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 bisect import bisect_left, bisect_right\nimport math\nimport sys\ninput = sys.stdin.readline\n\n\ndef main():\n    N = int(input())\n    X = list(map(int, input().split()))\n    L = int(input())\n    ln = int(math.log(N, 2))\n    dpl = [[0] * N for _ in range(ln+1)]\n    dpr = [[0] * N for _ in range(ln+1)]\n    l = 0\n    r = 0\n    for i in range(N):\n        x = X[i]\n        while X[l] + L < x:\n            l += 1\n        while r < N-1 and x + L >= X[r+1]:\n            r += 1\n        dpl[0][i] = l\n        dpr[0][i] = r\n    for k in range(1, ln+1):\n        for i in range(N):\n            dpl[k][i] = dpl[k-1][dpl[k-1][i]]\n            dpr[k][i] = dpr[k-1][dpr[k-1][i]]\n    Q = int(input())\n    for _ in range(Q):\n        a, b = list(map(int, input().split()))\n        a -= 1\n        b -= 1\n        ans = 0\n        if a < b:\n            for k in range(ln+1)[::-1]:\n                if dpr[k][a] < b:\n                    a = dpr[k][a]\n                    ans += 2**k\n            if a < b:\n                ans += 1\n        else:\n            # a > b\n            for k in range(ln+1)[::-1]:\n                if dpl[k][a] > b:\n                    a = dpl[k][a]\n                    ans += 2**k\n            if a > b:\n                ans += 1\n        print(ans)\n\n\ndef __starting_point():\n    main()\n\n__starting_point()'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 15297