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 CPP):

Solution:
#include<bits/stdc++.h>
using namespace std;
using ll = long long;
using P = pair<ll,string>;
using Map = map<string,ll>;



int main(){
	ll N;
	cin >> N;
	string S;
	cin >> S;
	ll wcounter=0;
	for(ll i=0;i<N;i++){
		if(S[i]=='.')wcounter++;
	;}
	ll ans=wcounter;
	ll num=wcounter;
	for(ll i=0;i<N;i++){
		if(S[i]=='#')num++;
		else if(S[i]=='.')num--;
		ans=min(ans,num)
	;}
	cout<<ans<<endl;

return 0;
}