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: Time Limit Exceeded)

#include<stdio.h>
#include<math.h>
#include<stdlib.h>
#include<string.h>
#include<stdbool.h>

#define MOD 998244353

#define MIN(a,b) ((a)<(b)?(a):(b))
#define MAX(a,b) ((a)>(b)?(a):(b))

typedef long long int64;

int main(void){
    int N;
    scanf("%d",&N);
    
    char S[N];

    int BL[N],BR[N],B=0;

    for(int i = 0; i < N; i++)
    {
        BL[i]=BR[i]=0;
    }

    scanf("%s",S);
    

    for(int i = 0; i < N; i++)
    {
        if(S[i]=='#'){
            for(int j=i;j<N;j++){
                BL[j]++;
            }
            for(int j=0;j<=i;j++){
                BR[j]++;
            }
            B++;
        }
    }

    int dp[N];

    for(int i = 0; i < N-1; i++)
    {
        dp[i]=BL[i]+N-i-1-BR[i+1];
        //printf("%3d %3d %3d\n",BL[i],BR[i],dp[i]);
    }

    dp[N-1]=N-B;
    
    int ans=MIN(B,N);

    for(int i = 0; i < N; i++)
    {
        ans=MIN(ans,dp[i]);
    }
    
    printf("%d",ans);
    

    
    
    return 0;
}