Minimum Replacements Required to Make a Matrix Balanced

Replace some ? with R or W; the remaining ? may be left as they are. Every row and every column must have equal numbers of R and W. Find the minimum number of replacements, or output −1 if it is impossible.

This site uses a standard input/output protocol.

输入格式

The first line contains N, followed by two strings of length N over R/W/?. This site uses 1≤N≤100000.

输出格式

Output a single integer, the answer.

样例 1

输入：

5
WR???
R???W

输出：

4

样例 2

输入：

1
R
R

输出：

-1

样例 3

输入：

2
??
??

输出：

0

样例说明

Example 1: first fill the two single ? cells, then use one double-? column to balance the row counts, for 4 replacements. Example 2: a fixed same-color column can never be balanced, so −1. Example 3: with all ?, both colors count 0 and are already balanced, so 0 replacements.