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 PHP7 (7.0.15) (judge verdict: Accepted)

<?php

fscanf(STDIN, "%d", $N);
$S = str_split(trim(fgets(STDIN)));

# 初期位置の右側の全ての白石
$count_white = 0;
for ( $i = 0 ;$i < $N ;$i++ ) {
    if ($S[$i] == '.') {
        $count_white++;
    }
}

# 初期位置の左側の全ての黒石（初期位置はゼロなので0）
$count_black = 0;

$ans[] = $count_white + $count_black;

for ( $i = 0 ;$i < $N ;$i++ ) {
    if ($S[$i] == '#') {
        $count_black++;
    }
    if ($S[$i] == '.') {
        $count_white--;
    }
    $ans[] = $count_white + $count_black;
}

echo min($ans);