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 Pascal (FPC 2.6.2) (judge verdict: Wrong Answer)

type itemp = ^item;
     item = record
        cont : integer;
        next : itemp;
     end;
var s,temp:char;
    i,j,n,t,tn,ans,tans:integer;
    sn,tsn:itemp;

procedure additem(var p : itemp;item:integer);{頭から追加}
var q : itemp;
begin
  q := p;
  new(p);
  p^.cont:=item;
  p^.next := q
end;

begin
  readln(n);
  sn:=nil;
  t:=0;
  tn:=1;
  temp:='.';
  for i:=1 to n do begin
    read(s);
    if s=temp then t := t + 1 else begin
      additem(sn,t);
      t := 1;
      tn := tn + 1;
      temp := s
    end;
  end;
  additem(sn,t);
  if temp = '*' then additem(sn,t);
  tn := tn div 2 + 1;
  ans:=n;
  for i:=0 to tn do begin
    j := 0;
    tsn := sn;
    tans := 0;
    while tsn<>nil do begin
      j := j + 1;
      if (j <= i*2) and (j mod 2 = 0) then tans := tans + tsn^.cont;
      if (j > i*2) and (j mod 2 = 1) then tans := tans + tsn^.cont;
      tsn:=tsn^.next
    end;
    if tans<ans then ans := tans;
  end;
  writeln(ans);
end.