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;
#define rep(i,n) for(int i=0;i<n;i++)
#define Rep(i,s,n) for(int i=s;i<n;i++)
typedef long long ll;
ll a[100000];
ll dp[18][100000];
int main() {
	int n;cin >> n;
	rep(i, n)cin >> a[i];
	ll l;cin >> l;
	rep(i, n) {
		int k = upper_bound(a, a + n, a[i] + l) - a;k--;
		dp[0][i] = k;
	}
	Rep(i, 1, 18) {
		rep(j, n) {
			dp[i][j] = dp[i - 1][dp[i - 1][j]];
		}
	}
	int q;cin >> q;
	rep(aaa, q) {
		int s, t;cin >> s >> t;s--;t--;
		if (s > t)swap(s, t);
		int out = 0;
		while (s < t) {
			rep(j, 18) {
				if (dp[j][s] >= t) {
					if (j > 0) {
						out += 1 << (j - 1);
						s = dp[j - 1][s];
					}
					else {
						out++;
						s = t;
					}
					break;
				}
			}
		}
		cout << out << endl;
	}
	return 0;
}