Problem:
Score : 700 points

Problem Statement

N hotels are located on a straight line. The coordinate of the i-th hotel (1 \leq i \leq N) is x_i.

Tak the traveler has the following two personal principles:

He never travels a distance of more than L in a single day.

He never sleeps in the open. That is, he must stay at a hotel at the end of a day.

You are given Q queries. The j-th (1 \leq j \leq Q) query is described by two distinct integers a_j and b_j.
For each query, find the minimum number of days that Tak needs to travel from the a_j-th hotel to the b_j-th hotel following his principles.
It is guaranteed that he can always travel from the a_j-th hotel to the b_j-th hotel, in any given input.

Constraints

2 \leq N \leq 10^5

1 \leq L \leq 10^9

1 \leq Q \leq 10^5

1 \leq x_i < x_2 < ... < x_N \leq 10^9

x_{i+1} - x_i \leq L

1 \leq a_j,b_j \leq N

a_j \neq b_j

N,\,L,\,Q,\,x_i,\,a_j,\,b_j are integers.

Partial Score

200 points will be awarded for passing the test set satisfying N \leq 10^3 and Q \leq 10^3.

Input

The input is given from Standard Input in the following format:

N
x_1 x_2 ... x_N
L
Q
a_1 b_1
a_2 b_2
:
a_Q b_Q

Output

Print Q lines.
The j-th line (1 \leq j \leq Q) should contain the minimum number of days that Tak needs to travel from the a_j-th hotel to the b_j-th hotel.

Sample Input 1

9
1 3 6 13 15 18 19 29 31
10
4
1 8
7 3
6 7
8 5

Sample Output 1

4
2
1
2

For the 1-st query, he can travel from the 1-st hotel to the 8-th hotel in 4 days, as follows:

Day 1: Travel from the 1-st hotel to the 2-nd hotel. The distance traveled is 2.

Day 2: Travel from the 2-nd hotel to the 4-th hotel. The distance traveled is 10.

Day 3: Travel from the 4-th hotel to the 7-th hotel. The distance traveled is 6.

Day 4: Travel from the 7-th hotel to the 8-th hotel. The distance traveled is 10.

Solution in Java8 (OpenJDK 1.8.0) (judge verdict: Time Limit Exceeded)

import java.io.ByteArrayInputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.InputMismatchException;
 
public class Main{
  static InputStream is;
  static PrintWriter out;
  static String INPUT = "";
  
  static void solve()
  {
    int n = ni();
    int[] x = na(n);
    int l = ni();
    int q = ni();
    int[][] ab = new int[q][2];
    for(int i=0; i<q; i++){
      ab[i] = na(2);
    }

    int[] max = new int[n];
    Arrays.fill(max,-1);
    for(int i=0; i<n-1; i++){
      int tmp_d = 0;
      int j=i;
      while(j+1<n && tmp_d + x[j+1] - x[j] <= l){
        tmp_d += x[j+1] - x[j];
        j++;
      }
      max[i] = j;
    }
    int[] max_r = new int[n];
    Arrays.fill(max_r,-1);
    for(int i=n-1; i>0; i--){
      int tmp_d = 0;
      int j=i;
      while(j-1>=0 && tmp_d + x[j] - x[j-1] <= l){
        tmp_d += x[j] - x[j-1];
        j--;
      }
      max_r[i] = j;
    }

    // クエリごとに処理
    for(int i=0; i<q; i++){
      int tmp_x = ab[i][0]-1;
      int count = 0;
      if(ab[i][0]-1<ab[i][1]-1){
        while(tmp_x < ab[i][1]-1){
          tmp_x = max[tmp_x];
          count++;
        }  
      }else{
        while(tmp_x > ab[i][1]-1){
          tmp_x = max_r[tmp_x];
          count++;
        } 
      }
      pl(count);
    }

  }
 
  
  public static void main(String[] args) throws Exception
  {
    long S = System.currentTimeMillis();
    is = INPUT.isEmpty() ? System.in : new ByteArrayInputStream(INPUT.getBytes());
    out = new PrintWriter(System.out);
    
    solve();
    out.flush();
    long G = System.currentTimeMillis();
    tr(G-S+"ms");
  }

  private static void pr(Object o){
    System.out.print(o);
  }
  private static void pl(Object o){
    System.out.println(o);
  }
  
  private static boolean eof()
  {
    if(lenbuf == -1)return true;
    int lptr = ptrbuf;
    while(lptr < lenbuf)if(!isSpaceChar(inbuf[lptr++]))return false;
    
    try {
      is.mark(1000);
      while(true){
        int b = is.read();
        if(b == -1){
          is.reset();
          return true;
        }else if(!isSpaceChar(b)){
          is.reset();
          return false;
        }
      }
    } catch (IOException e) {
      return true;
    }
  }
  
  private static byte[] inbuf = new byte[1024];
  static int lenbuf = 0, ptrbuf = 0;
  
  private static int readByte()
  {
    if(lenbuf == -1)throw new InputMismatchException();
    if(ptrbuf >= lenbuf){
      ptrbuf = 0;
      try { lenbuf = is.read(inbuf); } catch (IOException e) { throw new InputMismatchException(); }
      if(lenbuf <= 0)return -1;
    }
    return inbuf[ptrbuf++];
  }
  
  private static boolean isSpaceChar(int c) { return !(c >= 33 && c <= 126); }
//  private static boolean isSpaceChar(int c) { return !(c >= 32 && c <= 126); }
  private static int skip() { int b; while((b = readByte()) != -1 && isSpaceChar(b)); return b; }
  
  private static double nd() { return Double.parseDouble(ns()); }
  private static char nc() { return (char)skip(); }
  
  private static String ns()
  {
    int b = skip();
    StringBuilder sb = new StringBuilder();
    while(!(isSpaceChar(b))){
      sb.appendCodePoint(b);
      b = readByte();
    }
    return sb.toString();
  }
  
  private static char[] ns(int n)
  {
    char[] buf = new char[n];
    int b = skip(), p = 0;
    while(p < n && !(isSpaceChar(b))){
      buf[p++] = (char)b;
      b = readByte();
    }
    return n == p ? buf : Arrays.copyOf(buf, p);
  }
  
  private static char[][] nm(int n, int m)
  {
    char[][] map = new char[n][];
    for(int i = 0;i < n;i++)map[i] = ns(m);
    return map;
  }
  
  private static int[] na(int n)
  {
    int[] a = new int[n];
    for(int i = 0;i < n;i++)a[i] = ni();
    return a;
  }
  
  private static int ni()
  {
    int num = 0, b;
    boolean minus = false;
    while((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'));
    if(b == '-'){
      minus = true;
      b = readByte();
    }
    
    while(true){
      if(b >= '0' && b <= '9'){
        num = num * 10 + (b - '0');
      }else{
        return minus ? -num : num;
      }
      b = readByte();
    }
  }
  
  private static long nl()
  {
    long num = 0;
    int b;
    boolean minus = false;
    while((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'));
    if(b == '-'){
      minus = true;
      b = readByte();
    }
    
    while(true){
      if(b >= '0' && b <= '9'){
        num = num * 10 + (b - '0');
      }else{
        return minus ? -num : num;
      }
      b = readByte();
    }
  }
  
  private static void tr(Object... o) { if(INPUT.length() != 0)System.out.println(Arrays.deepToString(o)); }
}