#include "split.h"
#include <bits/stdc++.h>
using namespace std;
const int maxn = 1e5 + 5;
int n, m;
vector<int> adj[maxn];
vector<int> adj1[maxn];
bool vis[maxn];
int fa[maxn], sz[maxn];
void dfs(int u) {
sz[u] = vis[u] = 1;
for (int v:adj[u]) if (!vis[v]) {
fa[v] = u;
adj1[u].push_back(v); adj1[v].push_back(u);
dfs(v);
sz[u] += sz[v];
}
}
vector<int> ord;
void dfs1(int u, int p) {
ord.push_back(u);
for (int v:adj1[u]) if (v != p) dfs1(v, u);
}
vector<int> ans;
int root = -1;
int dsu[maxn], nodes[maxn];
int rt(int u) {
if (dsu[u] == u) return u;
return dsu[u] = rt(dsu[u]);
}
void merge(int u, int v) {
u = rt(u), v = rt(v);
if (u != v) {
nodes[v] += nodes[u];
dsu[u] = v;
}
}
void dfs2(int u, int p) {
for (int v:adj1[u]) if (v != p) {
merge(v, u);
dfs2(v, u);
}
}
void dfs3(int u, int RT) {
ord.push_back(u);
vis[u] = 1;
for (int v:adj[u]) if (!vis[v] && rt(v) == RT) dfs3(v, RT);
}
void dfs4(int u) {
ord.push_back(u);
vis[u] = 1;
for (int v:adj[u]) if (!vis[v] && !ans[v]) dfs4(v);
}
vector<int> find_split(int N, int a, int b, int c, vector<int> p, vector<int> q) {
n = N, m = p.size();
vector<pair<int,int>> vec = {{a, 1}, {b, 2}, {c, 3}};
sort(vec.begin(), vec.end());
for (int i=0;i<m;i++) {adj[p[i]].push_back(q[i]); adj[q[i]].push_back(p[i]);}
fa[0] = -1;
dfs(0);
a = vec[0].first, b = vec[1].first;
ans.resize(n);
for (int i=0;i<n;i++) ans[i] = 0;
for (int i=0;i<n;i++) {
if (a <= sz[i] && sz[i] <= n-a) {
if (sz[i] <= n-b) {
for (int j=0;j<n;j++) ans[j] = vec[2].second;
ord.clear();
dfs1(i, fa[i]);
for (int j=0;j<a;j++) ans[ord[j]] = vec[0].second;
ord.clear();
dfs1(fa[i], i);
for (int j=0;j<b;j++) ans[ord[j]] = vec[1].second;
} else {
for (int j=0;j<n;j++) ans[j] = vec[2].second;
ord.clear();
dfs1(i, fa[i]);
for (int j=0;j<b;j++) ans[ord[j]] = vec[1].second;
ord.clear();
dfs1(fa[i], i);
for (int j=0;j<a;j++) ans[ord[j]] = vec[0].second;
}
return ans;
}
}
for (int i=0;i<n;i++) if (n - sz[i] < a) {
bool flag = true;
for (int v:adj[i]) if (sz[v] >= a) flag = false;
if (flag) root = i;
}
for (int i=0;i<n;i++) dsu[i] = i, nodes[i] = 1;
for (int v:adj1[root]) dfs2(v, root);
for (int i=0;i<m;i++) {
int u = rt(p[i]), v = rt(q[i]);
if (u == root || v == root || u == v) continue;
merge(u, v);
if (nodes[v] >= a) {
ord.clear();
for (int j=0;j<n;j++) vis[j] = 0;
dfs3(v, v);
for (int j=0;j<a;j++) ans[ord[j]] = vec[0].second;
ord.clear();
for (int j=0;j<n;j++) vis[j] = 0;
dfs4(root);
for (int j=0;j<b;j++) ans[ord[j]] = vec[1].second;
for (int j=0;j<n;j++) if (!ans[j]) ans[j] = vec[2].second;
return ans;
}
}
return ans;
}
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