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;

using int64 = long long;


int N, L, Q, X[100000];
int step[21][100000];

int main() {

  cin >> N;
  for(int i = 0; i < N; i++) {
    cin >> X[i];
  }
  cin >> L >> Q;

  int ptr = 0;
  for(int i = 0; i < N; i++) {
    while(ptr < N && X[i] + L >= X[ptr]) ++ptr;
    step[0][i] = ptr - 1;
  }
  for(int i = 1; i < 21; i++) {
    for(int j = 0; j < N; j++) {
      step[i][j] = step[i - 1][step[i - 1][j]];
    }
  }
  while(Q--) {
    int x, y;
    cin >> x >> y;
    --x, --y;
    if(x > y) swap(x, y);
    int ret = 0;
    for(int i = 20; i >= 0; i--) {
      if(step[i][x] < y) {
        ret |= 1 << i;
        x = step[i][x];
      }
    }
    cout << ret + 1 << endl;
  }

}