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>
typedef long long i64;
using std::cout;
using std::endl;
using std::cin;

int main(){
	int n; cin >> n; std::vector<int> x(n);
	for(int i = 0; i < n; i++) cin >> x[i];
	int L, Q; cin >> L >> Q;
	
	int cnt = 0;
	std::vector<std::vector<int>> dp(21, std::vector<int>(n, -1));
	for(int i = 0; i < n; i++) {
		while(cnt < n and x[cnt] - x[i] <= L) cnt++;
		dp[0][i] = cnt - 1;
	}
	
	for(int i = 1; i < 21; i++) {
		for(int j = 0; j < n; j++) {
			dp[i][j] = dp[i - 1][dp[i - 1][j]];
		}
	}
	
	for(int q = 0; q < Q; q++) {
		int a, b; cin >> a >> b; a--; b--;
		if(a > b) std::swap(a, b);
		
		int ans = 0;
		for(int i = 20; i >= 0; i--) {
			if(dp[i][a] < b) {
				ans |= (1 << i);
				a = dp[i][a];
			}
		}
	
		cout << ans + 1 << endl;
	}
	return 0;
}
