#include <bits/stdc++.h>
// #include "grader.cpp"
using namespace std;
const int N = 1e5 + 10;
int n, m, sz[3], tmp[3], subsz[N], h[N], mnh[N], A, B, par[N];
bool vis[N], done, impossible;
vector<int> g[N], ans;
void color(int v, int col){
// cout << "coloring " << v << " with color = " << col << ", remaining of this color are " << tmp[col - 1] << " and ans[v] = " << ans[v] << endl;
if (tmp[col - 1] == 0) return;
if (ans[v]) return;
tmp[col - 1]--;
ans[v] = col;
for (int u : g[v])
if (h[u] == h[v] + 1)
color(u, col);
}
void pre_dfs(int v, int p = -1){
vis[v] = 1;
mnh[v] = h[v];
subsz[v] = 1;
for (int u : g[v]){
if (u == p) continue;
if (vis[u]){ // back edge
mnh[v] = min(mnh[v], h[u]);
continue;
}
// child of u.
h[u] = h[v] + 1;
par[u] = v;
pre_dfs(u, v);
mnh[v] = min(mnh[v], mnh[u]);
subsz[v] += subsz[u];
}
}
void dfs(int v, int p = -1){
vis[v] = 1;
bool bad = 0;
for (int u : g[v]){
if (u == p) continue;
if (vis[u])
continue;
// child of u.
dfs(u, v);
if (done) return;
bad |= (subsz[u] >= sz[0]);
}
bad |= (subsz[v] < sz[0]);
if (bad) return;
// subsz[v] >= a and subsz[child(v)] < a.
int forced = 1; // v is itself forced.
vector<int> free;
for (int u : g[v]){
if (h[u] != h[v] + 1) continue;
if (mnh[u] >= h[v])
forced += subsz[u];
else free.push_back(u);
}
while (forced < sz[0]){
int u = free.back();
free.pop_back();
forced += subsz[u];
}
// cout << "AT v = " << v << endl;
if (n - forced >= sz[1]){
int cur = v;
while (cur != 0 && tmp[B - 1] > 0){
cur = par[cur];
ans[cur] = B;
tmp[B - 1]--;
}
for (int u : free)
color(u, B);
color(v, A);
for (int u : g[0])
color(u, B);
}
else if (n - forced >= sz[0]){
int cur = v;
while (cur != 0 && tmp[A - 1] > 0){
cur = par[cur];
ans[cur] = A;
tmp[A - 1]--;
}
for (int u : free)
color(u, A);
color(v, B);
for (int u : g[0])
color(u, A);
}
else
impossible = 1;
done = 1;
}
vector<int> find_split(int N, int a, int b, int c, vector<int> p, vector<int> q){
tmp[0] = a, tmp[1] = b, tmp[2] = c;
sz[0] = a, sz[1] = b, sz[2] = c;
sort(sz, sz + 3);
if (sz[0] == a and sz[1] == b){
A = 1;
B = 2;
}
else if (sz[0] == a and sz[1] == c){
A = 1;
B = 3;
}
else if (sz[0] == b and sz[1] == a){
A = 2;
B = 1;
}
else if (sz[0] == b and sz[1] == c){
A = 2;
B = 3;
}
else if (sz[0] == c and sz[1] == a){
A = 3;
B = 1;
}
else{
A = 3;
B = 2;
}
// cout << A << " -- " << B << endl;
n = N;
m = p.size();
for (int i=0; i<m; i++){
g[p[i]].push_back(q[i]);
g[q[i]].push_back(p[i]);
}
ans.resize(n, 0);
pre_dfs(0);
memset(vis, 0, sizeof vis);
dfs(0);
if (impossible) return ans;
for (int v = 0; v < n; v ++)
if (!ans[v]) ans[v] = 6 - (A + B);
return ans;
}
