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<stdio.h>
#include<bits/stdc++.h>
using namespace std;
int n,l,q,a,b,x[100000],jump[100000][17];
int main(){
    scanf("%d",&n);
    for(int i=0;i<n;i++)scanf("%d",&x[i]);
    scanf("%d",&l);
    for(int i=n-1,j=n-1;i>=0;i--){
        while(x[j]-x[i]>l)j--;
        jump[i][0]=j;
        for(int k=1;k<=16;k++){
            jump[i][k]=jump[jump[i][k-1]][k-1];
        }
    }
    scanf("%d",&q);
    while(q--){
        scanf("%d %d",&a,&b);
        if(a>b)swap(a,b);
        a--;
        b--;
        int an=0;
        for(int i=16;i>=0&&a<b-1;){
            if(jump[a][i]>b-1){
                i--;
                continue;
            }
            an+=(1<<i);
            a=jump[a][i];
        }
        an++;
        printf("%d\n",an);
    }
    return 0;
}