class point24 
 {
 	int []number=new int [4];							//存放輸入的四個數
 	char []four={'+','-','*','/'};						//存放四種操作符號
 	int [][]allnum=new int[24][4];						//存放四個數的24種排列形式
 	char [][]out=new char[500][11];						//存放所用找到的符合條件的表達式
 	int []type=new int[500];							//指明out數組中表達式是五種形式中的哪一種
 	public  boolean []outmark=new boolean [500];				//標記out數組中的表達式是否輸出
 	char [][]tempout=new char[500][11];					//存放所得表達式的后序形式
 	int index=0;
 	public int howlong=0;										//out數組的游標
 	char []houzhui=new char[11];
 	boolean []already=new boolean[24];
 	public void update(int a[])
 	{
 		number[0]=a[0];
		number[1]=a[1];
		number[2]=a[2];
		number[3]=a[3];
 	}						//存放一個后綴表達式
	public point24()
	{	
		number[0]=1;
		number[1]=1;
		number[2]=1;
		number[3]=1;
	}		//構造函數
	public void quanpailie()
	{		
		allnum[0]=new int[]{number[0],number[1],number[2],number[3]};
		allnum[1]=new int[]{number[0],number[1],number[3],number[2]};
		allnum[2]=new int[]{number[0],number[2],number[1],number[3]};
		allnum[3]=new int[]{number[0],number[2],number[3],number[1]};
		allnum[4]=new int[]{number[0],number[3],number[2],number[1]};
		allnum[5]=new int[]{number[0],number[3],number[1],number[2]};
		
		allnum[6]=new int[]{number[1],number[0],number[2],number[3]};		
		allnum[7]=new int[]{number[1],number[0],number[3],number[2]};
		allnum[8]=new int[]{number[1],number[2],number[0],number[3]};
		allnum[9]=new int[]{number[1],number[2],number[3],number[0]};
		allnum[10]=new int[]{number[1],number[3],number[2],number[0]};
		allnum[11]=new int[]{number[1],number[3],number[0],number[2]};
		
		allnum[12]=new int[]{number[2],number[0],number[1],number[3]};		
		allnum[13]=new int[]{number[2],number[0],number[3],number[1]};
		allnum[14]=new int[]{number[2],number[1],number[0],number[3]};
		allnum[15]=new int[]{number[2],number[1],number[3],number[0]};
		allnum[16]=new int[]{number[2],number[3],number[0],number[1]};
		allnum[17]=new int[]{number[2],number[3],number[1],number[0]};
		
		allnum[18]=new int[]{number[3],number[0],number[2],number[1]};		
		allnum[19]=new int[]{number[3],number[0],number[1],number[2]};
		allnum[20]=new int[]{number[3],number[1],number[2],number[0]};
		allnum[21]=new int[]{number[3],number[1],number[0],number[2]};
		allnum[22]=new int[]{number[3],number[2],number[0],number[1]};
		allnum[23]=new int[]{number[3],number[2],number[1],number[0]};	
		
		for(int i=0;i<24;i++)
			for(int j=0;j<i;j++)
				if(allnum[i][0]==allnum[j][0] && allnum[i][1]==allnum[j][1]&&
				   allnum[i][2]==allnum[j][2]&&allnum[i][3]==allnum[j][3])
					already[i]=true;
	}							//得到全排列
	public int first(char a)
	{
		if(a=='*'||a=='/')
		return 3;
		else if(a=='+'||a=='-')
		return 1;
		else
		{
		System.out.println("this is wrong!");
		return -1;
		}
	}							//設定操作符的優先級
	public void makesmall(int lenth)
	{
	for(int count =0;count<lenth;count++)
	{
		for(int i=0;i<11;i++)
			if(out[count][i]=='('||out[count][i]==')')
				for(int j=i;j<10;j++)
					out[count][j]=out[count][j+1];
		for(int i=0;i<11;i++)
			if(out[count][i]=='('||out[count][i]==')')
				for(int j=i;j<10;j++)
					out[count][j]=out[count][j+1];
		out[count][7]='\0';out[count][8]='\0';
		out[count][9]='\0';out[count][10]='\0';	
	}	
	//	System.out.println(temp);
	}					//表達式去括號
	public boolean isop(char c)
	{
		if(c=='+'||c=='-'||c=='*'||c=='/')
		return true;
		else
		return false;
	}						//判斷是否為操作符
	public void insertleft(int a,int count)
	{
		int temp=0;
		if(a==0)
		{
			for(int i=9;i>=0;i--)
				out[count][i+1]=out[count][i];
			out[count][0]='(';
		}
		else
		{
			temp=0;
			while(!isop(out[count][temp])||a>1)
			{
				if(isop(out[count][temp]))
					a--;
				temp++;
			}
			for(int j=8;j>=temp;j--)
				out[count][j+2]=out[count][j+1];
			out[count][temp+1]='(';
		}
	}			//在當前位置添加'(’			
	public void insertright(int b,int count)
	{
		int temp=0;
		if(b==4)
		{
			temp=0;
			while(out[count][temp]!='\0')
				temp++;
			out[count][temp]=')';			
		}
		else
		{
			temp=0;
			while(!isop(out[count][temp])||b>1)
			{
				if(isop(out[count][temp]))
					b--;
				temp++;
			}
			for(int j=9;j>=temp;j--)
				out[count][j+1]=out[count][j];
			out[count][temp]=')';
		}
	}			//在當前位置添加'）’
	public void addthis(int index,int count)
	{
		switch(type[count])
		{
			case 1:							//((a+b)+c)+d
				if(index==1)
					{insertleft(0,count);insertright(2,count);}
				else
					{insertleft(0,count);insertright(3,count);}
				break;			
			case 2:							//(a+(b+c))+d
				if(index==1)
					{insertleft(1,count);insertright(3,count);}
				else
					{insertleft(0,count);insertright(3,count);}
				break;
			case 3:							//(a+b)+(c+d)
				if(index==1)
					{insertleft(0,count);insertright(2,count);}				
				else
					{insertleft(2,count);insertright(4,count);}
				break;
			case 4:							//a+((b+c)+d)
				if(index==1)
					{insertleft(1,count);insertright(3,count);}							
				else
					{insertleft(1,count);insertright(4,count);}	
				break;
			default:						//a+(b+(c+d))
				if(index==1)
					{insertleft(2,count);insertright(4,count);}
				else
					{insertleft(1,count);insertright(4,count);}
		}
	}			//指出括號添加的位置	
	public void makegood(int lenth)
	{
		char []tempop=new char[3];
		int count=0;
		while(count<lenth)
		{
			int tempopindex=0;
			int tempoutindex=0;
			while(tempoutindex<11)
			{
				if(isop(tempout[count][tempoutindex]))
				{
					tempop[tempopindex]=tempout[count][tempoutindex];
					tempopindex++;
				}
				tempoutindex++;
			}
			tempopindex=0;
			switch(type[count])
			{
				case 1:						//((a+b)+c)+d		
					if(first(tempop[0])<first(tempop[1]))
						addthis(1,count);
					if(first(tempop[1])<first(tempop[2]))
					{
						addthis(2,count);
					}
					break;
				case 2:						//(a+(b+c))+d
					if(first(tempop[0])<first(tempop[1])||first(tempop[0])==first(tempop[1])&&(tempop[1]=='-'||tempop[1]=='/'))
						addthis(1,count);
					if(first(tempop[1])<first(tempop[2]))
						addthis(2,count);
					break;
				case 3:						//(a+b)+(c+d)
					if(first(tempop[0])<first(tempop[2]))
						addthis(1,count);
					if(first(tempop[1])<first(tempop[2])||first(tempop[1])==first(tempop[2])&&(tempop[2]=='-'||tempop[2]=='/'))
						addthis(2,count);
					break;
				case 4:						//a+((b+c)+d)
					if(first(tempop[0])<first(tempop[1]))
						addthis(1,count);
					if(first(tempop[1])<first(tempop[2])||first(tempop[1])==first(tempop[2])&&(tempop[2]=='-'||tempop[2]=='/'))
						addthis(2,count);
					break;
				case 5:						//a+(b+(c+d))
					if(first(tempop[0])<first(tempop[1])||first(tempop[0])==first(tempop[1])&&(tempop[1]=='-'||tempop[1]=='/'))
						addthis(1,count);
					if(first(tempop[1])<first(tempop[2])||first(tempop[1])==first(tempop[2])&&(tempop[2]=='-'||tempop[2]=='/'))
						addthis(2,count);
					break;
			}
			count++;
		}
	}					//為沒有括號的表達式添加括號，使表達式正確
	public int length(char [] c)
	{
		int result=0;
		for(int i=0;i<11&&c[i]!='\0';i++)
			result++;
		return result;
	}						//獲得數組長度
	public boolean partsame(char []one,char[] two)
	{
		int len=length(one);
		if(len!=length(two))
			return false;
		if(len==1)
			if(one[0]==two[0])
				return true;
			else return false;
		else if(len==3)
		{
			if(one[2]!=two[2])
				return false;
			if(one[2]=='+'||one[2]=='*')
			{
				if(one[0]==two[0]&&one[1]==two[1]||one[0]==two[1]&&one[1]==two[0])
					return true;
				else return false;
			}
			else if(one[2]=='-'||one[2]=='/')
				if(one[0]==two[0]&&one[1]==two[1])
					return true;
				else return false;
			else
				{
					System.out.println("A op should be here!3333333333"+one[0]+one[1]+one[2]);
					return false;
				}
		}
		else if(len==5)
		{
			if(one[4]!=two[4])
				return false;
			if(one[4]=='+'||one[4]=='*')
			{
				if(isop(one[3])&&isop(two[3]))
				{
					if(one[0]!=two[0])
						return false;
					else
					{
						char[] list1 = {one[1],one[2],one[3],'\0'};
						char[] list2 = {two[1],two[2],two[3],'\0'};
						
						return(partsame(list1,list2));
					}
				}
				else if(!isop(one[3])&&!isop(two[3]))
				{

					if(one[3]!=two[3])
						return false;
					else
					{
						char[] list1 = {one[0],one[1],one[2],'\0'};
						char[] list2 = {two[0],two[1],two[2],'\0'};
						
						return(partsame(list1,list2));
					}
				}
				else if(!isop(one[3])&&isop(two[3]))
				{
					if(one[3]!=two[0])
						return false;
					else
					{
						char[] list1 = {one[0],one[1],one[2],'\0'};
						char[] list2 = {two[1],two[2],two[3],'\0'};
						
						return(partsame(list1,list2));
					}
				}
				else
				{
					if(one[0]!=two[3])
						return false;
					else
					{
						char[] list1 = {one[1],one[2],one[3],'\0'};
						char[] list2 = {two[0],two[1],two[2],'\0'};
						
						return(partsame(list1,list2));
					}
				}
			}
			else if(one[4]=='-'||one[4]=='/')
			{
				if(isop(one[3])&&isop(two[3]))
				{
					if(one[0]!=two[0])
						return false;
					else
					{
						char[] list1 = {one[1],one[2],one[3],'\0'};
						char[] list2 = {two[1],two[2],two[3],'\0'};
						
						return(partsame(list1,list2));
					}
				}
				else if(!isop(one[3])&&!isop(two[3]))
				{

					if(one[3]!=two[3])
						return false;
					else
					{
						char[] list1 = {one[0],one[1],one[2],'\0'};
						char[] list2 = {two[0],two[1],two[2],'\0'};
						
						return(partsame(list1,list2));
					}
				}
				else return false;
			}
			else
			{
				System.out.println("A op should be here!5555555555");
				return false;
			}
		}
		else
		{
			System.out.println("this is not correct len!");
			return false;
		}
	}//比較兩個子串是否相等
	public boolean isone(int count)
	{
		char first,second;
		int i=0;
		while(!isop(tempout[count][i]))
			i++;
		first=tempout[count][i++];
		while(!isop(tempout[count][i]))
			i++;
		second=tempout[count][i];
		if(first==second&&first==tempout[count][6]&&(first=='+'||first=='*'))
		return true;
		else
			return false;
	}
	public int istwo(int count)
	{
		char first,second;
		int i=0;
		while(!isop(tempout[count][i]))
			i++;
		first=tempout[count][i++];
		while(!isop(tempout[count][i]))
			i++;
		second=tempout[count][i];
		
		
		if((first==second||second==tempout[count][6])&&type[count]!=3&&(second=='+'||second=='*'))
		{
			if(first==second)
				return 3;
			else
				return 2;
		}
		if((first==tempout[count][6]||second==tempout[count][6])&&type[count]==3&&(tempout[count][6]=='+'||tempout[count][6]=='*'))
		{
			return 2;
		}
		return 0;
	}

	public boolean issame(int a,int b)
	{
		boolean result=true;
		char []one=new char[6];
		char []two=new char[6];
		int lenone=length(out[a]);
		int lentwo=length(out[b]);
		if(lenone!=lentwo)
			return false;
		for(int i=0;i<11;i++)
		{
			if(out[a][i]!=out[b][i])
			{result = false;break;}
				
		}
		if(result)
			return true;
		if(isone(a)&&isone(b))
		{
			return true;
		}
		if(istwo(a)!=0&&istwo(b)!=0&&tempout[a][6]==tempout[b][6])
		{
			if(istwo(a)!=istwo(b))
				return false;
			if(istwo(a)==3)
			{
				char ma,mb;
				if(isop(tempout[a][5]))
					ma=tempout[a][0];
				else ma=tempout[a][5];
				if(isop(tempout[b][5]))
					mb=tempout[b][0];
				else mb=tempout[b][5];
				if(ma==mb)
					return true;
				else return false;
			}
			else
			{
				char a1,a2,b1,b2;
				if(type[a]!=3)
				{
					if(isop(tempout[a][5]))
					{
						a1=tempout[a][0];
						if(isop(tempout[a][4]))
							a2=tempout[a][1];
						else a2=tempout[a][4];
					}
					else 
					{
						a1=tempout[a][5];
						if(isop(tempout[a][3]))
							a2=tempout[a][0];
						else a2=tempout[a][3];
					}
				}
				else
				{
					if(tempout[a][2]==tempout[a][6])
					{
						a1=tempout[a][0];
						a2=tempout[a][1];
					}
					else
					{
						a1=tempout[a][3];
						a2=tempout[a][4];
					}