Problem:
Score : 300 points

Problem Statement

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.

Sample Input 1

3
#.#

Sample Output 1

1

It is enough to change the color of the first stone to white.

Sample Input 2

5
#.##.

Sample Output 2

2

Sample Input 3

9
.........

Sample Output 3

0

Solution in Fortran (gfortran v4.8.4) (judge verdict: Accepted)

program main
  implicit none
  integer ::le,i,j,a=0,b=0,am,bm
  character(300000)::n
  read(*,*)j
  read(*,*)n
  le=len_trim(n)
  do i=1,le
    if(n(i:i)=='.')a=a+1
    if(n(i:i)=='#')b=b+1
  enddo
  am=a
  bm=b
  do j=1,le
    if(n(j:j)=='.')then
      a=a-1
      if(am>a)am=a
    else
      a=a+1
    endif
  enddo
  do j=le,1,-1
      if(n(j:j)=='#')then
      b=b-1
      if(bm>b)bm=b
    else
      b=b+1
    endif

  enddo
  write(*,*)min(am,bm)
end program main