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 C (GCC 5.4.1) (judge verdict: Accepted)

#include <stdlib.h>
#include <string.h>
#include <math.h>
#include <stdio.h>
int MIN(int a,int b){
    return a<b?a:b;
}
int compare(const void *a,const void *b){
    if(*(int *)a>*(int *)b)return 1;
    return -1;
}
int main()
{   int n,b[200001]={0},i,w[200001]={0};
    scanf("%d",&n);
    
    char s[n+1];
    int chk=0;
    scanf("%s",s);
    for(i=0;i<n;i++){
        if(s[i]=='.'){
            chk++;
        }
    }
    if(chk==0||chk==n){
        printf("0");
        return 0;
    }
    if(s[0]=='#'){
        w[0]=chk;
        b[0]=1;
    }else{
        w[0]=chk-1;
    }
    for(i=1;i<n;i++){
        if(s[i]=='#'){
            b[i]=b[i-1]+1;
            w[i]=w[i-1];
        }else{
            b[i]=b[i-1];
            w[i]=w[i-1]-1;
        }
    }
    int x=11451419;
    int ans[200001]={0};
    for(i=0;i<n;i++){
        if(b[i]==i+1&&w[i]==n-(i+1)){
          x=chk;  
        }
        ans[i]=b[i]+w[i];
    }
    qsort(ans,n,sizeof(int),compare);
    printf("%d",MIN(ans[0],x));
    return 0;
}