Problem:
Score : 300 points

Problem Statement

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.

Sample Input 1

3
#.#

Sample Output 1

1

It is enough to change the color of the first stone to white.

Sample Input 2

5
#.##.

Sample Output 2

2

Sample Input 3

9
.........

Sample Output 3

0

Solution in Go (1.6) (judge verdict: Accepted)

package main

import (
	"fmt"
)

func min(a, b int) int {
	if a < b {
		return a
	}
	return b
}

// min b[i+1] + (w[n] - w[i + 1]) 0 <= i < n
func main() {
	var n int
	var s string
	fmt.Scan(&n, &s)

	b := make([]int, n+1)
	for i := 0; i < n; i++ {
		b[i+1] = b[i]
		if s[i] == '#' {
			b[i+1]++
		}
	}
	ans := n
	for i := 0; i <= n; i++ {
		ans = min(ans, b[i]+n-i-b[n]+b[i])
	}
	fmt.Println(ans)
}