Problem:
Score : 700 points

Problem Statement

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.

Partial Score

200 points will be awarded for passing the test set satisfying N \leq 10^3 and Q \leq 10^3.

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.

Sample Input 1

9
1 3 6 13 15 18 19 29 31
10
4
1 8
7 3
6 7
8 5

Sample Output 1

4
2
1
2

For the 1-st query, he can travel from the 1-st hotel to the 8-th hotel in 4 days, as follows:

Day 1: Travel from the 1-st hotel to the 2-nd hotel. The distance traveled is 2.

Day 2: Travel from the 2-nd hotel to the 4-th hotel. The distance traveled is 10.

Day 3: Travel from the 4-th hotel to the 7-th hotel. The distance traveled is 6.

Day 4: Travel from the 7-th hotel to the 8-th hotel. The distance traveled is 10.

Solution in Julia (0.5.0) (judge verdict: Accepted)

function inI()
    a = Ref{Int64}(0)
    ccall(:scanf, Int32, (Ptr{UInt8}, Ref{Int64},), "%lld", a)
    Int(a[])
end

function outI(x::Int64)
    ccall(:printf, Void, (Ptr{UInt8}, Int64), "%lld\n", x)
end

let
    n = inI()
    x = Int[inI() for _ in 1:n]
    l = inI()
    q = inI()
    const lg = 20
    F = Array(Int, lg, n)
    B = Array(Int, lg, n)
    for i = 1:n
        F[1,i] = searchsortedlast(x, x[i]+l)
        B[1,i] = searchsortedfirst(x, x[i]-l)
    end

    for fe = 2:lg
        for i = 1:n
            F[fe,i] = F[fe-1,F[fe-1,i]]
            B[fe,i] = B[fe-1,B[fe-1,i]]
        end
    end

    for i = 1:q
        a = inI()
        b = inI()

        ans = 1
        if a < b
            for fe = lg:-1:1
                if F[fe,a] < b
                    a = F[fe,a]
                    ans += 2^(fe-1)
                end
            end
        else
            for fe = lg:-1:1
                if B[fe,a] > b
                    a = B[fe,a]
                    ans += 2^(fe-1)
                end
            end
        end
        outI(ans)
        #println(ans)
    end
end