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 C++14 (GCC 5.4.1) (judge verdict: Runtime Error)

#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
#define rep(i, n) for (ll i = 0; i < (ll)(n); i++)
const ll INF = 1LL << 60; //MAX 9223372036854775807

int main()
{
ll n ;
cin >> n ;
vector<ll> x(n+1);
rep(i, n){
  cin >> x[i];
}
x[n]=INF;
ll l , q ;
cin >> l >> q ;
vector<vector<ll>> dub(20, vector<ll>(n,0) );
ll st=0,en=1;
rep(i,n-1){
  while(x[en+1]-x[i]<=l)en++;
  dub[0][i]=en;
}
dub[0][n-1]=-1;
ll dep;
rep(i,19){
  rep(j,n){
    if(dub[i][j]==-1)dub[i+1][j]=-1;
    else dub[i+1][j]=dub[i][dub[i][j]];
  }
  if(dub[i+1][0]==-1){
    dep=i;
    break;
  }
}
rep(i,q){
  ll a , b ;
  cin >> a >> b ;
  a--;b--;
  if(a>b)swap(a,b);
  ll ans=0;
  for (ll i = dep; i >= 0; i--)
  {
    if(0<x[dub[i][a]] && x[dub[i][a]] <=x[b]){
      ans+=1LL<<i;
      a=dub[i][a];
    }
  }
  cout << ans << endl;

}
return 0;
}