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> 

using namespace std;

typedef long long ll; 
typedef pair<int, int> pii;

#define REP(i,n) for(int(i)=0;(i)<(int)(n);(i)++)

int n;
int x[110000];
int nxt[110000][40];
int L;

int query(int a, int b) {
	int ans = 0;
	for (int l = 20; l >= 0; l--) {
		if (nxt[a][l] < b) {
			a = nxt[a][l];
			ans += (1<<l);
		}
	}
	return ans+1;
}

int main() {
	scanf("%d", &n);
	REP(i,n) scanf("%d", x+i);

	scanf("%d", &L);
	REP(i,n) {
		nxt[i][0] = (upper_bound(x, x+n, x[i]+L) - x) - 1;
	}

	for (int l = 1; l < 32; l++) {
		REP(i,n) {
			nxt[i][l] = nxt[ nxt[i][l-1] ][l-1];
		}
	}

	int q;
	scanf("%d", &q);
	REP(i,q) {
		int a,b;
		scanf("%d %d", &a, &b); a--;b--;
		if (a > b) swap(a,b);
		printf("%d\n", query(a,b));
	}
}