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
read = sys.stdin.buffer.read
readline = sys.stdin.buffer.readline
readlines = sys.stdin.buffer.readlines
import bisect

n = int(readline())
x = list(map(int,readline().split()))
l = int(readline())
q = int(readline())
ab = list(map(int,read().split()))

dbl = [[] for _ in range(n)]
j = 0
for i in range(n):
    while(j < n-1):
        if(abs(x[j+1] - x[i]) > l):
            break
        j += 1
    dbl[i].append(j)

for i in range(30):
    if(dbl[0][-1] == n-1):
        break
    for j in range(n):
        dbl[j].append(dbl[ dbl[j][i] ][i])

def calc(a,b):
    if(dbl[a][0] >= b):
        return 1
    ind = bisect.bisect_left(dbl[a],b) - 1
    return 2**ind + calc(dbl[a][ind],b)

ans = []
it = iter(ab)
for a,b in zip(it,it):
    a -= 1
    b -= 1
    a,b = min(a,b),max(a,b)
    ans.append(calc(a,b))

print('\n'.join(map(str,ans)))