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<iostream>
#include<algorithm>
#include<vector>
using namespace std;
typedef long long int LL;
const LL MAX=1e9+7;
vector<LL> x;
int go[35][100005];
LL s[100005];
int main(){
	LL n,l,q;
	int i,j,k;
	LL a,b,c;
	cin>>n;
	for(i=0;i<n;i++){
		cin>>a;
		x.push_back(a);
	}
	cin>>l>>q;
	for(j=0;j<n;j++){
		auto itr=upper_bound(x.begin(),x.end(),x[j]+l);
		go[0][j]=(int)distance(x.begin(),itr-1);
	}
	for(i=1;i<=30;i++){
		for(j=0;j<n;j++){
			go[i][j]=go[i-1][go[i-1][j]];
		}
	}
	for(i=0;i<q;i++){
		cin>>a>>b;
		a--,b--;
		if(a>b)swap(a,b);
		for(j=30;j>=0;j--){
			if(go[j][a]>=b)continue;
			s[i]+=(1<<j);
			a=go[j][a];
		}
		s[i]++;
	}
	for(i=0;i<q;i++){
		cout<<s[i]<<endl;
	}
	return 0;
}
		
		
