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 Python (3.4.3) (judge verdict: Accepted)

import sys
import math 
ni = lambda: int(ns())
na = lambda: list(map(int, input().split()))
ns = lambda: input()
N,S = ni(),ns()
#print(S)
#累積和を計算
b_ = [0]*(N+1)
w_ = [0]*(N+1)
if(S[0]=="."):
    b_[0]=0
    w_[0]=1
else:
    b_[0]=1
    w_[0]=0
for i in range(1,N):
    if(S[i]=="."):
        b_[i] = b_[i-1]
        w_[i] = w_[i-1]+1
    else:
        b_[i] = b_[i-1]+1
        w_[i] = w_[i-1]
ans = w_[N-1]
for i in range(N):
    ans = min(ans,b_[i]+w_[N-1]-w_[i])
    #print(ans)
#print(b_,w_)
ans = min(ans, b_[N-1])
print(ans)