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 main(){
	int N; cin >> N; 
	int X[100010] = {}; 
	for(int i = 0; i < N; i++) cin >> X[i]; 
	int L, Q; cin >> L >> Q; 
	int A[100010][18] = {}; //A[iから始めて][2^j日で進める]
	for(int i = 0; i < N; i++){
		int a = upper_bound(X, X+N, X[i] + L) - X; 
		A[i][0] = a - 1; 
	}
	for(int j = 1; j < 18; j++){
		for(int i = 0; i < N; i++){
			A[i][j] = A[A[i][j-1]][j-1]; 
		}
	}
	for(int q = 0; q < Q; q++){
		int a, b; cin >> a >> b; 
		a--; b--; 
		if(a > b) swap(a, b); 
		int now = a; 
		int ans = 0; 
		for(int i = 17; i >= 0; i--){
			if(A[now][i] >= b) continue;  
			now = A[now][i]; 
			ans += (1 << i); 
		}
		cout << ans + 1 << endl; 
	}
}