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  • hdoj_2553N皇后问题

    N皇后问题

    Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 32768/32768 K (Java/Others)
    Total Submission(s): 4933    Accepted Submission(s): 2252


    Problem Description
    在N*N的方格棋盘放置了N个皇后,使得它们不相互攻击(即任意2个皇后不允许处在同一排,同一列,也不允许处在与棋盘边框成45角的斜线上。
    你的任务是,对于给定的N,求出有多少种合法的放置方法。

     

    Input
    共有若干行,每行一个正整数N≤10,表示棋盘和皇后的数量;如果N=0,表示结束。
     

    Output
    共有若干行,每行一个正整数,表示对应输入行的皇后的不同放置数量。
     

    Sample Input
    1 8 5 0
     

    Sample Output
    1 92 10

    因为是横向放置的,所以只需检查纵向和斜方向是否会攻击即可。

    即C[cur] == C[j] || cur - C[cur] == C[j] - j || cur + C[cur] == C[j] + j

    斜方向也可写成abs(cur-j) == abs(C[cur] - C[j])


    超时代码:

    #include <iostream>
    #include <cstring>
    #include <cstdio>
    using namespace std;
    #define MAX 15
    int n, tot;
    int C[MAX];
    int ans[MAX];
    
    void dfs(int cur)
    {
    	if(cur == n)
    	{
    		tot++;
    	}
    	else
    	{
    		for(int i = 0; i < n; i++)
    		{
    			bool flag = true;
    			C[cur] = i;
    			for(int j = 0; j < cur; j++)
    			{
    				if(C[cur] == C[j] || cur - C[cur] == j - C[j] || cur + C[cur] == j + C[j])
    				{
    					flag = false;
    					break;
    				}
    			}
    			if(flag)
    			{
    				dfs(cur + 1);
    			}
    		}
    	}
    }
    
    int main()
    {
    	while(scanf("%d", &n) != EOF)
    	{
    		if(n == 0)
    		{
    			break;
    		}
    		tot = 0;
    		dfs(0);
    		if(ans[n] != 0)
    		{
    			printf("%d\n", tot);
    		}
    		else
    		{
    			printf("%d\n", tot);
    			ans[n] = tot;
    		}
    	}
    	return 0;
    }

    修改版:

    #include<cstdio>
    #include<cstring>
    int board[12];
    int sum[12]={0};
    bool used[3][20];
    int n, ans;
    void dfs(int cur)
    {
    	int i;
    	if(cur == n)
    	{
    		ans++;
    	}
    	else
    	{
    		for(i = 0; i < n; i++)
    		{
    			if(!used[0][i] && !used[1][cur+i] && !used[2][cur-i+n])
    			{
    				board[cur] = i;
    				used[0][i] = used[1][cur+i] = used[2][cur-i+n] = 1;
    				dfs(cur + 1);
    				used[0][i] = used[1][cur+i] = used[2][cur-i+n] = 0;
    			}
    		}
    	}
    }
    int main()
    {
    	while(scanf("%d",&n) != EOF)
    	{
    		if(n == 0) break;
    		memset(used, 0, sizeof(used));
    		ans = 0;
    		if(sum[n] != 0)
    			printf("%d\n", sum[n]);
    		else
    		{
    			dfs(0);
    			printf("%d\n", ans);
    			sum[n] = ans;
    		}
    	}
    	return 0;
    }

    看别人写的,原来可以这么预处理:

    #include <iostream>
    #include <cstring>
    #include <cstdio>
    using namespace std;
    #define MAX 15
    int n, tot;
    int C[MAX];
    int ans[MAX];
    
    void dfs(int cur)
    {
    	if(cur == n)
    	{
    		tot++;
    	}
    	else
    	{
    		for(int i = 0; i < n; i++)
    		{
    			bool flag = true;
    			C[cur] = i;
    			for(int j = 0; j < cur; j++)
    			{
    				if(C[cur] == C[j] || cur - C[cur] == j - C[j] || cur + C[cur] == j + C[j])
    				{
    					flag = false;
    					break;
    				}
    			}
    			if(flag)
    			{
    				dfs(cur + 1);
    			}
    		}
    	}
    }
    
    int main()
    {
    	for(n = 1; n <= 10; n++)
    	{
    		tot = 0;
    		dfs(0);
    		ans[n] = tot;
    	}
    	while(scanf("%d", &n) != EOF)
    	{
    		if(n == 0)
    		{
    			break;
    		}
    		printf("%d\n", ans[n]);
    	}
    	return 0;
    }


    输出8皇后问题的所有解(92种):

    #include <iostream>
    #include <cstring>
    #include <cstdio>
    using namespace std;
    #define MAX 15
    int n, tot;
    int C[MAX];
    
    void dfs(int cur)
    {
    	if(cur == n)
    	{
    		tot++;
    		printf("No. %d\n", tot);
    		for(int i = 0; i < 8; i++)
    		{
    			for(int j = 0; j < 8; j++)
    			{
    				if(i == C[j])
    				{
    					cout << 1 << " ";
    				}
    				else
    				{
    					cout << 0 << " ";
    				}
    			}
    			cout << endl;
    		}
    	}
    	else
    	{
    		for(int i = 0; i < n; i++)
    		{
    			bool flag = true;
    			C[cur] = i;
    			for(int j = 0; j < cur; j++)
    			{
    				if(C[cur] == C[j] || cur - C[cur] == j - C[j] || cur + C[cur] == j + C[j])
    				{
    					flag = false;
    					break;
    				}
    			}
    			if(flag)
    			{
    				dfs(cur + 1);
    			}
    		}
    	}
    }
    
    int main()
    {
    	tot = 0;
    	n = 8;
    	dfs(0);
    	return 0;
    }
    NO. 1
    1 0 0 0 0 0 0 0 
    0 0 0 0 0 0 1 0 
    0 0 0 0 1 0 0 0 
    0 0 0 0 0 0 0 1 
    0 1 0 0 0 0 0 0 
    0 0 0 1 0 0 0 0 
    0 0 0 0 0 1 0 0 
    0 0 1 0 0 0 0 0 
    NO. 2
    1 0 0 0 0 0 0 0 
    0 0 0 0 0 0 1 0 
    0 0 0 1 0 0 0 0 
    0 0 0 0 0 1 0 0 
    0 0 0 0 0 0 0 1 
    0 1 0 0 0 0 0 0 
    0 0 0 0 1 0 0 0 
    0 0 1 0 0 0 0 0 
    NO. 3
    1 0 0 0 0 0 0 0 
    0 0 0 0 0 1 0 0 
    0 0 0 0 0 0 0 1 
    0 0 1 0 0 0 0 0 
    0 0 0 0 0 0 1 0 
    0 0 0 1 0 0 0 0 
    0 1 0 0 0 0 0 0 
    0 0 0 0 1 0 0 0 
    NO. 4
    1 0 0 0 0 0 0 0 
    0 0 0 0 1 0 0 0 
    0 0 0 0 0 0 0 1 
    0 0 0 0 0 1 0 0 
    0 0 1 0 0 0 0 0 
    0 0 0 0 0 0 1 0 
    0 1 0 0 0 0 0 0 
    0 0 0 1 0 0 0 0 
    NO. 5
    0 0 0 0 0 1 0 0 
    1 0 0 0 0 0 0 0 
    0 0 0 0 1 0 0 0 
    0 1 0 0 0 0 0 0 
    0 0 0 0 0 0 0 1 
    0 0 1 0 0 0 0 0 
    0 0 0 0 0 0 1 0 
    0 0 0 1 0 0 0 0 
    NO. 6
    0 0 0 1 0 0 0 0 
    1 0 0 0 0 0 0 0 
    0 0 0 0 1 0 0 0 
    0 0 0 0 0 0 0 1 
    0 1 0 0 0 0 0 0 
    0 0 0 0 0 0 1 0 
    0 0 1 0 0 0 0 0 
    0 0 0 0 0 1 0 0 
    NO. 7
    0 0 0 0 1 0 0 0 
    1 0 0 0 0 0 0 0 
    0 0 0 0 0 0 0 1 
    0 0 0 1 0 0 0 0 
    0 1 0 0 0 0 0 0 
    0 0 0 0 0 0 1 0 
    0 0 1 0 0 0 0 0 
    0 0 0 0 0 1 0 0 
    NO. 8
    0 0 1 0 0 0 0 0 
    1 0 0 0 0 0 0 0 
    0 0 0 0 0 0 1 0 
    0 0 0 0 1 0 0 0 
    0 0 0 0 0 0 0 1 
    0 1 0 0 0 0 0 0 
    0 0 0 1 0 0 0 0 
    0 0 0 0 0 1 0 0 
    NO. 9
    0 0 0 0 1 0 0 0 
    1 0 0 0 0 0 0 0 
    0 0 0 1 0 0 0 0 
    0 0 0 0 0 1 0 0 
    0 0 0 0 0 0 0 1 
    0 1 0 0 0 0 0 0 
    0 0 0 0 0 0 1 0 
    0 0 1 0 0 0 0 0 
    NO. 10
    0 0 0 0 0 0 1 0 
    1 0 0 0 0 0 0 0 
    0 0 1 0 0 0 0 0 
    0 0 0 0 0 0 0 1 
    0 0 0 0 0 1 0 0 
    0 0 0 1 0 0 0 0 
    0 1 0 0 0 0 0 0 
    0 0 0 0 1 0 0 0 
    NO. 11
    0 0 0 0 1 0 0 0 
    1 0 0 0 0 0 0 0 
    0 0 0 0 0 0 0 1 
    0 0 0 0 0 1 0 0 
    0 0 1 0 0 0 0 0 
    0 0 0 0 0 0 1 0 
    0 1 0 0 0 0 0 0 
    0 0 0 1 0 0 0 0 
    NO. 12
    0 0 0 1 0 0 0 0 
    1 0 0 0 0 0 0 0 
    0 0 0 0 1 0 0 0 
    0 0 0 0 0 0 0 1 
    0 0 0 0 0 1 0 0 
    0 0 1 0 0 0 0 0 
    0 0 0 0 0 0 1 0 
    0 1 0 0 0 0 0 0 
    NO. 13
    0 1 0 0 0 0 0 0 
    0 0 0 0 0 1 0 0 
    1 0 0 0 0 0 0 0 
    0 0 0 0 0 0 1 0 
    0 0 0 1 0 0 0 0 
    0 0 0 0 0 0 0 1 
    0 0 1 0 0 0 0 0 
    0 0 0 0 1 0 0 0 
    NO. 14
    0 0 0 0 1 0 0 0 
    0 0 1 0 0 0 0 0 
    1 0 0 0 0 0 0 0 
    0 0 0 0 0 0 1 0 
    0 1 0 0 0 0 0 0 
    0 0 0 0 0 0 0 1 
    0 0 0 0 0 1 0 0 
    0 0 0 1 0 0 0 0 
    NO. 15
    0 0 0 0 0 0 0 1 
    0 0 1 0 0 0 0 0 
    1 0 0 0 0 0 0 0 
    0 0 0 0 0 1 0 0 
    0 1 0 0 0 0 0 0 
    0 0 0 0 1 0 0 0 
    0 0 0 0 0 0 1 0 
    0 0 0 1 0 0 0 0 
    NO. 16
    0 0 0 1 0 0 0 0 
    0 0 0 0 0 1 0 0 
    1 0 0 0 0 0 0 0 
    0 0 0 0 1 0 0 0 
    0 1 0 0 0 0 0 0 
    0 0 0 0 0 0 0 1 
    0 0 1 0 0 0 0 0 
    0 0 0 0 0 0 1 0 
    NO. 17
    0 0 0 0 1 0 0 0 
    0 0 0 0 0 0 1 0 
    1 0 0 0 0 0 0 0 
    0 0 0 1 0 0 0 0 
    0 1 0 0 0 0 0 0 
    0 0 0 0 0 0 0 1 
    0 0 0 0 0 1 0 0 
    0 0 1 0 0 0 0 0 
    NO. 18
    0 0 0 0 0 1 0 0 
    0 0 1 0 0 0 0 0 
    1 0 0 0 0 0 0 0 
    0 0 0 0 0 0 0 1 
    0 0 0 1 0 0 0 0 
    0 1 0 0 0 0 0 0 
    0 0 0 0 0 0 1 0 
    0 0 0 0 1 0 0 0 
    NO. 19
    0 0 0 0 1 0 0 0 
    0 0 1 0 0 0 0 0 
    1 0 0 0 0 0 0 0 
    0 0 0 0 0 1 0 0 
    0 0 0 0 0 0 0 1 
    0 1 0 0 0 0 0 0 
    0 0 0 1 0 0 0 0 
    0 0 0 0 0 0 1 0 
    NO. 20
    0 0 0 0 0 1 0 0 
    0 0 1 0 0 0 0 0 
    1 0 0 0 0 0 0 0 
    0 0 0 0 0 0 0 1 
    0 0 0 0 1 0 0 0 
    0 1 0 0 0 0 0 0 
    0 0 0 1 0 0 0 0 
    0 0 0 0 0 0 1 0 
    NO. 21
    0 0 0 1 0 0 0 0 
    0 0 0 0 0 0 0 1 
    1 0 0 0 0 0 0 0 
    0 0 1 0 0 0 0 0 
    0 0 0 0 0 1 0 0 
    0 1 0 0 0 0 0 0 
    0 0 0 0 0 0 1 0 
    0 0 0 0 1 0 0 0 
    NO. 22
    0 0 0 0 0 0 0 1 
    0 0 0 1 0 0 0 0 
    1 0 0 0 0 0 0 0 
    0 0 1 0 0 0 0 0 
    0 0 0 0 0 1 0 0 
    0 1 0 0 0 0 0 0 
    0 0 0 0 0 0 1 0 
    0 0 0 0 1 0 0 0 
    NO. 23
    0 0 0 1 0 0 0 0 
    0 0 0 0 0 0 0 1 
    1 0 0 0 0 0 0 0 
    0 0 0 0 1 0 0 0 
    0 0 0 0 0 0 1 0 
    0 1 0 0 0 0 0 0 
    0 0 0 0 0 1 0 0 
    0 0 1 0 0 0 0 0 
    NO. 24
    0 0 0 1 0 0 0 0 
    0 0 0 0 0 0 1 0 
    1 0 0 0 0 0 0 0 
    0 0 0 0 0 0 0 1 
    0 0 0 0 1 0 0 0 
    0 1 0 0 0 0 0 0 
    0 0 0 0 0 1 0 0 
    0 0 1 0 0 0 0 0 
    NO. 25
    0 0 0 0 0 1 0 0 
    0 0 0 1 0 0 0 0 
    1 0 0 0 0 0 0 0 
    0 0 0 0 1 0 0 0 
    0 0 0 0 0 0 0 1 
    0 1 0 0 0 0 0 0 
    0 0 0 0 0 0 1 0 
    0 0 1 0 0 0 0 0 
    NO. 26
    0 0 0 0 0 1 0 0 
    0 0 1 0 0 0 0 0 
    1 0 0 0 0 0 0 0 
    0 0 0 0 0 0 1 0 
    0 0 0 0 1 0 0 0 
    0 0 0 0 0 0 0 1 
    0 1 0 0 0 0 0 0 
    0 0 0 1 0 0 0 0 
    NO. 27
    0 0 0 0 0 0 1 0 
    0 0 1 0 0 0 0 0 
    1 0 0 0 0 0 0 0 
    0 0 0 0 0 1 0 0 
    0 0 0 0 0 0 0 1 
    0 0 0 0 1 0 0 0 
    0 1 0 0 0 0 0 0 
    0 0 0 1 0 0 0 0 
    NO. 28
    0 0 0 0 1 0 0 0 
    0 0 0 0 0 0 1 0 
    1 0 0 0 0 0 0 0 
    0 0 1 0 0 0 0 0 
    0 0 0 0 0 0 0 1 
    0 0 0 0 0 1 0 0 
    0 0 0 1 0 0 0 0 
    0 1 0 0 0 0 0 0 
    NO. 29
    0 1 0 0 0 0 0 0 
    0 0 0 0 1 0 0 0 
    0 0 0 0 0 0 1 0 
    1 0 0 0 0 0 0 0 
    0 0 1 0 0 0 0 0 
    0 0 0 0 0 0 0 1 
    0 0 0 0 0 1 0 0 
    0 0 0 1 0 0 0 0 
    NO. 30
    0 1 0 0 0 0 0 0 
    0 0 0 0 0 0 0 1 
    0 0 0 0 0 1 0 0 
    1 0 0 0 0 0 0 0 
    0 0 1 0 0 0 0 0 
    0 0 0 0 1 0 0 0 
    0 0 0 0 0 0 1 0 
    0 0 0 1 0 0 0 0 
    NO. 31
    0 0 0 0 0 1 0 0 
    0 1 0 0 0 0 0 0 
    0 0 0 0 0 0 1 0 
    1 0 0 0 0 0 0 0 
    0 0 1 0 0 0 0 0 
    0 0 0 0 1 0 0 0 
    0 0 0 0 0 0 0 1 
    0 0 0 1 0 0 0 0 
    NO. 32
    0 0 0 0 0 0 1 0 
    0 1 0 0 0 0 0 0 
    0 0 0 1 0 0 0 0 
    1 0 0 0 0 0 0 0 
    0 0 0 0 0 0 0 1 
    0 0 0 0 1 0 0 0 
    0 0 1 0 0 0 0 0 
    0 0 0 0 0 1 0 0 
    NO. 33
    0 0 0 0 0 0 0 1 
    0 1 0 0 0 0 0 0 
    0 0 0 1 0 0 0 0 
    1 0 0 0 0 0 0 0 
    0 0 0 0 0 0 1 0 
    0 0 0 0 1 0 0 0 
    0 0 1 0 0 0 0 0 
    0 0 0 0 0 1 0 0 
    NO. 34
    0 0 0 0 1 0 0 0 
    0 1 0 0 0 0 0 0 
    0 0 0 0 0 0 0 1 
    1 0 0 0 0 0 0 0 
    0 0 0 1 0 0 0 0 
    0 0 0 0 0 0 1 0 
    0 0 1 0 0 0 0 0 
    0 0 0 0 0 1 0 0 
    NO. 35
    0 0 0 0 0 1 0 0 
    0 1 0 0 0 0 0 0 
    0 0 0 0 0 0 1 0 
    1 0 0 0 0 0 0 0 
    0 0 0 1 0 0 0 0 
    0 0 0 0 0 0 0 1 
    0 0 0 0 1 0 0 0 
    0 0 1 0 0 0 0 0 
    NO. 36
    0 0 0 0 1 0 0 0 
    0 1 0 0 0 0 0 0 
    0 0 0 0 0 1 0 0 
    1 0 0 0 0 0 0 0 
    0 0 0 0 0 0 1 0 
    0 0 0 1 0 0 0 0 
    0 0 0 0 0 0 0 1 
    0 0 1 0 0 0 0 0 
    NO. 37
    0 0 1 0 0 0 0 0 
    0 0 0 0 1 0 0 0 
    0 0 0 0 0 0 1 0 
    1 0 0 0 0 0 0 0 
    0 0 0 1 0 0 0 0 
    0 1 0 0 0 0 0 0 
    0 0 0 0 0 0 0 1 
    0 0 0 0 0 1 0 0 
    NO. 38
    0 0 0 0 0 1 0 0 
    0 0 0 1 0 0 0 0 
    0 0 0 0 0 0 1 0 
    1 0 0 0 0 0 0 0 
    0 0 0 0 0 0 0 1 
    0 1 0 0 0 0 0 0 
    0 0 0 0 1 0 0 0 
    0 0 1 0 0 0 0 0 
    NO. 39
    0 0 0 0 1 0 0 0 
    0 0 0 0 0 0 0 1 
    0 0 0 1 0 0 0 0 
    1 0 0 0 0 0 0 0 
    0 0 0 0 0 0 1 0 
    0 1 0 0 0 0 0 0 
    0 0 0 0 0 1 0 0 
    0 0 1 0 0 0 0 0 
    NO. 40
    0 0 1 0 0 0 0 0 
    0 0 0 0 0 1 0 0 
    0 0 0 0 0 0 0 1 
    1 0 0 0 0 0 0 0 
    0 0 0 0 1 0 0 0 
    0 0 0 0 0 0 1 0 
    0 1 0 0 0 0 0 0 
    0 0 0 1 0 0 0 0 
    NO. 41
    0 0 0 0 0 0 1 0 
    0 0 0 0 1 0 0 0 
    0 0 1 0 0 0 0 0 
    1 0 0 0 0 0 0 0 
    0 0 0 0 0 1 0 0 
    0 0 0 0 0 0 0 1 
    0 1 0 0 0 0 0 0 
    0 0 0 1 0 0 0 0 
    NO. 42
    0 0 0 0 0 1 0 0 
    0 0 0 1 0 0 0 0 
    0 0 0 0 0 0 1 0 
    1 0 0 0 0 0 0 0 
    0 0 1 0 0 0 0 0 
    0 0 0 0 1 0 0 0 
    0 1 0 0 0 0 0 0 
    0 0 0 0 0 0 0 1 
    NO. 43
    0 0 0 0 1 0 0 0 
    0 0 0 0 0 0 0 1 
    0 0 0 1 0 0 0 0 
    1 0 0 0 0 0 0 0 
    0 0 1 0 0 0 0 0 
    0 0 0 0 0 1 0 0 
    0 1 0 0 0 0 0 0 
    0 0 0 0 0 0 1 0 
    NO. 44
    0 0 1 0 0 0 0 0 
    0 0 0 0 0 1 0 0 
    0 0 0 1 0 0 0 0 
    1 0 0 0 0 0 0 0 
    0 0 0 0 0 0 0 1 
    0 0 0 0 1 0 0 0 
    0 0 0 0 0 0 1 0 
    0 1 0 0 0 0 0 0 
    NO. 45
    0 0 1 0 0 0 0 0 
    0 0 0 0 0 1 0 0 
    0 0 0 0 0 0 0 1 
    1 0 0 0 0 0 0 0 
    0 0 0 1 0 0 0 0 
    0 0 0 0 0 0 1 0 
    0 0 0 0 1 0 0 0 
    0 1 0 0 0 0 0 0 
    NO. 46
    0 0 0 0 1 0 0 0 
    0 0 0 0 0 0 1 0 
    0 0 0 1 0 0 0 0 
    1 0 0 0 0 0 0 0 
    0 0 1 0 0 0 0 0 
    0 0 0 0 0 0 0 1 
    0 0 0 0 0 1 0 0 
    0 1 0 0 0 0 0 0 
    NO. 47
    0 1 0 0 0 0 0 0 
    0 0 0 0 0 1 0 0 
    0 0 0 0 0 0 0 1 
    0 0 1 0 0 0 0 0 
    1 0 0 0 0 0 0 0 
    0 0 0 1 0 0 0 0 
    0 0 0 0 0 0 1 0 
    0 0 0 0 1 0 0 0 
    NO. 48
    0 1 0 0 0 0 0 0 
    0 0 0 0 1 0 0 0 
    0 0 0 0 0 0 1 0 
    0 0 0 1 0 0 0 0 
    1 0 0 0 0 0 0 0 
    0 0 0 0 0 0 0 1 
    0 0 0 0 0 1 0 0 
    0 0 1 0 0 0 0 0 
    NO. 49
    0 1 0 0 0 0 0 0 
    0 0 0 0 0 0 1 0 
    0 0 0 0 1 0 0 0 
    0 0 0 0 0 0 0 1 
    1 0 0 0 0 0 0 0 
    0 0 0 1 0 0 0 0 
    0 0 0 0 0 1 0 0 
    0 0 1 0 0 0 0 0 
    NO. 50
    0 0 0 0 0 0 1 0 
    0 1 0 0 0 0 0 0 
    0 0 0 0 0 1 0 0 
    0 0 1 0 0 0 0 0 
    1 0 0 0 0 0 0 0 
    0 0 0 1 0 0 0 0 
    0 0 0 0 0 0 0 1 
    0 0 0 0 1 0 0 0 
    NO. 51
    0 0 0 0 0 0 0 1 
    0 1 0 0 0 0 0 0 
    0 0 0 0 1 0 0 0 
    0 0 1 0 0 0 0 0 
    1 0 0 0 0 0 0 0 
    0 0 0 0 0 0 1 0 
    0 0 0 1 0 0 0 0 
    0 0 0 0 0 1 0 0 
    NO. 52
    0 0 0 1 0 0 0 0 
    0 1 0 0 0 0 0 0 
    0 0 0 0 0 0 0 1 
    0 0 0 0 0 1 0 0 
    1 0 0 0 0 0 0 0 
    0 0 1 0 0 0 0 0 
    0 0 0 0 1 0 0 0 
    0 0 0 0 0 0 1 0 
    NO. 53
    0 0 0 1 0 0 0 0 
    0 1 0 0 0 0 0 0 
    0 0 0 0 0 0 1 0 
    0 0 0 0 1 0 0 0 
    1 0 0 0 0 0 0 0 
    0 0 0 0 0 0 0 1 
    0 0 0 0 0 1 0 0 
    0 0 1 0 0 0 0 0 
    NO. 54
    0 0 1 0 0 0 0 0 
    0 0 0 0 0 1 0 0 
    0 1 0 0 0 0 0 0 
    0 0 0 0 0 0 1 0 
    1 0 0 0 0 0 0 0 
    0 0 0 1 0 0 0 0 
    0 0 0 0 0 0 0 1 
    0 0 0 0 1 0 0 0 
    NO. 55
    0 0 1 0 0 0 0 0 
    0 0 0 0 1 0 0 0 
    0 1 0 0 0 0 0 0 
    0 0 0 0 0 0 0 1 
    1 0 0 0 0 0 0 0 
    0 0 0 0 0 0 1 0 
    0 0 0 1 0 0 0 0 
    0 0 0 0 0 1 0 0 
    NO. 56
    0 0 0 0 0 1 0 0 
    0 0 0 0 0 0 0 1 
    0 1 0 0 0 0 0 0 
    0 0 0 1 0 0 0 0 
    1 0 0 0 0 0 0 0 
    0 0 0 0 0 0 1 0 
    0 0 0 0 1 0 0 0 
    0 0 1 0 0 0 0 0 
    NO. 57
    0 0 1 0 0 0 0 0 
    0 0 0 0 0 0 0 1 
    0 0 0 1 0 0 0 0 
    0 0 0 0 0 0 1 0 
    1 0 0 0 0 0 0 0 
    0 0 0 0 0 1 0 0 
    0 1 0 0 0 0 0 0 
    0 0 0 0 1 0 0 0 
    NO. 58
    0 0 1 0 0 0 0 0 
    0 0 0 0 1 0 0 0 
    0 0 0 0 0 0 0 1 
    0 0 0 1 0 0 0 0 
    1 0 0 0 0 0 0 0 
    0 0 0 0 0 0 1 0 
    0 1 0 0 0 0 0 0 
    0 0 0 0 0 1 0 0 
    NO. 59
    0 0 0 0 0 1 0 0 
    0 0 1 0 0 0 0 0 
    0 0 0 0 0 0 1 0 
    0 0 0 1 0 0 0 0 
    1 0 0 0 0 0 0 0 
    0 0 0 0 0 0 0 1 
    0 1 0 0 0 0 0 0 
    0 0 0 0 1 0 0 0 
    NO. 60
    0 0 0 0 0 1 0 0 
    0 0 1 0 0 0 0 0 
    0 0 0 0 1 0 0 0 
    0 0 0 0 0 0 1 0 
    1 0 0 0 0 0 0 0 
    0 0 0 1 0 0 0 0 
    0 1 0 0 0 0 0 0 
    0 0 0 0 0 0 0 1 
    NO. 61
    0 0 0 0 0 1 0 0 
    0 0 1 0 0 0 0 0 
    0 0 0 0 1 0 0 0 
    0 0 0 0 0 0 0 1 
    1 0 0 0 0 0 0 0 
    0 0 0 1 0 0 0 0 
    0 1 0 0 0 0 0 0 
    0 0 0 0 0 0 1 0 
    NO. 62
    0 0 0 1 0 0 0 0 
    0 0 0 0 0 0 0 1 
    0 0 0 0 1 0 0 0 
    0 0 1 0 0 0 0 0 
    1 0 0 0 0 0 0 0 
    0 0 0 0 0 0 1 0 
    0 1 0 0 0 0 0 0 
    0 0 0 0 0 1 0 0 
    NO. 63
    0 0 0 1 0 0 0 0 
    0 0 0 0 0 0 1 0 
    0 0 0 0 1 0 0 0 
    0 0 1 0 0 0 0 0 
    1 0 0 0 0 0 0 0 
    0 0 0 0 0 1 0 0 
    0 0 0 0 0 0 0 1 
    0 1 0 0 0 0 0 0 
    NO. 64
    0 0 0 1 0 0 0 0 
    0 0 0 0 0 1 0 0 
    0 0 0 0 0 0 0 1 
    0 0 1 0 0 0 0 0 
    1 0 0 0 0 0 0 0 
    0 0 0 0 0 0 1 0 
    0 0 0 0 1 0 0 0 
    0 1 0 0 0 0 0 0 
    NO. 65
    0 1 0 0 0 0 0 0 
    0 0 0 1 0 0 0 0 
    0 0 0 0 0 1 0 0 
    0 0 0 0 0 0 0 1 
    0 0 1 0 0 0 0 0 
    1 0 0 0 0 0 0 0 
    0 0 0 0 0 0 1 0 
    0 0 0 0 1 0 0 0 
    NO. 66
    0 0 0 1 0 0 0 0 
    0 1 0 0 0 0 0 0 
    0 0 0 0 1 0 0 0 
    0 0 0 0 0 0 0 1 
    0 0 0 0 0 1 0 0 
    1 0 0 0 0 0 0 0 
    0 0 1 0 0 0 0 0 
    0 0 0 0 0 0 1 0 
    NO. 67
    0 0 0 1 0 0 0 0 
    0 1 0 0 0 0 0 0 
    0 0 0 0 0 0 0 1 
    0 0 0 0 1 0 0 0 
    0 0 0 0 0 0 1 0 
    1 0 0 0 0 0 0 0 
    0 0 1 0 0 0 0 0 
    0 0 0 0 0 1 0 0 
    NO. 68
    0 0 1 0 0 0 0 0 
    0 0 0 0 0 0 1 0 
    0 1 0 0 0 0 0 0 
    0 0 0 0 0 0 0 1 
    0 0 0 0 1 0 0 0 
    1 0 0 0 0 0 0 0 
    0 0 0 1 0 0 0 0 
    0 0 0 0 0 1 0 0 
    NO. 69
    0 0 1 0 0 0 0 0 
    0 0 0 0 0 1 0 0 
    0 1 0 0 0 0 0 0 
    0 0 0 0 1 0 0 0 
    0 0 0 0 0 0 0 1 
    1 0 0 0 0 0 0 0 
    0 0 0 0 0 0 1 0 
    0 0 0 1 0 0 0 0 
    NO. 70
    0 0 1 0 0 0 0 0 
    0 0 0 0 0 1 0 0 
    0 1 0 0 0 0 0 0 
    0 0 0 0 0 0 1 0 
    0 0 0 0 1 0 0 0 
    1 0 0 0 0 0 0 0 
    0 0 0 0 0 0 0 1 
    0 0 0 1 0 0 0 0 
    NO. 71
    0 0 0 0 1 0 0 0 
    0 0 0 0 0 0 1 0 
    0 1 0 0 0 0 0 0 
    0 0 0 0 0 1 0 0 
    0 0 1 0 0 0 0 0 
    1 0 0 0 0 0 0 0 
    0 0 0 1 0 0 0 0 
    0 0 0 0 0 0 0 1 
    NO. 72
    0 0 0 0 1 0 0 0 
    0 0 0 0 0 0 1 0 
    0 1 0 0 0 0 0 0 
    0 0 0 0 0 1 0 0 
    0 0 1 0 0 0 0 0 
    1 0 0 0 0 0 0 0 
    0 0 0 0 0 0 0 1 
    0 0 0 1 0 0 0 0 
    NO. 73
    0 0 0 0 0 0 1 0 
    0 0 0 1 0 0 0 0 
    0 1 0 0 0 0 0 0 
    0 0 0 0 1 0 0 0 
    0 0 0 0 0 0 0 1 
    1 0 0 0 0 0 0 0 
    0 0 1 0 0 0 0 0 
    0 0 0 0 0 1 0 0 
    NO. 74
    0 0 0 0 0 0 1 0 
    0 0 0 1 0 0 0 0 
    0 1 0 0 0 0 0 0 
    0 0 0 0 0 0 0 1 
    0 0 0 0 0 1 0 0 
    1 0 0 0 0 0 0 0 
    0 0 1 0 0 0 0 0 
    0 0 0 0 1 0 0 0 
    NO. 75
    0 0 0 0 1 0 0 0 
    0 0 0 0 0 0 1 0 
    0 1 0 0 0 0 0 0 
    0 0 0 1 0 0 0 0 
    0 0 0 0 0 0 0 1 
    1 0 0 0 0 0 0 0 
    0 0 1 0 0 0 0 0 
    0 0 0 0 0 1 0 0 
    NO. 76
    0 0 1 0 0 0 0 0 
    0 0 0 0 0 1 0 0 
    0 0 0 0 0 0 0 1 
    0 1 0 0 0 0 0 0 
    0 0 0 1 0 0 0 0 
    1 0 0 0 0 0 0 0 
    0 0 0 0 0 0 1 0 
    0 0 0 0 1 0 0 0 
    NO. 77
    0 0 0 0 0 0 1 0 
    0 0 1 0 0 0 0 0 
    0 0 0 0 0 0 0 1 
    0 1 0 0 0 0 0 0 
    0 0 0 0 1 0 0 0 
    1 0 0 0 0 0 0 0 
    0 0 0 0 0 1 0 0 
    0 0 0 1 0 0 0 0 
    NO. 78
    0 0 0 1 0 0 0 0 
    0 0 0 0 0 0 1 0 
    0 0 0 0 1 0 0 0 
    0 1 0 0 0 0 0 0 
    0 0 0 0 0 1 0 0 
    1 0 0 0 0 0 0 0 
    0 0 1 0 0 0 0 0 
    0 0 0 0 0 0 0 1 
    NO. 79
    0 0 0 1 0 0 0 0 
    0 0 0 0 0 1 0 0 
    0 0 0 0 0 0 0 1 
    0 1 0 0 0 0 0 0 
    0 0 0 0 0 0 1 0 
    1 0 0 0 0 0 0 0 
    0 0 1 0 0 0 0 0 
    0 0 0 0 1 0 0 0 
    NO. 80
    0 0 0 0 1 0 0 0 
    0 0 1 0 0 0 0 0 
    0 0 0 0 0 0 0 1 
    0 0 0 1 0 0 0 0 
    0 0 0 0 0 0 1 0 
    1 0 0 0 0 0 0 0 
    0 0 0 0 0 1 0 0 
    0 1 0 0 0 0 0 0 
    NO. 81
    0 1 0 0 0 0 0 0 
    0 0 0 0 0 0 1 0 
    0 0 1 0 0 0 0 0 
    0 0 0 0 0 1 0 0 
    0 0 0 0 0 0 0 1 
    0 0 0 0 1 0 0 0 
    1 0 0 0 0 0 0 0 
    0 0 0 1 0 0 0 0 
    NO. 82
    0 0 0 1 0 0 0 0 
    0 1 0 0 0 0 0 0 
    0 0 0 0 0 0 1 0 
    0 0 1 0 0 0 0 0 
    0 0 0 0 0 1 0 0 
    0 0 0 0 0 0 0 1 
    1 0 0 0 0 0 0 0 
    0 0 0 0 1 0 0 0 
    NO. 83
    0 0 0 0 1 0 0 0 
    0 1 0 0 0 0 0 0 
    0 0 0 1 0 0 0 0 
    0 0 0 0 0 1 0 0 
    0 0 0 0 0 0 0 1 
    0 0 1 0 0 0 0 0 
    1 0 0 0 0 0 0 0 
    0 0 0 0 0 0 1 0 
    NO. 84
    0 0 1 0 0 0 0 0 
    0 0 0 0 0 0 1 0 
    0 1 0 0 0 0 0 0 
    0 0 0 0 0 0 0 1 
    0 0 0 0 0 1 0 0 
    0 0 0 1 0 0 0 0 
    1 0 0 0 0 0 0 0 
    0 0 0 0 1 0 0 0 
    NO. 85
    0 0 0 0 0 1 0 0 
    0 0 0 1 0 0 0 0 
    0 1 0 0 0 0 0 0 
    0 0 0 0 0 0 0 1 
    0 0 0 0 1 0 0 0 
    0 0 0 0 0 0 1 0 
    1 0 0 0 0 0 0 0 
    0 0 1 0 0 0 0 0 
    NO. 86
    0 0 0 0 0 1 0 0 
    0 0 1 0 0 0 0 0 
    0 0 0 0 0 0 1 0 
    0 1 0 0 0 0 0 0 
    0 0 0 1 0 0 0 0 
    0 0 0 0 0 0 0 1 
    1 0 0 0 0 0 0 0 
    0 0 0 0 1 0 0 0 
    NO. 87
    0 0 0 0 0 1 0 0 
    0 0 1 0 0 0 0 0 
    0 0 0 0 0 0 1 0 
    0 1 0 0 0 0 0 0 
    0 0 0 0 0 0 0 1 
    0 0 0 0 1 0 0 0 
    1 0 0 0 0 0 0 0 
    0 0 0 1 0 0 0 0 
    NO. 88
    0 0 0 1 0 0 0 0 
    0 0 0 0 0 0 1 0 
    0 0 1 0 0 0 0 0 
    0 0 0 0 0 0 0 1 
    0 1 0 0 0 0 0 0 
    0 0 0 0 1 0 0 0 
    1 0 0 0 0 0 0 0 
    0 0 0 0 0 1 0 0 
    NO. 89
    0 0 0 1 0 0 0 0 
    0 1 0 0 0 0 0 0 
    0 0 0 0 0 0 1 0 
    0 0 1 0 0 0 0 0 
    0 0 0 0 0 1 0 0 
    0 0 0 0 0 0 0 1 
    0 0 0 0 1 0 0 0 
    1 0 0 0 0 0 0 0 
    NO. 90
    0 0 0 0 1 0 0 0 
    0 1 0 0 0 0 0 0 
    0 0 0 1 0 0 0 0 
    0 0 0 0 0 0 1 0 
    0 0 1 0 0 0 0 0 
    0 0 0 0 0 0 0 1 
    0 0 0 0 0 1 0 0 
    1 0 0 0 0 0 0 0 
    NO. 91
    0 0 1 0 0 0 0 0 
    0 0 0 0 1 0 0 0 
    0 1 0 0 0 0 0 0 
    0 0 0 0 0 0 0 1 
    0 0 0 0 0 1 0 0 
    0 0 0 1 0 0 0 0 
    0 0 0 0 0 0 1 0 
    1 0 0 0 0 0 0 0 
    NO. 92
    0 0 1 0 0 0 0 0 
    0 0 0 0 0 1 0 0 
    0 0 0 1 0 0 0 0 
    0 1 0 0 0 0 0 0 
    0 0 0 0 0 0 0 1 
    0 0 0 0 1 0 0 0 
    0 0 0 0 0 0 1 0 
    1 0 0 0 0 0 0 0 
    




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