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>
const int MAXN = 1e5+1;
const int LOGV = 17;
int F[LOGV][MAXN];
int X[MAXN];
int main()
{
	int N, L, Q, i, j, logV, step;
	scanf("%d", &N);
	for(logV=1; (1<<(logV+1))<=N; ++logV);
	for(i=1; i<=N; ++i)
		scanf("%d", X+i);
	scanf("%d", &L);
	for(i=j=1; i<=N; ++i)
	{
		while(j<=N && X[j]-X[i]<=L) ++j;
		F[0][i] = j-1;
	}
	for(i=1; i<=logV; ++i)
		for(j=1; j+(1<<i)-1<=N; ++j)
			F[i][j] = F[i-1][F[i-1][j]];
	scanf("%d", &Q);
	int a, b;
	while (Q--)
	{
		scanf("%d%d", &a, &b);
		if(a > b)
			a ^= b ^= a ^= b;
		step = 0;
		for(i=logV; i>=0; --i)
			if(F[i][a] && F[i][a]<b)
				step += 1<<i,
				a = F[i][a];
		printf("%d\n", step+1);
	}
}