Sorted and Sorted

There are 2N balls, N white and N black, arranged in a row. The integers from 1 through N are written on the white balls, one on each ball, and they are also written on the black balls, one on each ball. The integer written on the i-th ball from the left (1 ≤ i ≤ 2N) is a_i, and the color of this ball is represented by a letter c_i. c_i = W represents the ball is white; c_i = B represents the ball is black.

Takahashi the human wants to achieve the following objective:

• For every pair of integers (i,j) such that 1 ≤ i < j ≤ N, the white ball with i written on it is to the left of the white ball with j written on it.
• For every pair of integers (i,j) such that 1 ≤ i < j ≤ N, the black ball with i written on it is to the left of the black ball with j written on it.

In order to achieve this, he can perform the following operation:

• Swap two adjacent balls.

Find the minimum number of operations required to achieve the objective.

Constraints

• 1 ≤ N ≤ 2000
• 1 ≤ a_i ≤ N
• c_i = W or c_i = B.
• If i ≠ j, (a_i,c_i) ≠ (a_j,c_j).

Input

Input is given from Standard Input in the following format:

N c_1 a_1 c_2 a_2 : c_{2N} a_{2N}

Output

Print the minimum number of operations required to achieve the objective.

Examples

Input

3 B 1 W 2 B 3 W 1 W 3 B 2

Output

4

Input

4 B 4 W 4 B 3 W 3 B 2 W 2 B 1 W 1

Output

18

Input

9 W 3 B 1 B 4 W 1 B 5 W 9 W 2 B 6 W 5 B 3 W 8 B 9 W 7 B 2 B 8 W 4 W 6 B 7

Output

41

inputFormat

Input

Input is given from Standard Input in the following format:

N c_1 a_1 c_2 a_2 : c_{2N} a_{2N}

outputFormat

Output

Print the minimum number of operations required to achieve the objective.

Examples

Input

3 B 1 W 2 B 3 W 1 W 3 B 2

Output

4

Input

4 B 4 W 4 B 3 W 3 B 2 W 2 B 1 W 1

Output

18

Input

9 W 3 B 1 B 4 W 1 B 5 W 9 W 2 B 6 W 5 B 3 W 8 B 9 W 7 B 2 B 8 W 4 W 6 B 7

Output

41

样例

9
W 3
B 1
B 4
W 1
B 5
W 9
W 2
B 6
W 5
B 3
W 8
B 9
W 7
B 2
B 8
W 4
W 6
B 7

41