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 bisect\nimport math\nN = int(input())\nx = list(map(int, input().split()))\nL = int(input())\n\nm = int(math.log(max(x), 2) + 1)\n#i番目のホテルから2 ** k 日以内に到達可能な\n#もっとも右にあるホテル\nr = [[-1] * N for k in range(m)]\nfor i in range(N):\n  base = x[i] + L\n  p = bisect.bisect_right(x, base)\n  #print(p)\n  r[0][i] = p - 1\n\n#ダブリング\nfor k in range(m - 1):\n  for i in range(N):\n    r[k + 1][i] = r[k][r[k][i]]\n#print(r)    \n   \ndef isOK(mid):\n  now = a\n  pp = int(math.log(mid, 2) + 1)\n  for i in range(pp):\n    if (mid >> i) & 1:\n      now = r[i][now]\n      #print(now, a + 1, b + 1, mid)\n  if now >= b:\n    return True\n  else:\n    return False\n  \nQ = int(input())\nfor i in range(Q):\n  a, b = list(map(int, input().split()))\n  a, b = a-1, b-1\n  if a > b:\n    a, b = b, a\n  ng = 0\n  ok = 2 ** m\n  while (abs(ok - ng) > 1):\n    mid = int((ok + ng) / 2)\n    #print(mid)\n    if isOK(mid):\n      ok = mid\n    else:\n      ng = mid\n  print(ok)\n         \n\n         \n         \n'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 13683