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=input()
S=raw_input()
L=[0]

for i,x in enumerate(S):
	if x=="#":
		L.append( L[-1]+1 )
	else:
		L.append( L[-1] )
			

ans=float("inf")
for i in range(N+1):
	b=L[i]			# black on left
	w=N-i-(L[-1]-L[i])	# white on right
	ans=min(ans , b+w)

print ans