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.

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.

Example

Input

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


Output

4
2
1
2
#include<bits/stdc++.h>
using namespace std;
#define rep(i,n) for(i=0;i<n;++i)
#define c(a) cin>>a;
int r[18][100000],x[100000],i,j,n,L,a,b,A,N;
int main(){
c(n)
rep(i,n)c(x[i])
c(L)
rep(i,n)r[0][i]=upper_bound(x,x+n,x[i]+L)-x-1;
rep(i,17)rep(j,n)r[i+1][j]=r[i][r[i][j]];
c(L)
rep(j,L){
c(a)c(b)--a;--b;
if(a>b)swap(a,b);
A=0;N=a;
for(i=17;i>=0;--i)if(r[i][N]<b){N=r[i][N];A+=1<<i;}
if(N<b)++A;
cout<<A<<endl;
}
}
