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 <cstdio>
#include <cstdlib>
#include <iostream>
#include <algorithm>
#include <cstring>
#include <cmath>
#define REP(i,n) for (int i=1;i<=(n);++i)
#define FOR(i,a,b) for (int i=(a);i<=(b);++i)
#define ROF(i,a,b) for (int i=(a);i>=(b);--i)
#define FEC(p,u) for (edge*p=head[u];p;p=p->nxt)
using namespace std;
typedef long long LL;

int n, L, Q, x[110000];
int a[110000][20];
int main(){
	scanf("%d", &n);
	REP(i,n) scanf("%d", x+i);
	scanf("%d%d", &L, &Q);
	REP(i,n) a[i][0] = upper_bound(x+i, x+n+1, x[i]+L)-x-1;
	FOR(j,1,17) REP(i,n) a[i][j] = a[a[i][j-1]][j-1];
	int u, v, ans;
	while (Q--){
		scanf("%d%d", &u, &v);
		if (u > v) swap(u, v);
		ans = 0;
		ROF(j,17,0) { 
			if (a[u][j] < v) {
				u = a[u][j];
				ans += 1<<j;
			}
		}
		printf("%d\n", ans+1);
	}
	return 0;
}
