#include <bits/stdc++.h>
#define pb push_back
//#define int int64_t
#define pii pair<int, int>
#define X first
#define Y second
#define all(x) (x).begin(),(x).end()
#define lb lower_bound
#define ub upper_bound
#define debug(x) cerr << "\n" << (#x) << " is " << (x) << endl;
using namespace std;
const int inf = 1e18;
void p(auto A){
for(auto e : A)cout << e << ' ';
cout << '\n';
}
struct edge{
int u, v, use;
edge(){
use = 1;
}
int f(int a){
if(a==u)return v;
else return u;
}
array<int, 3> get(){
return {u, v, use};
}
};
vector<int> find_split(int n, int a, int b, int c, vector<int> p, vector<int> q){
array<int, 3> col = {1, 2, 3};
array<int, 3> siz = {a, b, c};
sort(all(col), [&](int i, int j){return siz[i-1] < siz[j-1];});
sort(all(siz));
int m = p.size();
vector<edge>E(m);
vector<vector<int>> g(n);
for(int i = 0; i< m; i++){
int u = p[i];
int v = q[i];
g[u].pb(i);
g[v].pb(i);
E[i].v = v;
E[i].u = u;
}
vector<int> vis(n);
auto dfs1 = [&](auto&& self, int u, int par)->void{
vis[u] = 1;
for(auto e : g[u]){
int v = E[e].f(u);
if(v==par)continue;
if(vis[v]){
E[e].use = 0;
continue;
}
self(self, v, u);
}
};
dfs1(dfs1, 0, 0);
vector<int> sz(n, 1);
auto dfs2 = [&](auto&& self, int u, int par)->int{
int ret = -1;
int flag = 1;
for(auto e : g[u])if(E[e].use){
int v = E[e].f(u);
if(v==par)continue;
ret = max(ret, self(self, v, u));
sz[u]+=sz[v];
if(sz[v] > n/2)flag = 0;
}
if(n-sz[u] > n/2)flag = 0;
if(flag)ret = u;
return ret;
};
int root = dfs2(dfs2, 0, 0);
//debug(root);
vector<int>P(n, -1);
auto find = [&](int u)->int{
while(P[u] >= 0)u = P[u];
return u;
};
int start = -1;
for(int i = 0; i< n; i++)if(i != root && -P[i] >= siz[0])start = i;
if(start ==-1)for(auto e : E){
auto [u, v, use] = e.get();
if(!use)continue;
if(u == root)continue;
if(v == root)continue;
u = find(u);
v = find(v);
if(u == v)continue;
if(P[u] > P[v])swap(u, v);
P[u]+=P[v];
P[v] = u;
if(-P[u] >= siz[0])start = u;
}
if(start == -1)for(auto e : E){
auto [u, v, use] = e.get();
if(use)continue;
if(u==root)continue;
if(v==root)continue;
u=find(u);
v=find(v);
if(u==v)continue;
e.use = 1;
if(P[u]>P[v])swap(u, v);
P[u]+=P[v];
P[v]=u;
if(-P[u] >= siz[0])start = u;
}
vector<int>out(n);
if(start == -1){
return out;
}
if(-P[start] >= siz[1]){
swap(col[0], col[1]);
swap(siz[0], siz[1]);
}
vector<int>st;
st.pb(start);
while(siz[0]){
int u = st.back();
st.pop_back();
if(u == root)continue;
if(out[u])continue;
siz[0]--;
out[u] = col[0];
for(auto e : g[u])if(E[e].use)st.pb(E[e].f(u));
}
st.clear();
st.pb(root);
while(siz[1]){
int u = st.back();
st.pop_back();
if(out[u])continue;
siz[1]--;
out[u] = col[1];
for(auto e : g[u])if(E[e].use)st.pb(E[e].f(u));
}
for(auto& e : out)if(!e)e=col[2];
return out;
}
/*
void solve(){
int n, m; cin >> n >> m;
int a, b, c; cin >> a >> b >> c;
vector<int>P(m), Q(m);
for(int i = 0; i< m; i++)cin >> P[i] >> Q[i];
vector<int> ans = find_split(n, a, b, c, P, Q);
for(auto e : ans)cout << e << ' ';
}
signed main(){
ios_base::sync_with_stdio(false);
cin.tie(NULL);
int t = 1;
//cin >> t;
while(t--)solve();
}
*/
