Monochrome Points

There are 2N points on a circle numbered from 1 through 2N, in clockwise order. Each point is either white or black. There are N white points and N black points.

We will draw N line segments connecting these points so that the following conditions are satisfied.

• Each point is an end point of exactly one line segment.
• Each line segment connects a white point and a black point.

Among the N line segments, the number of pairs of line segments intersecting each other is called the intersection number. Write a program which, given the information of the colors of the points, calculates the maximum of the intersection number when we draw N line segments.

Read the following data from the standard input.

N S

Here S is a string of length 2N representing the colors of the points. Each character of S is either B or W, and the i-th character (1 ≤ i ≤ 2N) is the color of the i-th point. It is B if the point is black, and W if the point is white.

Write one line to the standard output. The output should contain the maximum of the intersection number when we draw N line segments satisfying the conditions.

• 1 ≤ N ≤ 200 000.
• S is a string of length 2N which consists of B and W. The character B appears N times in the string S, and the character W appears N times in the string S.