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
from functools import reduce
from fractions import gcd
import math
import bisect
import itertools
import sys
sys.setrecursionlimit(10**7)
input = sys.stdin.readline
INF = float("inf")


def main():
    N = int(input())
    x = list(map(int, input().split()))
    L = int(input())
    Q = int(input())

    LOG = 30    # 30 > log2(10**9)
    nxt = [[-1]*N for _ in range(LOG)]
    for i in range(N):
        nxt[0][i] = bisect.bisect_left(x, x[i]+L+1) - 1

    for k in range(LOG-1):
        for i in range(N):
            if nxt[k][i] == -1:
                nxt[k+1][i] = -1
            else:
                nxt[k+1][i] = nxt[k][nxt[k][i]]

    for _ in range(Q):
        a, b = map(int, input().split())
        if a > b:
            a, b = b, a
        a -= 1
        b -= 1
        ans = 0
        for k in reversed(range(LOG)):
            if nxt[k][a] < b:
                a = nxt[k][a]
                ans += 2 ** k
        print(ans + 1)



if __name__ == '__main__':
    main()