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>
#define MD 17
#define MN 100000
using namespace std;
inline int read()
{
    int x=0,f=1;char ch=getchar();
    while(ch<'0'||ch>'9'){if(ch=='-')f=-1;ch=getchar();}
    while(ch>='0'&&ch<='9'){x=x*10+ch-'0';ch=getchar();}
    return x*f;
}
int n,Q,x[MN+5],L,f[MD+1][MN+5];
int main()
{   
    n=read();
    for(int i=1;i<=n;++i) x[i]=read();
    L=read();f[0][n]=n;
    for(int i=n;--i;) 
        for(f[0][i]=f[0][i+1];x[f[0][i]]-x[i]>L;--f[0][i]);
    for(int i=1;i<=MD;++i) for(int j=1;j<=n;++j) f[i][j]=f[i-1][f[i-1][j]];
    for(Q=read();Q--;)
    {
        int a=read(),b=read();if(a>b) swap(a,b);int ans=0;
        for(int j=MD;~j;--j) if(f[j][a]<b) ans+=(1<<j),a=f[j][a];
        printf("%d\n",ans+1);
    }
    return 0;
}