Chefland has all the cities on a straight line. There are $N$ cities in Chefland numbered $1$ to $N$. City $i$ is located at coordinate $x_i$ on the x-axis. Guru wants to travel from city $A$ to city $B$. He starts at time t=0. He has following choices to travel.
- He can walk $1$ metre in $P$ secs.
- There is a train that travels from city $C$ to city $D$ which travels $1$ metre in $Q$ secs which starts at time t=$Y$ secs. Guru can take the train only at city $C$ and leave the train only at city $D$.
Can you help Guru find the minimum time he will need to travel from city $A$ to $B$. Note that you cannot board the train after time t =$Y$.

-----Input:-----
- First line will contain $T$, number of testcases. Then the testcases follow. 
- First line of each testcase contains eight space separated integers $N, A, B, C, D, P, Q, Y $. 
- Second line of each testcase contains $N$ space-separated integers with the $i$-th integer representing $x_i$.

-----Output:-----
For each testcase, output in a single line containing the minimum travel time.

-----Constraints-----
- $1 \leq T \leq 300$
- $2 \leq N \leq 300$
- $-1000 \leq x_i \leq 1000$
- $0 \leq Y \leq 100000$
- $1 \leq A,B,C,D \leq n $
- $A \neq B$
- $C \neq D$
- $1 \leq P, Q \leq 100$
- $x_i < x_j$  if $i < j$

-----Sample Input:-----
1
4 1 3 2 4 3 2 4
1 2 3 4

-----Sample Output:-----
6

-----EXPLANATION:-----
Guru can walk directly in 6 secs.
If Guru takes train, then he will need  atleast 11 secs.

Difficulty: UNKNOWN_DIFFICULTY

Starter code:

Solutions:
t = int(input())
for _ in range(t):
	(n, a, b, c, d, p, q, y) = list(map(int, input().split()))
	l = list(map(int, input().split()))
	ans = abs(l[b - 1] - l[a - 1]) * p
	x = abs(l[c - 1] - l[a - 1]) * p
	if x <= y:
		x = y + abs(l[d - 1] - l[c - 1]) * q + abs(l[b - 1] - l[d - 1]) * p
		ans = min(ans, x)
	print(ans)


t = int(input())
for _ in range(t):
	(n, a, b, c, d, p, q, y) = list(map(int, input().split()))
	lst = list(map(int, input().split()))
	dist1 = abs(lst[a - 1] - lst[b - 1])
	walk = dist1 * p
	acdist = abs(lst[a - 1] - lst[c - 1]) * p
	dist2 = abs(lst[c - 1] - lst[d - 1])
	dist3 = abs(lst[b - 1] - lst[d - 1])
	cdtime = dist2 * q
	bdtime = dist3 * p
	train = y + cdtime + bdtime
	if acdist <= y:
		print(min(walk, train))
	else:
		print(walk)


for t in range(int(input())):
	(n, a, b, c, d, p, q, y) = map(int, input().split())
	x = list(map(int, input().split()))
	bf = abs(x[a - 1] - x[b - 1]) * p
	bt = abs(x[a - 1] - x[c - 1]) * p
	if bt <= y:
		wbt = y + abs(x[d - 1] - x[b - 1]) * p + abs(x[d - 1] - x[c - 1]) * q
		print(min(bf, wbt))
	else:
		print(bf)


for _ in range(int(input())):
	(n, a, b, c, d, p, q, y) = map(int, input().split())
	x = list(map(int, input().split()))
	walk = abs(x[a - 1] - x[b - 1]) * p
	train = abs(x[a - 1] - x[c - 1]) * p
	if train <= y:
		walk_train = y + abs(x[d - 1] - x[b - 1]) * p + abs(x[d - 1] - x[c - 1]) * q
		print(min(walk, walk_train))
	else:
		print(walk)


t = int(input())
for _ in range(t):
	(n, a, b, c, d, p, q, y) = map(int, input().split())
	x = list(map(int, input().split()))
	t1 = p * abs(x[a - 1] - x[b - 1])
	if abs(x[c - 1] - x[a - 1]) * p <= y:
		t2 = q * abs(x[c - 1] - x[d - 1]) + abs(x[d - 1] - x[b - 1]) * p + y
		print(min(t1, t2))
	else:
		print(t1)


for t in range(int(input())):
	(n, a, b, c, d, p, q, y) = map(int, input().split())
	l = list(map(int, input().split()))
	foot = abs(l[b - 1] - l[a - 1]) * p
	train = 0
	if abs(l[c - 1] - l[a - 1]) * p > y:
		print(int(foot))
		continue
	else:
		train += y + abs(l[d - 1] - l[c - 1]) * q + abs(l[b - 1] - l[d - 1]) * p
	if train < foot:
		print(int(train))
	else:
		print(int(foot))


for _ in range(int(input())):
	(n, a, b, c, d, p, q, y) = map(int, input().split())
	ar = [int(x) for x in input().split()]
	temp1 = abs(ar[a - 1] - ar[c - 1]) * p
	if temp1 > y:
		temp1 = 10 ** 9
	elif temp1 == y:
		temp1 += abs(ar[c - 1] - ar[d - 1]) * q + abs(ar[d - 1] - ar[b - 1]) * p
	elif temp1 < y:
		temp1 += abs(ar[c - 1] - ar[d - 1]) * q + abs(ar[d - 1] - ar[b - 1]) * p + abs(temp1 - y)
	temp2 = abs(ar[a - 1] - ar[b - 1]) * p
	print(min(temp1, temp2))


from sys import stdin, stdout
from math import gcd
ans = []
for _ in range(int(stdin.readline())):
	(n, a, b, c, d, p, q, y) = list(map(int, stdin.readline().split()))
	nArr = list(map(int, stdin.readline().split()))
	wT = abs((nArr[b - 1] - nArr[a - 1]) * p)
	WTTT = abs((nArr[c - 1] - nArr[a - 1]) * p)
	if WTTT > y:
		ans.append(str(wT))
		continue
	tT = abs((nArr[c - 1] - nArr[d - 1]) * q)
	tTBCT = abs((nArr[d - 1] - nArr[b - 1]) * p)
	vTT = y + tT + tTBCT
	ans.append(str(wT) if wT < vTT else str(vTT))
stdout.write('\n'.join(ans))