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 rep(i,n) for(int i=0; i<(n); i++)
using namespace std;
const int MX = 100005;
int n, x[MX], nx[MX][20], l, q, a, b, ans, k;
int main(){
	scanf("%d", &n);
	rep(i,n) scanf("%d", x+i);
	scanf("%d%d", &l, &q);
	rep(i,n){
		while(a < n && x[a] - x[i] <= l) a++;
		a--;
		nx[i][0] = a;
	}
	rep(j,19) rep(i,n) nx[i][j+1] = nx[nx[i][j]][j];
	rep(i,q){
		scanf("%d%d", &a, &b);
		a--; b--; ans = 0;
		if(a > b) swap(a,b);
		while(a < b){
			for(k = 0; nx[a][k] < b; k++);
			if(k) k--;
			ans += 1 << k;
			a = nx[a][k];
		}
		printf("%d\n", ans);
	}
}