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<iostream>
#include<string>
#include<iomanip>
#include<set>
#include<vector>
#include<map>
#include<queue>
#include<algorithm>
using namespace std;
#define int long long
#define rep(i,n) for(int i = 0; i < n; i++)
#define INF (long long)(1e18)
#define MOD (int)(1e9+7)
#define min(a,b) (a>b?b:a)
#define max(a,b) (a>b?a:b)
#define yn(f) (f?"Yes":"No")
#define YN(f) (f?"YES":"NO")
#define pro "はいプロ　世界一○○が上手　○○界のtourist　○○時代の終焉を告げる者　実質○○　○○するために生まれてきた男"
#define Answer_to_the_Ultimate_Question_of_Life_the_Universe_and_Everything 42
#define MAX 110


int dxy[] = {1, -1, 0, 0};
int N, a, b, ans[MAX][MAX] = {};
set<int> R[MAX];

bool is_out_of_range(int z){
	return z <= 0 || N < z ;
}

void hoge(int y, int x){//cout<<y<<" "<<x<<"++++++++"<<endl;
	map<int,int> tm;
	vector<int> tv;
	int re = 0, ma = 0, count = 0;
	if(y == 1 && x == 1) return;
	for(int i = 0; i < 4; i++){
		int ny = y + dxy[i], nx = x + dxy[3-i];
		if(is_out_of_range(ny)||is_out_of_range(nx)) continue;
		count++;//cout<<"z --- "<<count<<" "<<ans[ny][nx]<<endl;
		if(ans[ny][nx] == 0)continue;
		for(int z : R[ans[ny][nx]]){
			tm[z]++;
			tv.push_back(z);
		}
	}
	tv.erase(unique(tv.begin(),tv.end()),tv.end());
	for(int z : tv){//cout<<z<<"  re"<<endl;
		if(tm[z] > ma && count == R[z].size()){
			ma = tm[z];
			re = z;
		}
	}
	ans[y][x] = re;//cout<<y<<" "<<x<<" "<<re<<" "<<count<<endl;
	// string hugehuge; cin>>hugehuge;
	for(int i = 0; i < 4; i++){
		int ny = y + dxy[i], nx = x + dxy[3-i];
		if(is_out_of_range(ny)||is_out_of_range(nx)) continue;
		if(ans[ny][nx] == 0)continue;
		R[ans[ny][nx]].erase(re);
		R[re].erase(ans[ny][nx]);
	}
}

int huga(){
	queue<pair<int,int>> Q;
	
	Q.push(make_pair(1,1));
	
	
	while(!Q.empty()){
		pair<int,int> P = Q.front();Q.pop();
		int y = P.first, x = P.second;// cout<<y<<" "<<x<<endl;
		for(int i = 0; i < 4; i++){
			int ny = y + dxy[i], nx = x + dxy[3-i];
			if(is_out_of_range(ny)||is_out_of_range(nx)) continue;
			if(ans[ny][nx]) continue;
			Q.push(make_pair(ny,nx));
			hoge(ny,nx);
		}
	}
}

signed main(){

	
	cin>>N;
	
	for(int i = 1; i <= 2*N*N-2*N; i++){
		cin>>a>>b;
		R[a].insert(b);
		R[b].insert(a);
		if(R[a].size() == 2) ans[1][1] = a;
		if(R[b].size() == 2) ans[1][1] = b;
	}
	
	huga();
	
	for(int i = 1; i <= N; i++){
		for(int j = 1; j <= N; j++){
			if(j!=1)cout<<" ";
			cout<<ans[i][j];
		}cout<<endl;
	}
	
	
	return 0;
}

C++: #include "iostream"
#include "climits"
#include "list"
#include "queue"
#include "stack"
#include "set"
#include "functional"
#include "algorithm"
#include "string"
#include "map"
#include "unordered_map"
#include "unordered_set"
#include "iomanip"
#include "cmath"
#include "random"
#include "bitset"
#include "cstdio"
#include "numeric"
#include "cassert"
#include "ctime"

using namespace std;

constexpr long long int MOD = 1000000007;
//constexpr int MOD = 1000000007;
//constexpr int MOD = 998244353;
//constexpr long long int MOD = 998244353;
constexpr double EPS = 1e-12;

//int N, M, K, T, H, W, L, R;
long long int N, M, K, T, H, W, L, R;

int main() {
	ios::sync_with_stdio(false);
	cin.tie(0);

	cin >> N;
	vector<vector<int>>edge(N*N + 1);
	for (int i = 0; i < 2 * N*N - 2 * N; i++) {
		cin >> L >> R;
		edge[L].push_back(R);
		edge[R].push_back(L);
	}
	vector<int>used(N*N + 1);
	vector<vector<int>>ans(N, vector<int>(N));
	for (int i = 1; i <= N*N; i++) {
		if (edge[i].size() == 2) {
			ans[0][0] = i;
			used[i] = 1;
			break;
		}
	}
	for (int i = 0; i + 1 < N; i++) {
		int nx = -1;
		for (auto j : edge[ans[0][i]]) {
			if (used[j])continue;
			if (nx == -1)nx = j;
			if (edge[nx].size() > edge[j].size())nx = j;
		}
		ans[0][i + 1] = nx;
		used[nx] = 1;
	}
	for (int i = 0; i < N - 1; i++) {
		for (int j = 0; j < N; j++) {
			for (auto k : edge[ans[i][j]]) {
				if (used[k])continue;
				used[k] = 1;
				ans[i + 1][j] = k;
				break;
			}
		}
	}
	for (auto i : ans) {
		for (int j = 0; j < N; j++) {
			if (j)cout << " ";
			cout << i[j];
		}
		cout << endl;
	}
}