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 = '#!/usr/bin/env python3\nimport bisect\n\n\ndef dist(tree, tree_i, tree_j, parent, a, b):\n    i = tree_i[b]\n    if tree_i[a] == i:\n        return tree_j[b] - tree_j[a]\n    else:\n        branch = tree[i]\n        branch_root = branch[0]\n        if branch_root < a:\n            return tree_j[b] - bisect.bisect_left(branch, a) + 1\n        else:\n            p = parent[branch_root]\n            if p < a:\n                return tree_j[b] + 1\n            else:\n                return tree_j[b] + 1 + dist(tree, tree_i, tree_j, parent, a, p)\n\n\ndef solve(n, x, l, q, qry):\n\n    g = [[] for _ in range(n)]\n    parent = [-1] * n\n    weight = [1] * n\n\n    for v in range(1, n):\n        p = bisect.bisect_left(x, x[v] - l)\n        g[p].append(v)\n        parent[v] = p\n\n    for v in range(n - 1, -1, -1):\n        for w in g[v]:\n            weight[v] += weight[w]\n\n    tree = [[0]]\n    tree_i = [-1] * n\n    tree_j = [0] * n\n    tree_i[0] = 0\n    for v in range(n):\n        mw = 0\n        c = -1\n        for w in g[v]:\n            if mw < weight[w]:\n                mw = weight[w]\n                c = w\n        if 0 <= c:\n            i = tree_i[v]\n            tree[i].append(c)\n            tree_i[c] = i\n            tree_j[c] = len(tree[i]) - 1\n            for w in g[v]:\n                if w != c:\n                    tree.append([w])\n                    tree_i[w] = len(tree) - 1\n\n    for tpl in qry:\n        a, b = tpl\n        if b < a:\n            a, b = b, a\n        print((dist(tree, tree_i, tree_j, parent, a, b)))\n\n\ndef main():\n    n = input()\n    n = int(n)\n    x = list(map(int, input().split()))\n    l = input()\n    l = int(l)\n    q = input()\n    q = int(q)\n    qry = []\n    for _ in range(q):\n        a, b = input().split()\n        a = int(a) - 1\n        b = int(b) - 1\n        qry.append((a, b))\n\n    solve(n, x, l, q, qry)\n\n\ndef __starting_point():\n    main()\n\n\n__starting_point()'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 14367