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++14 (GCC 5.4.1) (judge verdict: Accepted)

#include <bits/stdc++.h>
using namespace std;
typedef unsigned long long ull;
typedef long long ll;
typedef int Int;
typedef pair<Int,Int> pii;
typedef pair<Int,double> pid;
typedef pair<double,double> pdd;
typedef pair<Int,pii> pip;
typedef pair<double,Int> pdp;
#define A first
#define B second
#define pb(x) push_back(x)
#define ALL(x) x.begin(),x.end()
#define SZ(x) (x).size()
#define CLR(x) memset(x,0,sizeof x)
#define pdebug() printf("%d\n",__LINE__)
#define Itype(a) typeof(a.begin()) 
#define REP(i,a,b) for(int i = (a);i <= (b);i++)
#define FORO(i,n) REP(i,0,(int)n-1)
#define FORI(i,n) REP(i,1,(int)n)
#define FORIT(i,t) for(Itype(t) i = t.begin();i != t.end();i++)
#define eps 1e-6
#define sqr(x) ((x)*(x))
#define dist(_a,_b) sqrt(sqr(_a.A-_b.A)+sqr(_a.B-_b.B))
#define norm(_a) sqrt(sqr(_a.A)+sqr(_a.B))
template<typename T>void getMin(T &a,T b) { if(a > b) a = b; }
template<typename T>void getMax(T &a,T b) { if(a < b) a = b; }
const int inf = 1000000007;

int main() {
    ios::sync_with_stdio(false);
    cin.tie(0);

    int N;
    string S;
    cin >> N >> S;
    int dp[N][2];

    for(int i = 0;i < N;i++) {
        if(i > 0) {
            dp[i][0] = dp[i - 1][0] + (S[i] == '#');
            dp[i][1] = min(dp[i - 1][1], dp[i - 1][0]) + (S[i] == '.');
        } else {
            dp[i][0] = S[i] == '#';
            dp[i][1] = S[i] == '.';
        }
    }

    cout << min(dp[N - 1][0], dp[N - 1][1]) << endl;
    return 0;
}