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>
using namespace std;

int x[100010], nx[100010][20];

int main() {
	int N, L, Q;
	cin >> N;
	for(int i=1; i<=N; ++i) cin >> x[i];
	cin >> L;
	int now=1;
	for(int i=1; i<=N; ++i){
		while(now<N){
			if(x[now+1]-x[i]<=L){
				++now;
			}
			else break;
		}
		nx[i][0]=now;
	}
	nx[N][0]=nx[N+1][0]=N+1;
	int mx=0;
	while(nx[1][mx]<N){
		for(int j=1; j<=N+1; ++j){
			nx[j][mx+1]=nx[nx[j][mx]][mx];
		}
		++mx;
	}
	cin >> Q;
	for(int q=0; q<Q; ++q){
		int a, b;
		cin >> a >> b;
		if(a>b) swap(a, b);
		int ans=0, tak=a;
		for(int i=mx; i>=0; --i){
			if(nx[tak][i]<b){
				ans |= (1<<i);
				tak=nx[tak][i];
			}
		}
		cout << ans+1 << endl;
	}
	return 0;
}