# 2042. Eating Together

The cows are so very silly about their dinner partners. They have organized themselves into three groups (conveniently numbered 1, 2, and 3) that insist upon dining together. The trouble starts when they line up at the barn to enter the feeding area.

Each cow i carries with her a small card upon which is engraved D_i (1 <= D_i <= 3) indicating her dining group membership. The entire set of N (1 <= N <= 30,000) cows has lined up for dinner but it’s easy for anyone to see that they are not grouped by their dinner-partner cards.

FJ’s job is not so difficult. He just walks down the line of cows changing their dinner partner assignment by marking out the old number and writing in a new one. By doing so, he creates groups of cows like 111222333 or 333222111 where the cows’ dining groups are

sorted in either ascending or descending order by their dinner cards.

FJ is just as lazy as the next fellow. He’s curious: what is the absolute mminimum number of cards he must change to create a proper grouping of dining partners? He must only change card numbers and must not rearrange the cows standing in line.

### 输入格式

• Line 1: A single integer: N

• Lines 2..N+1: Line i describes the i-th cow’s current dining group with a single integer: D_i

### 输出格式

5

1

3

2

1

1

INPUT DETAILS:

Five cows in line: first cow and last two cows prefer dining group 1; second cow likes group 3; third cow likes group 2.

### 样例

Input
* Line 1: A single integer representing the minimum number of changes that must be made so that the final sequence of cows is sorted in either ascending or descending order

Output
1
OUTPUT DETAILS:
We would need at least two changes to turn this into an increasing sequence (changing both non-1's to a 1).
However, changing the first "1" to a "3" yields a decreasing sequence with just one change, which is optimal.


24 人解决，34 人已尝试。

25 份提交通过，共有 68 份提交。

4.8 EMB 奖励。