Problem: 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.

Examples

Input

3
#.#


Output

1


Input

3
.#


Output

1


Input

5
.##.


Output

2


Input

9
.........


Output

0

Solution (in PYTHON3):

Solution:
n=int(input()) 
s=list(input())

dp=[0]*(n+1)
for i in range(n):
  if s[i]=="#":
    dp[0]+=1

for i in range(n):
  if s[n-i-1]=="#":
    dp[i+1]=dp[i]-1
  else:
    dp[i+1]=dp[i]+1

print(min(dp))