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;
typedef long long ll;
typedef pair<int,int> pii;
bool used[10005];
vector<int> G[10005];
int indeg[10005];
int N;
int board[105][105];
void firstdfs(int s,int now)
{
    used[s]=true;
    board[0][now-1]=s;
    if(now==N) return;
    for(int i=0;i<int(G[s].size());i++)
    {
        int to=G[s][i];
        if(now<N-1 && !used[to] && indeg[to]==3)
        {
            firstdfs(to,now+1);
            return;
        }
        else if(now==N-1 && !used[to] && indeg[to]==2)
        {
            firstdfs(to,now+1);
            return;
        }
    }
}

int main(void)
{
    cin >> N;
    memset(used,false,sizeof(used));
    memset(board,0,sizeof(board));
    memset(indeg,0,sizeof(indeg));
    for(int i=0;i<2*N*N-2*N;i++)
    {
        int a,b;
        cin >> a >> b;
        a--,b--;
        G[a].push_back(b);
        G[b].push_back(a);
        indeg[a]++;
        indeg[b]++;
    }
    int start;
    for(int i=0;i<N*N;i++) 
    {
        if(indeg[i]==2) 
        {
            start=i;
            break;
        }
    }
    board[0][0]=start;
    used[start]=true;
    firstdfs(start,1);
    for(int y=0;y<N-1;y++)
    {
        for(int x=0;x<N;x++)
        {
            int now=board[y][x];
            if(y!=N-2)
            {          
                for(int i=0;i<int(G[now].size());i++)
                {
                    int to=G[now][i];
                    if(x==0 || x==N-1)
                    {
                        if(!used[to] && indeg[to]==3)
                        {
                            board[y+1][x]=to;
                            used[to]=true;
                            break;
                        }
                    }
                    else
                    {
                        if(!used[to] && indeg[to]==4)
                        {
                            board[y+1][x]=to;
                            used[to]=true;
                            break;
                        }
                    }
                }
            }
            else
            {
                for(int i=0;i<int(G[now].size());i++)
                {
                    int to=G[now][i];
                    if(x==0 || x==N-1)
                    {
                        if(!used[to] && indeg[to]==2)
                        {
                            board[y+1][x]=to;
                            used[to]=true;
                            break;
                        }
                    }
                    else
                    {
                        if(!used[to] && indeg[to]==3)
                        {
                            board[y+1][x]=to;
                            used[to]=true;
                            break;
                        }
                    }
                }
            }
            
        }
    }
    for(int y=0;y<N;y++)
    {
        for(int x=0;x<N;x++)
        {
            if(x!=N-1) cout << board[y][x]+1 << ' ';
            else cout << board[y][x]+1 << endl;
        }
    }
return 0;   

}

C++: #include<iostream>
#include<string>
#include<iomanip>
#include<set>
#include<vector>
#include<map>
#include<queue>
#include<algorithm>
using namespace std;
#define int short
#define MAX 110


int dxy[4] = {-1, 1, 0, 0};
int dd[] = {0,1};
int N, a, b, ans[MAX][MAX] = {};
set<int> R[MAX*MAX];

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

inline void hoge(int y, int x){
	int tm[MAX*MAX] = {};
	set<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++;
		if(ans[ny][nx] == 0)continue;
		for(int z : R[ans[ny][nx]]){
			tm[z]++;
			tv.insert(z);
		}
	}
	for(int z : tv){
		if(tm[z] >= ma && count == R[z].size()){
			ma = tm[z];
			re = z;
		}
	}
	ans[y][x] = re;
	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;
		for(int i = 0; i < 2; i++){
			int ny = y + dd[i], nx = x + dd[1-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;
}