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 PYTHON):

Solution:
n=int(raw_input())
s=raw_input()

temp=s.count("#")
if temp==0 or temp==n:
    print(0)
else:
    head=0
    tail=n-temp
    ret=tail+head
    for c in s:
        if c=="#":
            head+=1
        else:
            tail-=1
        temp2=head+tail
        if temp2<ret:
            ret=temp2
    print(ret)