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;
int n;
int l;
int q;
int a[100001];
int s;
int b;
int f[100001][33];
int main(){
    cin>>n;
    for(int i=1;i<=n;++i) scanf("%d",&a[i]);
    cin>>l>>q;
    for(int i=1;i<=n;++i){
    	int x=upper_bound(a+1,a+n+1,a[i]+l)-a-1;
    	if(a[i]+l>=a[n]) f[i][0]=n;
    	else f[i][0]=x;
    }
    for(int j=1;j<=30;j++)
        for(int i=1;i<=n;i++)
            f[i][j]=f[f[i][j-1]][j-1];
    while(q--){
		scanf("%d %d",&s,&b);
		int i=1;
		int ans=0;
		if(s>b) s^=b^=s^=b;
		for(int i=30;i>=0;--i)
			if(f[s][i]<b)
				ans+=(1<<i),
				s=f[s][i];
			printf("%d\n",ans+1);
	}
	return 0;
}