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 MAXN 100005
#define INF int(1e9)
#define dis(l,r) (x[r] - x[l])
#define LL long long
using namespace std;

int N,L,Q;
LL x[MAXN];

int dp[MAXN][21];

void init(){
	
	int p = 1;
	for(int i=1;i<=N;i++){
		while(p+1<=N && dis(i,p+1)<=L) ++p;
		
		dp[i][0] = p;
	}
	
	for(int j=1;j<=20;j++){
		for(int i=1;i<=N;i++){
			dp[i][j] = dp[dp[i][j-1]][j-1];
		}
	}
}

int walk(int s, int t){
	int ans = 0;
	for(int j=20;j>=0;j--){
		if(dp[s][j] && dp[s][j] < t){
			ans += (1<<j);
			s = dp[s][j];
		}
	}
	return ans + 1;
}

int main(){
	
	cin>>N;
	
	for(int i=1;i<=N;i++){
		cin>>x[i];
	}	
	
	cin>>L>>Q;
	
	init();
	
	int s,t;
	while(Q--){
		cin>>s>>t;
		if(s > t) swap(s,t);
		cout<<walk(s,t)<<endl;
	}
	return 0;
}

