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>
#define LOG 25
#define N 100005
using namespace std;

int n,l,q,x,y,a[N],dp[LOG][N];

int main() {

  scanf("%d",&n);
  for(int i=1;i<=n;i++) {
    scanf("%d",&a[i]);
  }
  scanf("%d",&l);
  int son=1;
  for(int i=1;i<=n;i++) {
    while(a[i]+l>=a[son+1] && son+1<=n) son++;
    dp[0][i]=son;
  }
  for(int p=1;p<=20;p++) {
    for(int i=1;i<=n;i++) {
      dp[p][i]=dp[p-1][dp[p-1][i]];
    }
  }
  scanf("%d",&q);
  while(q--) {
    int ans=0;
    scanf("%d %d",&x,&y);
    if(x>y) swap(x,y);
    for(int p=20;p>=0;p--) {
      if(dp[p][x]<y) {
        ans+=(1<<p);
        x=dp[p][x];
      }
    }
    printf("%d\n",ans+1);
  }

}
