Go: package main

import (
	"bufio"
	"fmt"
	"os"
	"strconv"
	"strings"
)

func main() {
	io := NewIo()
	defer io.Flush()
	N := io.NextInt()
	nodes := make([]Node, N*N+1)
	for i := 0; i < 2*N*N-2*N; i++ {
		a, b := io.NextInt(), io.NextInt()
		nodes[a].adj = append(nodes[a].adj, b)
		nodes[b].adj = append(nodes[b].adj, a)
	}
	ninja(nodes, N, io)
}

type Node struct {
	adj []int
}

func ninja(nodes []Node, N int, io *Io) {
	used := make([]bool, N*N+1)
	m := make([][]int, N)
	fst := 0
	for i := 0; i < N; i++ {
		m[i] = make([]int, N)
		for j := 0; j < N; j++ {
			if len(nodes[i*N+j].adj) == 2 {
				fst = i*N + j
			}
		}
	}
	m[0][0] = fst
	used[fst] = true
	for j := 1; j < N; j++ {
		u := 0
		deg := 3
		if j == N-1 {
			deg = 2
		}
		for _, v := range nodes[m[0][j-1]].adj {
			if !used[v] && len(nodes[v].adj) == deg {
				u = v
			}
		}
		m[0][j] = u
		used[u] = true
	}
	for i := 1; i < N; i++ {
		for j := 0; j < N; j++ {
			u := 0
			for _, v := range nodes[m[i-1][j]].adj {
				if !used[v] {
					u = v
				}
			}
			m[i][j] = u
			used[u] = true
		}
	}
	for _, a := range m {
		io.PrintIntSlice(a)
	}
}

// I/O template
type Io struct {
	reader    *bufio.Reader
	writer    *bufio.Writer
	tokens    []string
	nextToken int
}

func NewIo() *Io {
	return &Io{
		reader: bufio.NewReader(os.Stdin),
		writer: bufio.NewWriter(os.Stdout),
	}
}

func (io *Io) Flush() {
	err := io.writer.Flush()
	if err != nil {
		panic(err)
	}
}

func (io *Io) NextLine() string {
	var buff []byte
	for {
		line, isPrefix, err := io.reader.ReadLine()
		if err != nil {
			panic(err)
		}
		buff = append(buff, line...)
		if !isPrefix {
			break
		}
	}
	return string(buff)
}

func (io *Io) Next() string {
	for io.nextToken >= len(io.tokens) {
		line := io.NextLine()
		io.tokens = strings.Fields(line)
		io.nextToken = 0
	}
	s := io.tokens[io.nextToken]
	io.nextToken++
	return s
}

func (io *Io) NextInt() int {
	i, err := strconv.Atoi(io.Next())
	if err != nil {
		panic(err)
	}
	return i
}

func (io *Io) NextFloat() float64 {
	i, err := strconv.ParseFloat(io.Next(), 64)
	if err != nil {
		panic(err)
	}
	return i
}

func (io *Io) Println(a ...interface{}) {
	fmt.Fprintln(io.writer, a...)
}

func (io *Io) Printf(format string, a ...interface{}) {
	fmt.Fprintf(io.writer, format, a...)
}

func (io *Io) PrintIntSlice(a []int) {
	b := []interface{}{}
	for _, x := range a {
		b = append(b, x)
	}
	io.Println(b...)
}

func (io *Io) PrintStringSlice(a []string) {
	b := []interface{}{}
	for _, x := range a {
		b = append(b, x)
	}
	io.Println(b...)
}

func Log(name string, value interface{}) {
	fmt.Fprintf(os.Stderr, "%s=%+v\n", name, value)
}

func ExampleIo() {
	io := NewIo()
	defer io.Flush()
	a := make([]int, 0, 3)
	a[0], a[1], a[2] = io.NextInt(), io.NextInt(), io.NextInt()
	io.Println(a)
	io.PrintIntSlice(a)
	Log("io", a)
}

C++: #include<bits/stdc++.h>
using namespace std;

int main(){

    int n; cin >> n;
    vector<vector<int> > g(n * n);
    for(int i = 0; i < 2 * n * (n - 1); i++){
        int a, b; cin >> a >> b;
        a--;
        b--;
        g[a].push_back(b);
        g[b].push_back(a);
    }

    map<pair<int, int>, int> M;
    vector<int> kado;
    for(int i = 0; i < n * n; i++) if(g[i].size() == 2) kado.push_back(i);
    vector<vector<int> > info(n * n, vector<int> (2));

    int s = kado[0];
    queue<pair<int, int> > que;
    vector<bool> used(n * n, false);
    que.push({s, 0});
    used[s] = true;
    
    while(!que.empty()){

        int node = que.front().first;
        int dis = que.front().second;
        info[node][0] = dis;
        que.pop();
        //cout << node << " " << dis << endl;
        for(int i = 0; i < (int)g[node].size(); i++){
            
            int next_node = g[node][i];
            int next_dis = dis + 1;
            if(!used[next_node]){
                used[next_node] = true;
                que.push({next_node, next_dis});
            }
        }
    }

    s = kado[1];
    if(info[s][0] > n) s = kado[2];
    queue<pair<int, int> > que2;
    vector<bool> used2(n * n, false);
    que2.push({s, 0});
    used2[s] = true;
    
    while(!que2.empty()){

        int node = que2.front().first;
        int dis = que2.front().second;
        info[node][1] = dis;
        que2.pop();

        for(int i = 0; i < (int)g[node].size(); i++){
            
            int next_node = g[node][i];
            int next_dis = dis + 1;
            if(!used2[next_node]){
                used2[next_node] = true;
                que2.push({next_node, next_dis});
            }
        }
    }


    for(int i = 0; i < n * n; i++){
        M[{info[i][0], info[i][1]}] = i;
    }


    /*for(int i = 0; i < n * n; i++){
        cout << i << ": " << info[i][0] << " " << info[i][1] << endl;
    }*/



    for(int i = 0; i < n; i++){
        for(int j = 0; j < n; j++){
            int param_0 = i + j;
            int param_1 = n - i - 1 + j;
            cout << M[{param_0, param_1}] + 1 << " ";
        }
        cout << endl;
    }

    return 0;
}

C++: #include <bits/stdc++.h>
using namespace std;

int main() {
    int n; cin >> n;
    vector<vector<int>> g(n * n);
    for(int i = 0; i < 2 * n * n - 2 * n; ++i) {
        int a, b; cin >> a >> b;
        g[a - 1].push_back(b - 1);
        g[b - 1].push_back(a - 1);
    }

    vector<bool> used(n * n);
    vector<vector<int>> ans(n, vector<int>(n, -1));
    for(int i = 0; i < n * n; ++i) { // r1
        if(g[i].size() == 2u) {
            int cur = i;
            ans[0][0] = cur;
            used[cur] = true;
            for(int j = 0; j < n - 1; ++j) {
                int nxt = -1;
                for(auto to : g[cur]) {
                    if(used[to] || (nxt != -1 && g[nxt].size() < g[to].size())) continue;
                    nxt = to;
                }
                cur = ans[0][j + 1] = nxt;
                used[nxt] = true;
            }
            break;
        }
    }
    for(int i = 0; i < n - 1; ++i) {
        for(int j = 0; j < n; ++j) {
            for(auto to : g[ans[i][j]]) {
                if(used[to]) continue;
                ans[i + 1][j] = to;
                used[to] = true;
            }
        }
    }

    for(int i = 0; i < n; ++i) {
        for(int j = 0; j < n; ++j) {
            cout << ans[i][j] + 1 << " \n"[j + 1 == n];
        }
    }
}