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;
typedef pair<ll,ll> pll;
const int maxn=1e5+5;
vector<ll> V;
ll dp[maxn][30];
int pos[maxn];
int main() {
    int n,L,Q;cin>>n;
    for(int i=1;i<=n;i++) cin>>pos[i];cin>>L>>Q;
	pos[n+1]=2e9+5;
	for(int l=1,r=1;l<=n;l++) {
		while(pos[r]-pos[l]<=L) r++;
		dp[l][0]=r-1;
	}
	for(int i=1;i<30;i++) for(int j=1;j<=n;j++)
		dp[j][i]=dp[dp[j][i-1]][i-1];
    for(int i=1;i<30;i++) for(int j=1;j<=n;j++)
    	if(dp[j][i]==0) dp[j][i]=n+1;
    while(Q--){
    	int l,r,ans=0;cin>>l>>r;
    	if(l>r) swap(l,r);
    	for(int i=29;i>=0;i--) {
    		if(dp[l][i]>=r) continue;
    		else ans+=(1<<i),l=dp[l][i];
    	}
   		cout<<ans+1<<endl;
    }
    return 0;
}