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 bisect import bisect
N = int(input())
xs = list(map(int,input().split()))
L = int(input())
Q = int(input())
qs = [tuple(map(lambda x:int(x)-1, input().split())) for i in range(Q)]

K = len(bin(N)) - 1
dp = [[None]*N for i in range(K)]
for i,x in enumerate(xs):
    dp[0][i] = bisect(xs, x+L) - 1
for k in range(K-1):
    for i in range(N):
        dp[k+1][i] = dp[k][dp[k][i]]

def enough(fr,to,n):
    now = fr
    bn = bin(n)
    ln = len(bn)-2
    for i,c in enumerate(bn[2:]):
        if c=='0': continue
        now = dp[ln-1-i][now]
        if now >= to:
            return True
    return False

ans = []
for a,b in qs:
    if a>b: a,b = b,a
    ok = N
    ng = 0
    while ok-ng > 1:
        m = (ok+ng)//2
        if enough(a,b,m):
            ok = m
        else:
            ng = m
    ans.append(ok)

print(*ans,sep='\n')