// Hallelujah, praise the one who set me free
// Hallelujah, death has lost its grip on me
// You have broken every chain, There's salvation in your name
// Jesus Christ, my living hope
#include <bits/stdc++.h>
#include "Alicelib.h"
using namespace std;
#define REP(i, s, e) for (int i = (s); i < (e); i++)
#define RREP(i, s, e) for (int i = (s); i >= (e); i--)
template <class T>
inline bool mnto(T& a, T b) {return b < a ? a = b, 1 : 0;}
template <class T>
inline bool mxto(T& a, T b) {return a < b ? a = b, 1: 0;}
typedef unsigned long long ull;
typedef long long ll;
typedef long double ld;
#define FI first
#define SE second
typedef pair<int, int> ii;
typedef pair<ll, ll> pll;
typedef tuple<int, int, int> iii;
#define ALL(_a) _a.begin(), _a.end()
#define SZ(_a) (int) _a.size()
#define pb push_back
typedef vector<int> vi;
typedef vector<ll> vll;
typedef vector<ii> vii;
typedef vector<iii> viii;
#ifndef DEBUG
#define cerr if (0) cerr
#endif
const int INF = 1000000005;
const ll LINF = 1000000000000000005ll;
const int MAXN = 1100;
namespace {
int n, m;
bool g[MAXN][MAXN], h[MAXN][MAXN];
inline void add(int u, int v) {
h[u][v] = h[v][u] = 1;
}
inline void answer() {
vii eg;
REP (i, 0, m) {
REP (j, i + 1, m) {
if (h[i][j]) {
eg.pb({i, j});
}
}
}
InitG(m, SZ(eg));
REP (i, 0, SZ(eg)) {
MakeG(i, eg[i].FI, eg[i].SE);
}
}
}
void Alice(int N, int E, int A[], int B[]) {
n = N;
REP (i, 0, E) {
g[A[i]][B[i]] = g[B[i]][A[i]] = 1;
}
REP (i, 0, n) {
REP (j, 0, n) {
h[i][j] = g[i][j];
}
}
if (n <= 2) {
m = n;
answer();
return;
}
int lg = 32 - __builtin_clz(n - 1);
m = n + min(lg + 3, 12);
REP (l, 0, lg) {
REP (i, 0, n) {
if (i >> l & 1) {
add(n + l, i);
}
}
if (l) {
add(n + l, n + l - 1);
}
}
if (lg == 10) {
REP (i, n, n + lg + 1) {
add(n + lg, i);
}
REP (i, 0, n + lg) {
add(n + lg + 1, i);
}
} else {
add(n + lg, n + lg - 1);
REP (i, n, n + lg + 1) {
add(n + lg + 1, i);
}
REP (i, 0, n + lg + 1) {
add(n + lg + 2, i);
}
}
answer();
}
// Hallelujah, praise the one who set me free
// Hallelujah, death has lost its grip on me
// You have broken every chain, There's salvation in your name
// Jesus Christ, my living hope
#include <bits/stdc++.h>
#include "Boblib.h"
using namespace std;
#define REP(i, s, e) for (int i = (s); i < (e); i++)
#define RREP(i, s, e) for (int i = (s); i >= (e); i--)
template <class T>
inline bool mnto(T& a, T b) {return b < a ? a = b, 1 : 0;}
template <class T>
inline bool mxto(T& a, T b) {return a < b ? a = b, 1: 0;}
typedef unsigned long long ull;
typedef long long ll;
typedef long double ld;
#define FI first
#define SE second
typedef pair<int, int> ii;
typedef pair<ll, ll> pll;
typedef tuple<int, int, int> iii;
#define ALL(_a) _a.begin(), _a.end()
#define SZ(_a) (int) _a.size()
#define pb push_back
typedef vector<int> vi;
typedef vector<ll> vll;
typedef vector<ii> vii;
typedef vector<iii> viii;
#ifndef DEBUG
#define cerr if (0) cerr
#endif
const int INF = 1000000005;
const ll LINF = 1000000000000000005ll;
const int MAXN = 1100;
namespace {
int n, m;
bool g[MAXN][MAXN], h[MAXN][MAXN];
inline void add(int u, int v) {
h[u][v] = h[v][u] = 1;
}
int deg[MAXN];
bool isb[MAXN], vis[MAXN];
int id[MAXN];
inline bool rmv(int u, int v) {
if (!g[u][v]) {
return 0;
}
g[u][v] = g[v][u] = 0;
deg[u]--; deg[v]--;
return 1;
}
inline void answer() {
vii eg;
REP (i, 0, m) {
REP (j, i + 1, m) {
if (h[i][j]) {
eg.pb({i, j});
}
}
}
InitMap(m, SZ(eg));
REP (i, 0, SZ(eg)) {
MakeMap(eg[i].FI, eg[i].SE);
}
}
}
void Bob(int V, int U, int C[], int D[]) {
REP (i, 0, U) {
g[C[i]][D[i]] = g[D[i]][C[i]] = 1;
}
n = V;
if (n <= 2) {
m = n;
REP (i, 0, n) {
REP (j, 0, n) {
h[i][j] = g[i][j];
}
}
answer();
return;
}
REP (x, 1, MAXN) {
int lg = 32 - __builtin_clz(x - 1);
if (x + min(12, lg + 3) == n) {
m = x;
break;
}
}
assert(m);
int lg = 32 - __builtin_clz(m - 1);
ii mx = {0, 0};
REP (i, 0, n) {
REP (j, 0, n) {
deg[i] += g[i][j];
}
mxto(mx, {deg[i], i});
}
assert(mx.FI == n - 2);
int r = -1;
REP (i, 0, n) {
if (i == mx.SE) {
continue;
}
if (!rmv(mx.SE, i)) {
assert(r == -1);
r = i;
}
}
assert(deg[r] == lg + 1);
REP (i, 0, n) {
isb[i] = rmv(r, i);
}
vi bits;
if (lg == 10) {
ii mn = {INF, INF};
REP (i, 0, n) {
if (!isb[i]) {
continue;
}
int bdeg = 0;
REP (j, 0, n) {
bdeg += isb[j] && g[i][j];
}
if (bdeg == 1) {
mnto(mn, {deg[i], i});
}
}
assert(mn.SE != INF);
bits.pb(mn.SE);
vis[mn.SE] = 1;
} else {
int e = -1;
REP (i, 0, n) {
if (isb[i] && deg[i] == 1) {
REP (j, 0, n) {
if (isb[j] && g[i][j]) {
e = i;
break;
}
}
if (e != -1) {
break;
}
}
}
assert(e != -1);
assert(deg[e] == 1);
REP (i, 0, n) {
if (rmv(e, i)) {
bits.pb(i);
vis[i] = 1;
}
}
}
while (SZ(bits) < lg) {
REP (i, 0, n) {
if (vis[i] || !isb[i]) {
continue;
}
if (rmv(bits.back(), i)) {
vis[i] = 1;
bits.pb(i);
break;
}
}
}
reverse(ALL(bits));
REP (l, 0, lg) {
REP (i, 0, n) {
id[i] |= rmv(bits[l], i) << l;
}
}
REP (i, 0, n) {
REP (j, 0, n) {
if (g[i][j]) {
assert(id[i] < m && id[j] < m);
add(id[i], id[j]);
}
}
}
answer();
}
