2*n+2]);
                }
                long sp[][][];int seg[],MAX=Integer.MAX_VALUE,MIN=Integer.MIN_VALUE;
                void build(){
                 for(int j=1;j<=20;j++){
                  for(int i=100000;i>=1;i--){
                   if(i-(1<<(j-1))<0)break;
                   sp[0][i][j]=Math.min(sp[0][i][j-1],sp[0][i-(1<<(j-(j>1?2:1)))][j-1]);
                   sp[1][i][j]=Math.max(sp[1][i][j-1],sp[1][i-(1<<(j-(j>1?2:1)))][j-1]);
                  }
                 }
                }
           }
        static class InputReader {
            BufferedReader br;
            StringTokenizer st;
            public InputReader(InputStream stream) {
                br = new BufferedReader(new InputStreamReader(stream));
                st = null;
            }

            String next() {
                while (st == null || !st.hasMoreTokens()) {
                    String s = null;
                    try {
                        s = br.readLine();
                    } catch (IOException e) {
                        e.printStackTrace();
                    }
                    if (s == null)
                        return null;
                    st = new StringTokenizer(s);
                }
                return st.nextToken();
            }

            boolean hasMoreTokens() {
                while (st == null || !st.hasMoreTokens()) {
                    String s = null;
                    try {
                        s = br.readLine();
                    } catch (IOException e) {
                        e.printStackTrace();
                    }
                    if (s == null)
                        return false;
                    st = new StringTokenizer(s);
                }
                return true;
            }

            public int nextInt() {
                return Integer.parseInt(next());
            }
            public long nextLong() {
                return Long.parseLong(next());
            }
            public double nextDouble() {
                return Double.parseDouble(next());
            }
        }
    }