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 = "def reachN(i0, n):\n    if n == 0:\n        return i0\n    maxbit = ceil(log2(n))\n    kL = []\n    for i in range(maxbit+1):\n        if n>>i & 1:\n            kL.append(i)\n    #print(kL)\n    i = i0\n    for k in kL[::-1]:\n        if start < goal:\n            i = dp[k][i]      #; print('norm', i)\n        else:\n            i = dpInv[k][i]   #; print('inv', i)\n    return i   \n\ndef fun(n):\n    if start < goal:\n        return reachN(start, n) >= goal\n    else:\n        return reachN(start, n) <= goal\n\n#def reach(x, L):\n #   return bisect.bisect_left(xL, x+L)\n\ndef binMin(l, r):\n    if r-l == 1:\n        return r\n    m = (l+r) // 2\n    if fun(m):\n        r = m\n    else:\n        l = m\n    return binMin(l, r)\n\nimport bisect\nfrom math import log2, ceil\n\nN = int(input())\nxL = [-float('inf')] + [int(i) for i in input().split()]   #; print(xL)\nLmax = int(input())\n\nkmax = ceil(log2(len(xL)-2))                               #; print(kmax)\ndp = [[len(xL)-1]*(N+1) for _ in range(kmax+1)]\nfor i in range(1, N+1):\n    dp[0][i] = bisect.bisect_right(xL, xL[i]+Lmax) - 1\n#print2(dp)\nfor k in range(1, kmax+1):\n    for i in range(1, N):\n        dp[k][i] = dp[k-1][dp[k-1][i]]\n#print2(dp); print()\n\ndpInv = [[1]*(N+1) for _ in range(kmax+1)]\nfor i in range(N, 1, -1):\n    dpInv[0][i] = bisect.bisect_left(xL, xL[i]-Lmax)\nfor k in range(1, kmax+1):\n    for i in range(N, 1, -1):\n        dpInv[k][i] = dpInv[k-1][dpInv[k-1][i]]\n#print2(dpInv)\n\nQ = int(input())\nfor _ in range(Q):\n    start, goal = list(map(int, input().split()))\n    ans = binMin(0, abs(goal-start))\n    print(ans)\n"
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 14325