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 Lua (5.3.2) (judge verdict: Accepted)

local n = io.read("*n")
local fact = {1}
for i = 2, n do
  fact[i] = i * fact[i - 1]
end
local function getrank(a)
  local box = {}
  for i = 1, n do box[i] = false end
  local r = 0
  for i = 1, n do
    for j = 1, a[i] - 1 do
      if not box[j] then
        r = r + fact[n - i]
      end
    end
    box[a[i]] = true
  end
  return r
end
local t = {}
for i = 1, n do
  t[i] = io.read("*n")
end
local ar = getrank(t)
for i = 1, n do
  t[i] = io.read("*n")
end
local br = getrank(t)
print(math.abs(ar - br))