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 short
#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];


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;
	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;
		}
	}
	
	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();
		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(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 <algorithm>
#include <cassert>
#include <cmath>
#include <cstdio>
#include <deque>
#include <iomanip>
#include <iostream>
#include <map>
#include <queue>
#include <set>
#include <stack>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>
using std::cerr;
using std::cin;
using std::cout;
using std::endl;



int main(void) {
  cout << std::fixed << std::setprecision(10);
  cin.tie(0);
  std::ios::sync_with_stdio(false);

  int n;
  cin>>n;
  std::unordered_set<int> node[10001];
  for(int i=0;i<2*n*n-2*n;i++){
    int a,b;
    cin>>a>>b;
    node[a].insert(b);
    node[b].insert(a);
  }

  int result[101][101]={};


  for(int i=1;i<=n*n;i++){
    if(node[i].size() == 2){
      result[1][1]=i;
      int down=*(node[i].begin()),right=*(++node[i].begin());
      result[2][1]=down;
      result[1][2]=right;
      for(auto x:node[down]){
        for(auto y:node[right]){
          if(x==y&&x!=result[1][1]){
            result[2][2]=x;
          }
        }
      }
      break;
    }
  }

  for(int layer=3;layer<=n;layer++){
    //下側を詰める
    for(auto x:node[result[layer-1][1]]){
      if(x!=result[layer-2][1]&&x!=result[layer-1][2]){
        result[layer][1]=x;
        break;
      }
    }
    for(int c=2;c<=layer-1;c++){
      int left=result[layer][c-1],up=result[layer-1][c];
      for(auto x:node[left]){
        for(auto y:node[up]){
          if(x==y&&result[layer-1][c-1]!=x){
            result[layer][c]=x;
          }
        }
      }

    }


    //右側とラストを詰める
    for(auto x:node[result[1][layer-1]]){
      if(x!=result[1][layer-2]&&x!=result[2][layer-1]){
        result[1][layer]=x;
        break;
      }
    }
    for(int r=2;r<=layer;r++){
      int left=result[r][layer-1],up=result[r-1][layer];
      for(auto x:node[left]){
        for(auto y:node[up]){
          if(x==y&&result[r-1][layer-1]!=x){
            result[r][layer]=x;
          }
        }
      }
    }
  }

  for(int i=1;i<=n;i++){
    for(int j=1;j<n;j++){
      cout<<result[i][j]<<" ";
    }
    cout<<result[i][n]<<endl;
  }



  return 0;
}