Problem: problem

There are the following games.

N characters are lined up in a vertical row. The color of these characters is red, blue, or yellow, and in the initial state, four or more characters of the same color are not lined up in a row. The player can select a character at a certain position and change it to another color. By this operation, if four or more characters of the same color are lined up in a row, those characters will disappear. When four or more characters of the same color are lined up in a row due to the disappearance of the characters, those characters also disappear, and this chain continues until there are no more places where four or more characters of the same color are lined up in a row. .. The purpose of this game is to reduce the number of characters remaining without disappearing.

For example, if the color of the sixth character from the top is changed from yellow to blue in the state at the left end of the figure below, five blue characters will disappear in a row, and finally three characters will remain without disappearing.

<image>


Given the color sequence of N characters in the initial state, create a program that finds the minimum value M of the number of characters that remain without disappearing when the color of the character is changed in only one place.



input

The input consists of multiple datasets. Each dataset is given in the following format.

The first line consists of only the number of characters N (1 ≤ N ≤ 10000). The following N lines contain one of 1, 2, and 3 integers, and the i + 1st line (1 ≤ i ≤ N) represents the color of the i-th character from the top in the initial state (1). Is red, 2 is blue, and 3 is yellow).

When N is 0, it indicates the end of input. The number of datasets does not exceed 5.

output

For each dataset, output the minimum value M of the number of characters remaining without disappearing on one line.

Examples

Input

12
3
2
1
1
2
3
2
2
2
1
1
3
12
3
2
1
1
2
3
2
1
3
2
1
3
0


Output

3
12


Input

None


Output

None

Solution (in CPP):

Solution:
#include<cstdio>
#include<vector>
using namespace std;
int num;//キャラクタの最大数
vector<int> vec;//キャラクタの格納
int ans;//出力する答え
//
int Input();//入力
void Show();//現在のキャラクタの表示
int Delete();//同じキャラクタが4つ連なったら消滅させる。消滅できなかったら0を返す
int Combo();//コンボさせる。戻り値は残ったキャラクタ数
int Calc();//最高の手順を探す
//
int main(void)
{
	while(Input()){
		printf("%d\n",Calc());
	}
		fflush(stdin);
		getchar();
	return 0;
}
//
int Input()
{
	vec.clear();
	int ibuf;
	scanf("%d",&num);
	if(num!=0){
		for(int f1=0;f1<num;f1++){
			scanf("%d",&ibuf);
			vec.push_back(ibuf);
		}
	}
	else return 0;
	return 1;
}
//
void Show()
{
	printf("Show~\n");
	for(int f1=0;f1<(int)vec.size();f1++){
		printf("%d\n",vec[f1]);
	}
	printf("~Show\n");
}
//
int Delete()
{
	int mem;
	int ret=0;
	for(int f1=0;f1<(int)vec.size()-3;f1++){
		if(vec[f1]==vec[f1+1]&&vec[f1]==vec[f1+2]&&vec[f1]==vec[f1+3]){
			ret=1;
			mem=vec[f1];
			for(int f2=f1;f2<(int)vec.size();f2++){
				if(mem==vec[f2]){
					vec.erase(vec.begin()+f2);
					f2--;
				}
				else{
					break;
				}
			}
		}
	}
	return ret;
}
//
int Combo()
{
	vector<int> mem;
	int ret;
	mem=vec;
	while(Delete());
	ret=vec.size();
	vec=mem;
	return ret;
}
//
int Calc()
{
	vector<int> mem=vec;
	int ret=10001;
	//
	for(int f1=1;f1<(int)vec.size()-1;f1++){
		vec=mem;
		if(vec[f1]!=vec[f1-1]){
			for(int f2=1;f2<=3;f2++){
				vec[f1]=f2;
				int m=Combo();
				ret>m?ret=m:0;
			}
		}
	}
	vec=mem;
	//
	return ret;
}