codefoces 603A (数学 水~)

A. Alternative Thinking

time limit per test

2 seconds

memory limit per test

256 megabytes

input

standard input

output

standard output

Kevin has just recevied his disappointing results on the USA Identification of Cows Olympiad (USAICO) in the form of a binary string of length n. Each character of Kevin's string represents Kevin's score on one of the n questions of the olympiad—'1' for a correctly identified cow and '0' otherwise.

However, all is not lost. Kevin is a big proponent of alternative thinking and believes that his score, instead of being the sum of his points, should be the length of the longest alternating subsequence of his string. Here, we define an alternating subsequence of a string as a not-necessarily contiguous subsequence where no two consecutive elements are equal. For example, {0, 1, 0, 1},{1, 0, 1}, and {1, 0, 1, 0} are alternating sequences, while {1, 0, 0} and {0, 1, 0, 1, 1} are not.

Kevin, being the sneaky little puffball that he is, is willing to hack into the USAICO databases to improve his score. In order to be subtle, he decides that he will flip exactly one substring—that is, take a contiguous non-empty substring of his score and change all'0's in that substring to '1's and vice versa. After such an operation, Kevin wants to know the length of the longest possible alternating subsequence that his string could have.

Input

The first line contains the number of questions on the olympiad n (1 ≤ n ≤ 100 000).

The following line contains a binary string of length n representing Kevin's results on the USAICO.

Output

Output a single integer, the length of the longest possible alternating subsequence that Kevin can create in his string after flipping a single substring.

Sample test(s)

input

8
10000011

output

5

input

2
01

output

2

Note

In the first sample, Kevin can flip the bolded substring '10000011' and turn his string into '10011011', which has an alternating subsequence of length 5: '10011011'.

In the second sample, Kevin can flip the entire string and still have the same score.

题意是给一串01序列，选择一段子区间将其反转，问最长能得到多长的子序列使得子序列相邻两

个数字不同，子序列不一定连续．

初始序列的最长子序列长度经过操作后可能增加２，可能增加１，也可能不增加．如果初始序列存

在长度大于等于３的形如000,111的子区间的话就可以加２，方法是选择这样一个子区间，把中间

一个字符反转；如果存在两个以上的形如11, 00的子区间，也可以加２方法是任选两个子区间，这

两个子区间的中间位为间隔反转；如果只有一个长度为２的子区间就只能加一，方法是去这个子区

间的中间到序列的末尾反转．

#include <bits/stdc++.h>
using namespace std;
#define maxn 111111

char a[maxn];
int n;

int main () {
    while (scanf ("%d", &n) == 1) {
        scanf ("%s", a);
        if (n == 2 || n == 3 || n == 1) {
            printf ("%d\n", n);
            continue;
        }
        int ans = 1;
        for (int i = 1; i < n; i++) {
            if (a[i] != a[i-1])
                ans++;
        }
        bool flag = 0;
        for (int i = 2; i < n; i++) {
            if (a[i] == a[i-1] && a[i] == a[i-2]) {
                printf ("%d\n", ans+2);
                flag = 1;
                break;
            }
        }
        if (!flag) {
            int cnt = 0;
            for (int i = 1; i < n; i++) {
                if (a[i] == a[i-1]) {
                    cnt++;
                }
            }
            if (cnt >= 2) {
                ans += 2;
            }
            else if (cnt == 1)
                ans += 1;
            printf ("%d\n", ans);
        }
    }
    return 0;
}