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
import sys,queue,math,copy,itertools,bisect,collections,heapq

def main():
    LI = lambda : [int(x) for x in sys.stdin.readline().split()]
    _LI = lambda : [int(x)-1 for x in sys.stdin.readline().split()]
    NI = lambda : int(sys.stdin.readline())

    N = NI()
    x = LI()
    L = NI()
    m = N.bit_length()
    f = [[N-1] * N for _ in range(m)]
    j = 0
    for i in range(N-1):
        while x[i] + L >= x[j+1]:
            j += 1
            if j >= N-1: break
        else:
            f[0][i] = j
            continue
        break
    for k in range(1,m):
        for i in range(N):
            f[k][i] = f[k-1][f[k-1][i]]

    for _ in range(NI()):
        ans = 0
        a,b = _LI()
        if a > b: a,b = b,a

        for k in range(m-1,-1,-1):
            if f[k][a] < b:
                a = f[k][a]
                ans += 2**k
        print(ans+1)



if __name__ == '__main__':
    main()