Vacations
Contest: Codeforces Round 363 (Div. 1)
Difficulty rating: 1400
Tags: dp

Vasya has n days of vacations! So he decided to improve his IT skills and do sport. Vasya knows the following information about each of this n days: whether that gym opened and whether a contest was carried out in the Internet on that day. For the i-th day there are four options:

1. on this day the gym is closed and the contest is not carried out;
2. on this day the gym is closed and the contest is carried out;
3. on this day the gym is open and the contest is not carried out;
4. on this day the gym is open and the contest is carried out.

On each of days Vasya can either have a rest or write the contest (if it is carried out on this day), or do sport (if the gym is open on this day).

Find the minimum number of days on which Vasya will have a rest (it means, he will not do sport and write the contest at the same time). The only limitation that Vasya has — he does not want to do the same activity on two consecutive days: it means, he will not do sport on two consecutive days, and write the contest on two consecutive days.

Input format:
The first line contains a positive integer n (1 ≤ n ≤ 100) — the number of days of Vasya's vacations.

The second line contains the sequence of integers a1, a2, ..., an (0 ≤ ai ≤ 3) separated by space, where:

- ai equals 0, if on the i-th day of vacations the gym is closed and the contest is not carried out;
- ai equals 1, if on the i-th day of vacations the gym is closed, but the contest is carried out;
- ai equals 2, if on the i-th day of vacations the gym is open and the contest is not carried out;
- ai equals 3, if on the i-th day of vacations the gym is open and the contest is carried out.

Output format:
Print the minimum possible number of days on which Vasya will have a rest. Remember that Vasya refuses:

- to do sport on any two consecutive days,
- to write the contest on any two consecutive days.

Constraints:
Time limit: 1.0 s
Memory limit: 256.0 MB

Note:
In the first test Vasya can write the contest on the day number 1 and do sport on the day number 3. Thus, he will have a rest for only 2 days.

In the second test Vasya should write contests on days number 1, 3, 5 and 7, in other days do sport. Thus, he will not have a rest for a single day.

In the third test Vasya can do sport either on a day number 1 or number 2. He can not do sport in two days, because it will be contrary to the his limitation. Thus, he will have a rest for only one day.

Example input:
4
1 3 2 0

Example output:
2

Example input:
7
1 3 3 2 1 2 3

Example output:
0

Editorial:
This problem can be solved with dynamic programming. Let's solve the opposite problem and find the maximum number of days which Vasya will not have a rest. We need o use two-dimensional array d, where d[i][j] equals to the maximum number of days, which Vasya will not have a rest, if i days passed and j equals to:
• 0, if Vasya had a rest during the i-th day,
• 1, if Vasya participated in the contest on the i-th day,
• 2, if Vasya went to gym on the i-th day.
Then the transitions for the day number i look like:
• d[i][0] must be updated with maximum value of the array d for the previous day;
• if there will be a contest on the i-th day (i. e. ai equals to 1 or 3), than we update d[i][1] with values d[i - 1][0] + 1 and d[i - 1][2] + 1;
• if the gym is open on the i-th day (i. e. ai equals to 2 or 3), than we update d[i][2] with values d[i - 1][0] + 1 and d[i - 1][1] + 1.
After that we need to choose max from all values of the array d for the last day and print n - max.