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< int > deg(n * n);
    vector< vector< int > > to(n * n);
    for (int i = 0; i < 2 * n * n - 2 * n; ++i) {
        int a, b;
        cin >> a >> b;

        a--;
        b--;

        deg[a]++;
        deg[b]++;

        to[a].emplace_back(b);
        to[b].emplace_back(a);
    }

    int v;
    vector< vector< int > > ans(n, vector< int >(n, -1));
    vector< bool > used(n * n);

    int st;
    for (int i = 0; i < n * n; ++i) {
        if (deg[i] != 2) continue;
        st = i;
    }

    vector< int > dx({1, 0, -1, 0});
    vector< int > dy({0, 1, 0, -1});
    for (auto u: to[st]) {
        if (used[u]) continue;
        v = u;
    }

    used[st] = true;
    ans[0][0] = st;

    int pre = st;
    int x = 1, y = 0;
    int idx = 0;
    
    while (v != st) {
        ans[x][y] = v;
        used[v] = true;

        int next;
        for (auto u: to[v]) {
            if (u == pre) continue;
            if (deg[u] == 4) continue;
            next = u;
        }

        if (deg[v] == 2) idx++;
        pre = v;
        v = next;
        x += dx[idx];
        y += dy[idx];
    }

    for (int i = 0; i < n - 1; ++i) {
        for (int j = 1; j < n - 1; ++j) {
            int v = ans[i][j];
            for (auto u: to[v]) {
                if (used[u]) continue;
                ans[i + 1][j] = u;
                used[u] = true;
            }
        }
    }

    for (auto a: ans) {
        for (int i = 0; i < n; ++i) {
            cout << a[i] + 1 << (i + 1 == n ? '\n' : ' ');
        }
    }
}

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


int dxy[4] = {-1, 1, 0, 0};
int dd[] = {0,1};
int N, a, b, ans[MAX][MAX] = {};
vector<int> R[MAX*MAX];
//ものすごくアホだった(2回目)

template<typename T>
void remove(vector<T>& vector, unsigned int index)
{
    vector.erase(vector.begin() + index);
}

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

inline void hoge(int y, int x){
	 //cout<<y<<" "<<x<<endl; 
	// sleep(2);
	//string hogehoge;
	//cin>>hogehoge;
	if(y == 1){
		for(int z : R[ans[y][x-1]]){
			// cout<<z<<" -----"<<endl;
			if(R[z].size() == 4)continue;
			ans[y][x] = z;
		}
	} else {
		for(int z : R[ans[y-1][x]]){
			// cout<<z<<" -----"<<endl;
			ans[y][x] = z;
		}
	}
	// cout<<ans[y][x]<<" ans "<<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] == 0)continue;
		for(int i = 0; i < R[ans[ny][nx]].size(); i++){
			if(R[ans[ny][nx]][i] == ans[y][x]) remove(R[ans[ny][nx]],i);
		}
		for(int i = 0; i < R[ans[y][x]].size(); i++){
			if(R[ans[y][x]][i] == ans[ny][nx]) remove(R[ans[y][x]],i);
		}
		
		// R[ans[ny][nx]].erase(ans[y][x]);
		// R[ans[y][x]].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();//string hogehoge; cin>>hogehoge;
		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].push_back(b);
		R[b].push_back(a);
		
		// if(a==950) cout<<"a "<<b<<endl;
		// if(b==950) cout<<"b "<<a<<endl;
	}
	for(int i = 1; i <= 2*N*N-2*N; i++){
		if(R[i].size() == 2) ans[1][1] = i;
	}
	
	// cout<<ans[1][1]<<" "<<R[ans[1][1]].size()<<endl;
	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;
}