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
def examE():
    N = I()
    X = LI()
    L = I(); Q = I()
    n = N.bit_length()+1
    dp = [[0] * n for _ in range(N)]
    for i in range(N):
        dp[i][0] = bisect.bisect_right(X, X[i] + L) - 1
    for i in range(1, n):
        for j in range(N):
            if dp[j][i - 1] < N:
                index = dp[dp[j][i - 1]][i - 1]
                if index == j:
                    dp[j][i] = N
                else:
                    dp[j][i] = index
            else:
                dp[j][i] = N
    def fast_day(a, b):
        if a > b:
            a, b = b, a
        res = 0
        for i in range(n):
            if a >= b:
                return res
            c = max(0, bisect.bisect_left(dp[a], b) - 1)
            #最低かかる2**?の日数
            a = dp[a][c]
            #そこまで行く
            res += 2 ** c
    for _ in range(Q):
        a, b = map(int, input().split())
        print(fast_day(a - 1, b - 1))
#    print(dp)

import sys,copy,bisect,itertools,heapq,math
from heapq import heappop,heappush,heapify
from collections import Counter,defaultdict,deque
def I(): return int(sys.stdin.readline())
def LI(): return list(map(int,sys.stdin.readline().split()))
def LS(): return sys.stdin.readline().split()
def S(): return sys.stdin.readline().strip()
mod = 10**9 + 7
inf = float('inf')

examE()
