There are N buckets arranged in a row. Each bucket either is empty or contains a ball. The buckets are specified as a string buckets consisting of characters "." (empty bucket) and "B" (bucket with a ball). For example, for buckets = "B.BB.B..B", the row of buckets appears as follows:

In one move you can take the ball out of any bucket and place it in another (empty) bucket. Your goal is to arrange the balls to create an alternating sequence of full and empty buckets, in other words, the distance between two consecutive balls should be equal to 2. Note that the sequence may start at any bucket.

For example, in the figure below, the balls are placed correctly.

Write a function:

int solution(string &buckets);

that, given a string buckets of length N, returns the minimum number of moves required to create the described sequence. If it is impossible to create a correct sequence, return -1.

Examples

1. Given buckets = "..B....B.BB", the function should return 2.

In the beginning, the row of buckets appears as follows:

First, you can move the ball from bucket 10 to bucket 5.

Second, you can move the ball from bucket 2 to bucket 3.

Now, the balls are in buckets 3, 5, 7 and 9, creating a correct sequence.

2. Given buckets = "BB.B.BBB...", the function should return 4.

You can move the balls from buckets 1, 3, 5 and 7 to buckets 2, 4, 8 and 10.

3. Given buckets = "..BBB.BB", the function should return -1 because it is impossible to create a correct sequence.