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 <cstdio>
#include <algorithm>

int n,x[200005],l,q,Next[200005][21];

int main()
{
    //freopen("in.txt","r",stdin);
    scanf("%d",&n);
    for(int i=1;i<=n;++i)scanf("%d",&x[i]);
    scanf("%d%d",&l,&q);
    for(int i=n,j=n;i>=1;--i)
    {
        while(x[j]-x[i]>l)--j;
        Next[i][0]=j;
        for(int k=1;k<=20;++k)Next[i][k]=Next[Next[i][k-1]][k-1];
    }
    for(int a,b;q--;)
    {
        scanf("%d%d",&a,&b);
        if(a>b)std::swap(a,b);
        if(a==b){puts("0");continue;}
        int Ans=0;
        for(int i=20;i>=0;--i)
            if(Next[a][i]<b)
                Ans+=1<<i,a=Next[a][i];
        printf("%d\n",Ans+1);
    }
    return 0;
}