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:
# -*- coding: utf-8 -*-
n = int(raw_input())
s = str(raw_input())

ans=[]
black=[]
for i in range(0,n):
    ans.append(-1)
    black.append(-1)
ans[0]=0
if s[0]==".":
    black[0]=0
else:
    black[0]=1

for i in range(1,n):
    if s[i] == ".":
        black[i] = black[i-1]
        ans[i] = min(black[i-1], ans[i-1]+1)
    else:
        black[i] = black[i-1] + 1
        ans[i] = min(ans[i-1], black[i-1]+1)

print ans[n-1]