Stones

There are N stones arranged in a row. Every stone is painted white or black. A string S represents the color of the stones. The i-th stone from the left is white if the i-th character of S is ., and the stone is black if the character is #.

Takahashi wants to change the colors of some stones to black or white so that there will be no white stone immediately to the right of a black stone. Find the minimum number of stones that needs to be recolored.

Constraints

• 1 \leq N \leq 2\times 10^5
• S is a string of length N consisting of . and #.

Input

Input is given from Standard Input in the following format:

N S

Output

Print the minimum number of stones that needs to be recolored.

Examples

Input

3 #.#

Output

1

Input

3 .#

Output

1

Input

5 .##.

Output

2

Input

9 .........

Output

0

inputFormat

Input

Input is given from Standard Input in the following format:

N S

outputFormat

Output

Print the minimum number of stones that needs to be recolored.

Examples

Input

3 #.#

Output

1

Input

3 .#

Output

1

Input

5 .##.

Output

2

Input

9 .........

Output

0

样例

3
.#

1