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 dpdot[200005],dpsq[200005];
int main()
{
    int n;
    string s;
    cin >> n >> s;
    for(int i=1;i<=n;i++)
    {
        if(s[i-1]=='#') dpsq[i]++;
        else dpdot[i]++;
        dpdot[i]+=dpdot[i-1];
        dpsq[i]+=dpsq[i-1];
    }
    int ans=1e9;
    for(int i=0;i<=n;i++) ans=min(ans,dpsq[i]+dpdot[n]-dpdot[i]);
    cout << ans;
}