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 = "from heapq import heappush,heappop,heapify\nfrom collections import deque,defaultdict,Counter\nimport itertools\nfrom itertools import permutations,combinations,groupby\nimport sys\nimport bisect\nimport string\nimport math\nimport time\nimport random\ndef S_():\n    return input()\ndef LS():\n    return [i for i in input().split()]\ndef I():\n    return int(input())\ndef MI():\n    return map(int,input().split())\ndef LI():\n    return [int(i) for i in input().split()]\ndef LI_():\n    return [int(i)-1 for i in input().split()]\ndef NI(n):\n    return [int(input()) for i in range(n)]\ndef NI_(n):\n    return [int(input())-1 for i in range(n)]\ndef StoI():\n    return [ord(i)-97 for i in input()]\ndef ItoS(nn):\n    return chr(nn+97)\ndef LtoS(ls):\n    return ''.join([chr(i+97) for i in ls])\ndef GI(V,E,Directed=False,index=0):\n    org_inp=[]\n    g=[[] for i in range(n)]\n    for i in range(E):\n        inp=LI()\n        org_inp.append(inp)\n        if index==0:\n            inp[0]-=1\n            inp[1]-=1\n        if len(inp)==2:\n            a,b=inp\n            g[a].append(b)\n            if not Directed:\n                g[b].append(a)\n        elif len(inp)==3:\n            a,b,c=inp\n            aa=(inp[0],inp[2])\n            bb=(inp[1],inp[2])\n            g[a].append(bb)\n            if not Directed:\n                g[b].append(aa)\n    return g,org_inp\ndef bit_combination(k,n=2):\n    rt=[]\n    for tb in range(n**k):\n        s=[tb//(n**bt)%n for bt in range(k)]\n        rt+=[s]\n    return rt\ndef show(*inp,end='\\n'):\n    if show_flg:\n        print(*inp,end=end)\nYN=['Yes','No']\nmo=10**9+7\ninf=float('inf')\nl_alp=string.ascii_lowercase\nu_alp=string.ascii_uppercase\nts=time.time()\n#sys.setrecursionlimit(10**5)\ninput=lambda: sys.stdin.readline().rstrip()\n\ndef ran_input():\n    import random\n    n=random.randint(4,16)\n    rmin,rmax=1,10\n    a=[random.randint(rmin,rmax) for _ in range(n)]\n    return n,a\n\nshow_flg=False\nshow_flg=True\n\nans=0\n\nn=I()\nm=n.bit_length()\nx=LI()\nL=I()\nq=I()\n\nr=[0]*n\n\n\nfor i in range(n):\n    r[i]=bisect.bisect(x,x[i]+L)-1\n    \nnb=[r]\nnx=[0]*n\n\nfor k in range(m):\n    nx=[0]*n\n    for i in range(n):\n        nx[i]=r[r[i]]\n    nb.append(nx)\n    r=nx\n\nfor _ in range(q):\n    a,b=LI_()\n    if a>b:\n        a,b=b,a\n    \n    t=0\n    for p in range(m,-1,-1):\n        if nb[p][a]<b:\n            t+=1<<p\n            a=nb[p][a]\n    \n    print(t+1)\n"
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 17664