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;
#define all(x) (x).begin(),(x).end()
const int mod=1000000007,MAX=10005,INF=1<<29;
vector<int> G[MAX];
int cnt[MAX],used[MAX];

int main(){
    
    std::ifstream in("text.txt");
    std::cin.rdbuf(in.rdbuf());
    cin.tie(0);
    ios::sync_with_stdio(false);
    
    int N;cin>>N;
    
    for(int i=0;i<2*N*N-2*N;i++){
        int a,b;cin>>a>>b;
        cnt[a]++;
        cnt[b]++;
        G[a].push_back(b);
        G[b].push_back(a);
    }
    
    vector<vector<int>> ans(N,vector<int>(N));
    
    for(int i=1;i<=N*N;i++){
        if(cnt[i]==2){
            ans[0][0]=i;
            used[i]=1;
            break;
        }
    }
    
    for(int i=0;i<N;i++){
        for(int j=0;j+1<N;j++){
            for(int a:G[ans[i][j]]){
                if(used[a]==1) continue;
                if(i==0&&cnt[a]==4) continue;
                bool ok=false;
                
                if(i) for(int b:G[a]) if(b==ans[i-1][j+1]) ok=true;
                if(i&&!ok) continue;
                ans[i][j+1]=a;
                used[a]=1;
                break;
            }
        }
        if(i+1<N){
            for(int a:G[ans[i][0]]){
                if(used[a]==1) continue;
                ans[i+1][0]=a;
                used[a]=1;
            }
        }
    }
    
    for(int i=0;i<N;i++){
        for(int j=0;j<N;j++){
            if(j) cout<<" ";
            cout<<ans[i][j];
        }
        cout<<endl;
    }
}

C++: #include <bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef unsigned long long ull;
typedef pair<ll, ll> P;
typedef pair<ll, P> P3;
typedef pair<P ,P> PP;
constexpr ll MOD = ll(1e9) + 7;
constexpr int IINF = INT_MAX;
constexpr ll LLINF = LLONG_MAX;
constexpr int MAX_N = int(1e5) + 5;
constexpr double EPS = 1e-9;
constexpr int di[] = {0, 1, 0, -1}, dj[] = {1, 0, -1, 0};

int n, ans[100][100], dir = 0;
vector<vector<int> > g;
bool used[10000];

int main() {
    cin >> n;
    g.resize(n*n);
    for(int i=0;i<2*(n*n-n);i++){
        int a, b;
        cin >> a >> b;
        a--; b--;
        g[a].push_back(b);
        g[b].push_back(a);
    }
    
    int s = -1;
    for(int i=0;i<n*n;i++){
        if(g[i].size()==2){
            s = i;
            break;
        }
    }
    for(int i=0;i<n;i++){
        ans[0][i] = s;
        used[s] = true;
        for(auto v : g[s]){
            if(used[v]) continue;
            if(g[v].size()<=3){
                s = v;
                break;
            }
        }
    }
    for(int i=1;i<n;i++){
        for(int j=0;j<n;j++){
            for(auto v : g[ans[i-1][j]]){
                if(used[v]) continue;
                ans[i][j] = v;
                used[v] = true;
            }
        }
    }

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

C++: #include <iostream>
#include <set>
#include <vector>
#include <string>
#include <algorithm>
#include <utility>
#define llint long long
#define inf 1000000000

using namespace std;
typedef pair<llint, llint> P;

llint n;
vector<llint> G[10005];
bool used[10005];
llint ans[105][105];

int main(void)
{
  cin >> n;
  llint u, v;
  for(int i = 1; i <= 2*n*n-2*n; i++){
    cin >> u >> v;
    G[u].push_back(v);
    G[v].push_back(u);
  }
  for(int i = 1; i <= n*n; i++){
    if(G[i].size() == 2){
      v = i;
      break;
    }
  }

  ans[1][1] = v, used[v] = true;
  for(int i = 2; i <= n; i++){
    for(int j = 0; j < G[v].size(); j++){
      u = G[v][j];
      if(used[u]) continue;
      if(G[u].size() > 3) continue;
      v = u;
      ans[1][i] = v;
      used[v] = true;
      break;
    }
  }
  for(int i = 2; i <= n; i++){
    for(int j = 1; j <= n; j++){
      int v = ans[i-1][j];
      for(int k = 0; k < G[v].size(); k++){
        int u = G[v][k];
        if(used[u]) continue;
        ans[i][j] = u;
        used[u] = true;
        break;
      }
    }
  }

  for(int i = 1; i <= n; i++){
    for(int j = 1; j <= n; j++){
      cout << ans[i][j];
      if(j < n) cout << ' ';
      else cout << endl;
    }
  }

  return 0;
}