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 MAX 110

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

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

inline void hoge(int y, int x){
	int temp[MAX] = {};
	set<int> tv;
	int ma = 0, re = 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]]){
			temp[z]++;
			tv.insert(z);
		}
	}

	for(int z : tv){
		if(temp[z] > ma && count == R[z].size()){
			ma = temp[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; //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[i]>>b[i];
		tt.push_back(a[i]);
		tt.push_back(b[i]);
	}
	
	sort(tt.begin(),tt.end());
	
	tt.erase(unique(tt.begin(),tt.end()),tt.end());
	
	int i = 1;
	for(int z : tt){//cout<<i<<" "<<z<<endl;
		X[i] = z;
		T[z] = i++;
	}
	
	for(int i = 1; i <= 2*N*N-2*N; i++){
		R[T[a[i]]].insert(T[b[i]]);
		R[T[b[i]]].insert(T[a[i]]);
		if(R[T[a[i]]].size() == 2) ans[1][1] = T[a[i]];
		if(R[T[b[i]]].size() == 2) ans[1][1] = T[b[i]];
	}
	
	
	huga();
	
	for(int i = 1; i <= N; i++){
		for(int j = 1; j <= N; j++){
			if(j!=1)cout<<" ";
			cout<<X[ans[i][j]];
		}cout<<endl;
	}
	
	
	return 0;
}

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

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

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

    int start = -1;
    for (int i = 0; i < n * n; i++) {
        if (adj[i].size() == 2) {
            start = i;
            break;
        }
    }
    assert(start != -1);

    vector<vector<int>> ans(n, vector<int>(n));
    vector<bool> used(n * n);
    used[start] = true;
    ans[0][0] = start;
    int dx[] = {-1, 0};
    int dy[] = {0, -1};
    for (int i = 0; i < n; i++) {
        for (int j = 0; j < n; j++) {
            if (i == 0 && j == 0) continue;
            vector<int> need;
            for (int k = 0; k < 2; k++) {
                int x = i + dx[k], y = j + dy[k];
                if (0 <= x && x < n && 0 <= y && y < n) {
                    need.push_back(ans[x][y]);
                }
            }
            int deg = 4;
            if (i == 0 || i == n - 1 || j == 0 || j == n - 1) deg = 3;
            if ((i == 0 || i == n - 1) && (j == 0 || j == n - 1)) deg = 2;
            bool found = false;
            for (int k = 0; k < n * n; k++) {
                if (used[k]) continue;
                if (adj[k].size() != deg) continue;
                bool dame = false;
                for (int a : need) {
                    if (find(adj[k].begin(), adj[k].end(), a) == adj[k].end()) {
                        dame = true;
                        break;
                    }
                }
                if (dame) continue;
                ans[i][j] = k;
                used[k] = true;
                found = true;
                break;
            }
            assert(found);
        }
    }

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