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)

n = int(input())
s = input().strip()

wcs, bcs = [0], [0]
wc, bc = 0, 0
if s[0] == '#':
  bc = 1
for prevs, _s in zip(s, s[1:]):
  if prevs != _s:
    bcs.append(bc + bcs[-1])
    if _s == '#':
      bc = 1
    else:
      bc = 0
  else:
    if _s == '#':
      bc += 1
bcs.append(bc + bcs[-1])

wc, bc = 0, 0
if s[-1] == '.':
  wc = 1
for prevs, _s in zip(s[::-1], s[::-1][1:]):
  if prevs != _s:
    wcs.append(wc + wcs[-1])
    if _s == '.':
      wc = 1
    else:
      wc = 0
  else:
    if _s == '.':
      wc += 1
wcs.append(wc + wcs[-1])

minbw = pow(10, 6)
for bc, wc in zip(bcs, wcs[::-1]):
  if bc + wc < minbw:
    minbw = bc + wc
print(minbw)