#include "worldmap.h"
#include <bits/stdc++.h>
#ifdef LOCAL
#include "Debug.h"
#else
#define debug(...) 42
#endif
using namespace std;
struct DisjointSet
{
int n;
vector<int> ds, sz;
DisjointSet(int n): n(n)
{
ds = sz = vector<int>(n);
for (int i = 0; i < n; i++)
{
ds[i] = i;
sz[i] = 1;
}
}
int get(int x)
{
return x == ds[x] ? x : ds[x] = get(ds[x]);
}
int join(int x, int y)
{
int dx = get(x), dy = get(y);
if (dx == dy)
return 0;
if (sz[dx] < sz[dy])
swap(dx, dy);
ds[dy] = dx;
sz[dx] += sz[dy];
return 1;
}
};
const int N = 44;
vector<int> a[N];
int depth[N];
void dfs(int x, vector<int> &path)
{
path.push_back(x);
for (int y : a[x])
if (depth[y] < 0)
{
depth[y] = depth[x] + 1;
dfs(y, path);
path.push_back(x);
}
}
vector<vector<int>> create_map(int n, int m, vector<int> A, vector<int> B) {
for (int &x : A)
x--;
for (int &x : B)
x--;
for (int i = 0; i < n; i++)
{
a[i].clear();
depth[i] = -1;
}
DisjointSet ds(n);
vector<vector<int>> adj(n, vector<int>(n));
for (int i = 0; i < m; i++)
{
if (ds.join(A[i], B[i]))
{
a[A[i]].push_back(B[i]);
a[B[i]].push_back(A[i]);
}
adj[A[i]][B[i]] = adj[B[i]][A[i]] = 1;
}
vector<int> path;
depth[0] = 0;
dfs(0, path);
for (int i = 0; i + 1 < size(path); i++)
{
int x = path[i], y = path[i + 1];
adj[x][y] = adj[y][x] = 0;
}
vector<int> hasNonPathEdges(n);
hasNonPathEdges[path[0]] = 1;
for (int x = 0; x < n; x++)
for (int y = x + 1; y < n; y++)
hasNonPathEdges[x] |= adj[x][y];
vector<int> isDummy(size(path)), seen(n);
for (int i = 0; i < size(path); i++)
{
int x = path[i];
if (!seen[x] && hasNonPathEdges[x]) seen[x] = 1;
else isDummy[i] = 1;
}
// trim unnecessary backward edges
while (size(path) >= 2)
{
int x = path[size(path) - 2], y = path[size(path) - 1];
if (depth[x] < depth[y])
break;
path.pop_back();
}
int len = size(path), colNeed = 0;
isDummy.resize(len);
for (int i = 0; i < len; i++)
if (isDummy[i]) colNeed++;
else colNeed += 2;
int k = max(n * 2, colNeed);
debug(path); debug(isDummy); debug(k);
vector<vector<int>> ans(k, vector<int>(k, -1));
for (int i = 0, parity = 0, col = 0; i < len; i++)
{
int x = path[i];
if (isDummy[i])
{
for (int row = 0; row < k; row++)
if (parity) ans[row][col - 1 + row % 2] = x;
else ans[row][col - row % 2] = x;
col++;
continue;
}
if (parity == 0)
{
for (int row = 0; row < k; row++)
if (row % 2 == 0) ans[row][col] = x;
else
{
ans[row][col + 1] = x;
if (col)
ans[row][col - 1] = x;
}
for (int y = 0; y < k / 2; y++)
ans[y * 2 + 1][col] = y < n && adj[x][y] ? y : x;
}
else
{
for (int row = 0; row < k; row++)
if (row % 2) ans[row][col] = x;
else ans[row][col - 1] = ans[row][col + 1] = x;
for (int y = 0; y < k / 2; y++)
ans[y * 2][col] = y < n && adj[x][y] ? y : x;
}
parity ^= 1;
col += 2;
}
for (int i = 0; i < k; i++)
for (int &x : ans[i])
if (x < 0) x = path.back() + 1;
else x++;
return ans;
}
