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.

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.

Example

Input

9
1 3 6 13 15 18 19 29 31
10
4
1 8
7 3
6 7
8 5


Output

4
2
1
2
from collections import defaultdict,deque
import sys,heapq,bisect,math,itertools,string,queue,datetime
sys.setrecursionlimit(10**8)
INF = float('inf')
mod = 10**9+7
def inpl(): return list(map(int, input().split()))
def inpls(): return list(input().split())

N = int(input())
xx = inpl()
L = int(input())

K = N.bit_length()
db_r = [[0]*K for i in range(N)]
for i,x in enumerate(xx):
    ind = bisect.bisect_right(xx,x+L)
    db_r[i][0] = ind-1

for k in range(1,K):
    for i in range(N):
        db_r[i][k] = db_r[db_r[i][k-1]][k-1]

def check(a,b,d):
    L = d.bit_length()
    for k in range(L):
        if d & (1<<k):
            a = db_r[a][k]
    return a >= b

Q = int(input())
for i in range(Q):
    a,b = inpl()
    a -= 1
    b -= 1
    a,b = min(a,b),max(a,b)
    OK = N
    NG = 0
    while OK-NG>1:
        mid = (OK+NG)//2
        if check(a,b,mid): OK = mid
        else: NG = mid
    print(OK)
