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 long long ll;
#define INF (1<<30)
#define INFLL (1ll<<60)
typedef pair<int, int> P;
typedef pair<int, P> E;
#define MOD (1000000007ll)
#define l_ength size

void mul_mod(ll& a, ll b){
	a *= b;
	a %= MOD;
}

void add_mod(ll& a, ll b){
	a += b;
	a %= MOD;
}


string s;
bool done[225816][2];
int memo[225816][2],n;

int solve(int p, int c){
	if(p==n){
		return 0;
	}
	if(done[p][c]){
		return memo[p][c];
	}
	done[p][c] = true;
	if(c){
		memo[p][c] = ((s[p]=='.')?1:0)+solve(p+1,c);
	}else{
		memo[p][c] = min(solve(p,1),((s[p]=='#')?1:0)+solve(p+1,c));
	}
	return memo[p][c];
}

int main(void){
	int i;
	cin >> n;
	cin >> s;
	cout << solve(0,0) << endl;
	return 0;
}