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;

int lg, N, L, Q, x[100009], nxt[18][100009];

int main ()
{
//freopen ("input", "r", stdin);
//freopen ("output", "w", stdout);

scanf ("%d", &N);
for (int i=1; i<=N; i++)
    scanf ("%d", &x[i]);
scanf ("%d", &L);
int j = 1;
for (int i=1; i<=N; i++)
{
    while (j < N && x[j + 1] - x[i] <= L) j ++;
    nxt[0][i] = j;
}
for (int i=1; (1 << i) < N; lg = i, i++)
    for (int j=1; j<=N; j++)
        nxt[i][j] = nxt[i - 1][nxt[i - 1][j]];
scanf ("%d", &Q);
while (Q --)
{
    int st, dr, ans = 0;
    scanf ("%d %d", &st, &dr);
    if (st > dr) swap (st, dr);
    for (int i=lg; i>=0; i--)
        if (nxt[i][st] < dr) ans |= 1 << i, st = nxt[i][st];
    printf ("%d\n", ans + 1);
}
return 0;
}
