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

-----Sample Output-----
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.

```python

USER_FILENAME = "<user_code>"
import sys, json, builtins
import math, heapq, bisect, itertools, functools, collections, statistics, fractions, decimal, operator, array, random, re, string, os, pathlib
try:
    import resource as _res
except Exception:
    _res = None
from collections import Counter, defaultdict, deque, OrderedDict
from functools import lru_cache, reduce
from itertools import accumulate, permutations, combinations, product
from math import gcd, ceil, floor, sqrt
from decimal import Decimal
try:
    from typing import *
except Exception:
    pass
try:
    sys.setrecursionlimit(1_000_000)
except Exception:
    pass
try:
    import site as _site
    try:
        _sys_sites = _site.getsitepackages() if hasattr(_site, "getsitepackages") else []
        for _p in _sys_sites:
            if _p and _p not in sys.path:
                sys.path.append(_p)
    except Exception:
        pass
    try:
        _usp = _site.getusersitepackages()
        if isinstance(_usp, str):
            _usp = [_usp]
        for _p in _usp:
            if _p and _p not in sys.path:
                sys.path.append(_p)
    except Exception:
        pass
except Exception:
    pass

ns = {"__name__": "__main__"}
for _k, _v in list(globals().items()):
    if not _k.startswith("_"):
        ns[_k] = _v
_CODE = '#!usr/bin/env python3\nfrom collections import defaultdict\nfrom collections import deque\nfrom heapq import heappush, heappop\nimport sys\nimport math\nimport bisect\nimport random\ndef LI(): return list(map(int, sys.stdin.readline().split()))\ndef I(): return int(sys.stdin.readline())\ndef LS():return list(map(list, sys.stdin.readline().split()))\ndef S(): return list(sys.stdin.readline())[:-1]\ndef IR(n):\n    l = [None for i in range(n)]\n    for i in range(n):l[i] = I()\n    return l\ndef LIR(n):\n    l = [None for i in range(n)]\n    for i in range(n):l[i] = LI()\n    return l\ndef SR(n):\n    l = [None for i in range(n)]\n    for i in range(n):l[i] = S()\n    return l\ndef LSR(n):\n    l = [None for i in range(n)]\n    for i in range(n):l[i] = SR()\n    return l\nmod = 1000000007\n\n#A\ndef A():\n    return\n\n#B\ndef B():\n    return\n\n#C\ndef C():\n    n = I()\n    x = LI()\n    l = I()\n    k = int(math.log(n,2))\n    f = [[i for j in range(k+1)] for i in range(n)]\n    for i in range(n-1):\n        j = bisect.bisect_left(x,x[i]+l)\n        if j < n:\n            if x[j] > x[i]+l:\n                f[i][0] = j-1\n            else:\n                f[i][0] = j\n        else:\n            f[i][0] = j-1\n    po2 = [1]*(k+1)\n    for i in range(k):\n        po2[i+1] = po2[i]*2\n    for j in range(k):\n        for i in range(n):\n            f[i][j+1] = f[f[i][j]][j]\n    q = I()\n    for i in range(q):\n        a,b = LI()\n        a,b = [min(a,b)-1, max(a,b)-1]\n        ans = 0\n        while a < b:\n            i = bisect.bisect_left(f[a],b)\n            ans += po2[max(0,i-1)]\n            a = f[a][max(0,i-1)]\n        print(ans)\n\n#D\ndef D():\n    return\n\n#E\ndef E():\n    return\n\n#F\ndef F():\n    return\n\n#G\ndef G():\n    return\n\n#H\ndef H():\n    return\n\n#Solve\ndef __starting_point():\n    C()\n\n__starting_point()'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 17955