Problem:
Score : 300 points

Problem Statement

We have two permutations P and Q of size N (that is, P and Q are both rearrangements of (1,~2,~...,~N)).

There are N! possible permutations of size N. Among them, let P and Q be the a-th and b-th lexicographically smallest permutations, respectively. Find |a - b|.

Notes

For two sequences X and Y, X is said to be lexicographically smaller than Y if and only if there exists an integer k such that X_i = Y_i~(1 \leq i < k) and X_k < Y_k.

Constraints

2 \leq N \leq 8

P and Q are permutations of size N.

Input

Input is given from Standard Input in the following format:

N
P_1 P_2 ... P_N
Q_1 Q_2 ... Q_N

Output

Print |a - b|.

Sample Input 1

3
1 3 2
3 1 2

Sample Output 1

3

There are 6 permutations of size 3: (1,~2,~3), (1,~3,~2), (2,~1,~3), (2,~3,~1), (3,~1,~2), and (3,~2,~1). Among them, (1,~3,~2) and (3,~1,~2) come 2-nd and 5-th in lexicographical order, so the answer is |2 - 5| = 3.

Sample Input 2

8
7 3 5 4 2 1 6 8
3 8 2 5 4 6 7 1

Sample Output 2

17517

Sample Input 3

3
1 2 3
1 2 3

Sample Output 3

0

Solution in Ruby (2.3.3) (judge verdict: Accepted)

N = gets.chomp.to_i
str = gets.split
a = Array.new(N)
for i in 0...N do
    a[i] = str[i].to_i
end
str = gets.split
b = Array.new(N)
for i in 0...N do
    b[i] = str[i].to_i
end
c = Array.new(N,1)
for i in 1...N do
    c[N-1-i] = c[N-i]*i
end
d = Array.new(0)
for i in 1..N do
    d.push(i)
end
e = Array.new(0)
for i in 1..N do
    e.push(i)
end

f = 1
i = 0
while d.size >= 2
    x = a[i]
    j = 0
    while x != d[j]
       j += 1 
    end
    f += c[i]*j
    d.delete_at(j)
    i += 1
end
g = 1
i = 0
while e.size >= 2
    x = b[i]
    j = 0
    while x != e[j]
       j += 1 
    end
    g += c[i]*j
    e.delete_at(j)
    i += 1
end

answer = (f-g).abs
puts answer