#include <bits/stdc++.h>

using namespace std;
vector<vector<int>> solutions; 

string serialize(const vector<int>& path) {
    string s;
    for (int x : path) s += char(x + '0');
    return s;
}

// 将字符串反序列化回 vector<int>
vector<int> deserialize(const string& s) {
    vector<int> path;
    for (char c : s) path.push_back(c - '0');
    return path;
}

// 生成旋转 90°（顺时针）棋盘序列
vector<int> rotate90(const vector<int>& path, int n) {
    vector<int> newPath(n);
    for (int i = 0; i < n; i++) {
        newPath[path[i]] = n - 1 - i;
    }
    return newPath;
}

// 镜像（水平翻转）
vector<int> mirrorH(const vector<int>& path, int n) {
    vector<int> newPath(n);
    for (int i = 0; i < n; i++) newPath[i] = n - 1 - path[i];
    return newPath;
}

// 生成最小的对称表示
string canonical(const vector<int>& path, int n) {
    vector<string> forms;
    vector<int> cur = path;

    // 4 次旋转 + 镜像旋转
    for (int k = 0; k < 4; k++) {
        forms.push_back(serialize(cur));
        forms.push_back(serialize(mirrorH(cur, n)));
        cur = rotate90(cur, n);
    }

    return *min_element(forms.begin(), forms.end());
}

bool isValid(const vector<int>& path, int row, int col) {
    for (int i = 0; i < row; i++) {
        int prevCol = path[i];
        if (prevCol == col) return false; // 同列冲突
        if (abs(row - i) == abs(col - prevCol)) return false; // 对角线冲突
    }
    return true;
}

//path[i] = j; (i, j)，定行动列 
void dfs(int _n, vector<int>& _path, int _i){	
	if(_i == _n){
		solutions.push_back(_path);
		return;
	}
	for(int j = 0; j < _n; j++){
			//检测 插入
			if(isValid(_path, _i, j)){
				_path[_i] = j;
				//调整引用path 
				dfs(_n, _path, _i + 1);
				//恢复引用path 
				_path[_i] = -1;
			}
	} 
} 

int main(){
	//考虑先放置每个皇后位i，后面通过移动行/列来确定
	//每个皇后的标志是列(i)，生成的数列是从1 - N行插入了哪列的皇后 
	int n;
	cin >> n;
	//vector<vector<int>> mat(n, vector<int>(n, 0));
	vector<int> path(n, -1);
	dfs(n, path, 0); 
	for(auto x : solutions){
		for(auto y : x){
			cout << y << " ";
		}
		cout << endl;
	}
	cout << endl;
	
	set<string> uniqueSolutions;
    for (auto& sol : solutions) {
        uniqueSolutions.insert(canonical(sol, n));
    }

    cout << "本质不同解数量: " << uniqueSolutions.size() << endl;

    // 输出去重后的解
    for (auto& s : uniqueSolutions) {
        vector<int> path = deserialize(s);
        for (int x : path) cout << x << " ";
        cout << endl;
    }
	return 0;
}
/*
8
0 4 7 5 2 6 1 3
0 5 7 2 6 3 1 4
0 6 3 5 7 1 4 2
0 6 4 7 1 3 5 2
1 3 5 7 2 0 6 4
1 4 6 0 2 7 5 3
1 4 6 3 0 7 5 2
1 5 0 6 3 7 2 4
1 5 7 2 0 3 6 4
1 6 2 5 7 4 0 3
1 6 4 7 0 3 5 2
1 7 5 0 2 4 6 3
2 0 6 4 7 1 3 5
2 4 1 7 0 6 3 5
2 4 1 7 5 3 6 0
2 4 6 0 3 1 7 5
2 4 7 3 0 6 1 5
2 5 1 4 7 0 6 3
2 5 1 6 0 3 7 4
2 5 1 6 4 0 7 3
2 5 3 0 7 4 6 1
2 5 3 1 7 4 6 0
2 5 7 0 3 6 4 1
2 5 7 0 4 6 1 3
2 5 7 1 3 0 6 4
2 6 1 7 4 0 3 5
2 6 1 7 5 3 0 4
2 7 3 6 0 5 1 4
3 0 4 7 1 6 2 5
3 0 4 7 5 2 6 1
3 1 4 7 5 0 2 6
3 1 6 2 5 7 0 4
3 1 6 2 5 7 4 0
3 1 6 4 0 7 5 2
3 1 7 4 6 0 2 5
3 1 7 5 0 2 4 6
3 5 0 4 1 7 2 6
3 5 7 1 6 0 2 4
3 5 7 2 0 6 4 1
3 6 0 7 4 1 5 2
3 6 2 7 1 4 0 5
3 6 4 1 5 0 2 7
3 6 4 2 0 5 7 1
3 7 0 2 5 1 6 4
3 7 0 4 6 1 5 2
3 7 4 2 0 6 1 5
4 0 3 5 7 1 6 2
4 0 7 3 1 6 2 5
4 0 7 5 2 6 1 3
4 1 3 5 7 2 0 6
4 1 3 6 2 7 5 0
4 1 5 0 6 3 7 2
4 1 7 0 3 6 2 5
4 2 0 5 7 1 3 6
4 2 0 6 1 7 5 3
4 2 7 3 6 0 5 1
4 6 0 2 7 5 3 1
4 6 0 3 1 7 5 2
4 6 1 3 7 0 2 5
4 6 1 5 2 0 3 7
4 6 1 5 2 0 7 3
4 6 3 0 2 7 5 1
4 7 3 0 2 5 1 6
4 7 3 0 6 1 5 2
5 0 4 1 7 2 6 3
5 1 6 0 2 4 7 3
5 1 6 0 3 7 4 2
5 2 0 6 4 7 1 3
5 2 0 7 3 1 6 4
5 2 0 7 4 1 3 6
5 2 4 6 0 3 1 7
5 2 4 7 0 3 1 6
5 2 6 1 3 7 0 4
5 2 6 1 7 4 0 3
5 2 6 3 0 7 1 4
5 3 0 4 7 1 6 2
5 3 1 7 4 6 0 2
5 3 6 0 2 4 1 7
5 3 6 0 7 1 4 2
5 7 1 3 0 6 4 2
6 0 2 7 5 3 1 4
6 1 3 0 7 4 2 5
6 1 5 2 0 3 7 4
6 2 0 5 7 4 1 3
6 2 7 1 4 0 5 3
6 3 1 4 7 0 2 5
6 3 1 7 5 0 2 4
6 4 2 0 5 7 1 3
7 1 3 0 6 4 2 5
7 1 4 2 0 6 3 5
7 2 0 5 1 4 6 3
7 3 0 2 5 1 6 4

本质不同解数量: 12
0 4 7 5 2 6 1 3
0 5 7 2 6 3 1 4
1 3 5 7 2 0 6 4
1 4 6 0 2 7 5 3
1 4 6 3 0 7 5 2
1 5 0 6 3 7 2 4
1 5 7 2 0 3 6 4
1 6 2 5 7 4 0 3
1 6 4 7 0 3 5 2
2 4 1 7 0 6 3 5
2 4 7 3 0 6 1 5
2 5 1 4 7 0 6 3
*/