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;
int n,k;
string s;
int dp[200009][2];
int main()
{
    cin>>n>>s;
    for(int i=n-1;i>=0;i--)
    {
        if(s[i]=='.')
        {
            dp[i][0]=min(dp[i+1][0],dp[i+1][1]);
            dp[i][1]=1+dp[i+1][1];
        }
        else if(s[i]=='#')
        {
            dp[i][0]=1+min(dp[i+1][0],dp[i+1][1]);
            dp[i][1]=dp[i+1][1];
        }
    }
    cout<<min(dp[0][0],dp[0][1]);
}