Vacations

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

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, ..., a_n (0 ≤ a_i ≤ 3) separated by space, where:

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

Output

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.

Examples

Input

4
1 3 2 0

Output

2

Input

7
1 3 3 2 1 2 3

Output

0

Input

2
2 2

Output

1

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.

   write   sports   rest
0    N        N	     Y
1    Y	      N      Y
2    N        Y      Y
3    Y        Y      Y
#include<iostream>
#include<cstring>//memset
using namespace std;
int n,dp[105][4];//dp[i][j]第i天選擇j（休息 寫 運動）的情況下 最少休息幾天 
int main()
{
	int x;
	//cout<<(0x3f)<<endl;
	cin>>n;//有多少天 
	memset(dp,0x3f,sizeof(dp));
	//如果n = 100 ai全部都是1的話應該會休息和寫交替進行 最少休息天數會達到50 dp[i][2]會一直沒有變化 
	//所以要保證取較小的時候 不發生錯誤 那麼初始化應該大於50 
	dp[0][0] = 0;
	for(int i=1;i<=n;i++){
		cin>>x;
		dp[i][0] = min(dp[i-1][0],min(dp[i-1][1],dp[i-1][2]))+1;//今天選擇休息 那麼需要從前一天中選擇最小的 然後+1 
		if(x==1 || x==3){//都是可以進行寫 
			dp[i][1] = min(dp[i-1][0],dp[i-1][2]);//今天選擇寫 不用+1 但是前一天不能是寫 所以從前一天是休息和運動的裏面選擇較少的 
		}
		if(x==2 || x==3){
			dp[i][2] = min(dp[i-1][0],dp[i-1][1]);//同理今天選擇跑步 前一天不能是跑步 
		}
	}
	printf("%d\n",min(dp[n][0],min(dp[n][1],dp[n][2])));
	return 0;
}