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 = 'import sys\ninput = lambda : sys.stdin.readline().rstrip()\nsys.setrecursionlimit(max(1000, 10**9))\nwrite = lambda x: sys.stdout.write(x+"\\n")\n\n\nn = int(input())\nx = list(map(int, input().split()))\nl = int(input())\nq = int(input())\nps = [None]*n\n# ps2 = [None]*n\nj = 0\nfor i in range(n):\n    if j<i:\n        j = i\n    while j+1<n and x[j+1]-x[i]<=l:\n        j += 1\n    ps[i] = j\n# ダブリング\ndef double(ps):\n    # global: n=psのサイズ\n    k = 0\n    n = len(ps)\n    while pow(2,k)<n:\n        k += 1\n    prev = [[None]*n for _ in range(k)] # ノードjから2^i個上の上司\n    for j in range(n):\n        prev[0][j] = ps[j]\n    for i in range(1,k):\n        for j in range(n):\n            p = prev[i-1][j]\n            if p>=0:\n                prev[i][j] = prev[i-1][p]\n            else:\n                prev[i][j] = p\n    return prev\ndl = double(ps)\nans = [None]*q\nfor i in range(q):\n    a,b = map(lambda x: int(x)-1, input().split())\n    a,b = min(a,b), max(a,b)\n#     print(a,b)\n    res = 0\n    tmp = float("inf")\n    for k in range(len(dl)-1, -1, -1):\n        if dl[k][a]<b:\n            a = dl[k][a]\n            res += pow(2,k)\n#         elif dl[k][a]==b:\n#             tmp = res+pow(2,k)\n#             break\n        else:\n            tmp = min(tmp, res+pow(2,k))\n    ans[i] = tmp\nwrite("\\n".join(map(str, ans)))'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 14393