Language: C++

//{{{
#pragma comment(linker, "/stack:200000000")
#pragma GCC optimize("O2")
#pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,avx,tune=native")

#include <bits/stdc++.h>
using namespace std;

#define putchar(x) cout << (x)
#define repeat(x) int _ = 0; _ < (x); ++_

#define SELECT(_1, _2, _3, _4, _5, _6, _7, _8, NAME,...) NAME
#define showvar(x) print_n(#x, "=", x);
#define dbg1(a) showvar(a) cout << endl;
#define dbg2(a, b) showvar(a) cout << ", "; dbg1(b);
#define dbg3(a, b, c) showvar(a) cout << ", "; dbg2(b, c);
#define dbg4(a, b, c, d) showvar(a) cout << ", "; dbg3(b, c, d);
#define dbg5(a, b, c, d, e) showvar(a) cout << ", "; dbg4(b, c, d, e);
#define dbg6(a, b, c, d, e, f) showvar(a) cout << ", "; dbg5(b, c, d, e, f);
#define dbg7(a, b, c, d, e, f, g) showvar(a) cout << ", "; dbg6(b, c, d, e, f, g);
#define dbg8(a, b, c, d, e, f, g, h) showvar(a) cout << ", "; dbg7(b, c, d, e, f, g, h);
#define debug(...) SELECT(__VA_ARGS__, dbg8, dbg7, dbg6, dbg5, dbg4, dbg3, dbg2, dbg1)(__VA_ARGS__)

template<typename T> constexpr auto range(T start, T stop, T step) {
    struct iterator {
        using difference_type = T;
        using value_type = T;
        using pointer = T*;
        using reference = T&;
        using iterator_category = random_access_iterator_tag;

        T i, step;
        T operator-(const iterator& other) const { return i - other.i; };
        bool operator!=(const iterator& other) const { return i != other.i; }
        auto& operator+=(const int& n) { i += step * n; return *this; }
        auto& operator++() { i += step; return *this; }
        auto& operator*() { return i; }
    };
    struct iterable_wrapper {
        T start, stop, step;
        auto begin() const { return iterator{ start, step }; }
        auto end() const { return iterator{ stop, step }; }
        size_t size() const { return (stop - start) / step; }

        iterable_wrapper(T start_, T stop_, T step_): start(start_), stop(stop_), step(step_) {
            stop = step > 0 ? max(start, stop) : min(start, stop);
            stop += (step - (stop - start) % step) % step;
        }
    };
    return iterable_wrapper(start, stop, step);
};
template<typename T> constexpr auto range(T start, T stop) { return range(start, stop, T(1)); }
template<typename T> constexpr auto range(T stop) { return range(T(0), stop, T(1)); }

template<typename T, typename Iter = decltype(rbegin(declval<T>()))>
auto reversed(T&& iterable) {
    struct iterable_wrapper {
        T iterable;
        auto begin() const { return std::rbegin(iterable); }
        auto end() const { return std::rend(iterable); }
        auto size() const { return iterable.size(); }
    };
    return iterable_wrapper{ forward<T>(iterable) };
}

template<typename T, typename Iter = decltype(begin(declval<T>()))>
constexpr auto printer(T&& iterable) {
    struct iterator {
        Iter iter, ed;
        auto operator!=(const iterator& other) const {
            auto ret = (iter != other.iter);
            if(not ret) cout << '\n';
            return ret;
        }
        auto& operator++() { ++iter; if(iter != ed) cout << ' '; return *this; }
        auto& operator*() { return *iter; }
    };
    struct iterable_wrapper {
        T iterable;
        auto begin() const { return iterator{ std::begin(iterable), std::end(iterable) }; }
        auto end() const { return iterator{ std::end(iterable), std::end(iterable) }; }
    };
    return iterable_wrapper{ forward<T>(iterable) };
};

template<class ...T> void absorb(T&& ...) {}
template<size_t L, size_t I, class T>
bool zip_it_ne(const T& it1, const T& it2) {
    if(not (get<I>(it1) != get<I>(it2))) return false;
    if(I + 1 == L) return true;
    return zip_it_ne<L, (I + 1) % L, T>(it1, it2);
}
template<size_t ...Is, class T, class ...Cs,
    class Iter = tuple<decltype(begin(declval<Cs>()))...>,
    class Ref = tuple<decltype(*begin(declval<Cs>()))&...>
    >
constexpr auto zip(index_sequence<Is...>, T&& iterables, Cs&&...) {
    struct iterator {
        Iter iter;
        unique_ptr<Ref> tref = nullptr;
        bool operator!=(const iterator& other) const {
            return zip_it_ne<sizeof...(Is), 0, Iter>(iter, other.iter);
        }
        auto& operator++() { absorb(++get<Is>(iter)...); return *this; }
        auto& operator*() { tref.reset(new Ref(tie(*get<Is>(iter)...))); return *tref; }
    };
    struct iterable_wrapper {
        T iterables;
        auto begin() const { return iterator { Iter{ std::begin(get<Is>(iterables))... } }; }
        auto end() const { return iterator { Iter{ std::end(get<Is>(iterables))... } }; }
        auto size() const { return min({ get<Is>(iterables).size()... }); }
    };
    return iterable_wrapper{ forward<T>(iterables) };
}
template<class ...Cs, class = tuple<decltype(begin(declval<Cs>()))...>>
constexpr auto zip(Cs&& ...cs) {
    return zip(index_sequence_for<Cs...>{}, tuple<Cs...>(forward<Cs>(cs)...), forward<Cs>(cs)...);
}

template<typename T, typename Iter = decltype(begin(declval<T>()))>
constexpr auto enumerate(T&& iterable) {
    return zip(range(iterable.size()), forward<T>(iterable));
}

template<size_t ...Is, typename T> auto getis(const T& t) { return tie(get<Is>(t)...); }
template<class T> void setmax(T& a, const T& b) { a = max(a, b); }
template<class T> void setmin(T& a, const T& b) { a = min(a, b); }

template<typename T, typename = void> struct is_container : false_type {};
template<typename T>
struct is_container<T, conditional_t<false, decltype(begin(declval<T>())), void>> : true_type {};
template<class T> using IsC = typename enable_if<is_container<T>::value and
    not std::is_same<T, string>::value>::type;
template<class T> using NotC = typename enable_if<not is_container<T>::value or
    std::is_same<T, string>::value>::type;
template<class T> inline NotC<T> print_1(const T& x) { cout << x; }
template<class T> inline IsC<T> print_1(const T& v) {
    for(auto it = v.begin(); it != v.end(); ++it) { if(it != v.begin()) putchar(' '); print_1(*it); }
}
inline void print_1(const tuple<>&) {};
template<size_t L, size_t I, class T> void print_tuple(const T& t) {
    if(I != 0) putchar(' '); print_1(get<I>(t));
    if(I + 1 < L) print_tuple<L, (I + 1) % L>(t);
}
template<class ...T> inline void print_1(const tuple<T...>& x) {
    print_tuple<sizeof...(T), 0, tuple<T...>>(x);
}
inline void print_n() {}
template<class T, class ...U> inline void print_n(const T& head, const U&... tail);
template<class T, class U> inline void print_1(const pair<T, U>& p) { print_n(p.first, p.second); }
template<class T, class ...U> inline void print_n(const T& head, const U&... tail) {
    print_1(head); if(sizeof...(tail)) putchar(' '); print_n(tail...);
}
template<class ...T> inline void print(const T& ...args) { print_n(args...); putchar('\n'); }
inline void read() {}
template<class T, class ...U> inline void read(T& head, U&... tail) { cin >> head; read(tail...); }

mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());
static int fastio = [](){ ios_base::sync_with_stdio(false); cin.tie(0); cout.precision(17); return 0; }();
//}}}
using PII = pair<int, int>;
using LL = long long;

const int MOD = 1e9 + 7;
const int INF = 0x3f3f3f3f;
const LL LLINF = 0x3f3f3f3f3f3f3f3f;
const int MAX_N = 200005;

int N;
int cnt[2];
int ans[MAX_N];
vector<int> vs[2];
vector<int> G[MAX_N];

void dfs(int v, int p, int color) {
    cnt[color] += 1;
    vs[color].push_back(v);
    for(int u : G[v]) {
        if(u != p) {
            dfs(u, v, 1 - color);
        }
    }
}

void solve() {
    read(N);
    for(int i : range(N - 1)) {
        int a, b;
        read(a, b);
        G[a].push_back(b);
        G[b].push_back(a);
    }
    array<int, 3> k = {};
    for(int i : range(1, N + 1)) {
        ++k[i % 3];
    }

    int c = 0;
    dfs(1, -1, c);
    if(cnt[c] > cnt[1 - c]) {
        c = 1 - c;
    }
    if(cnt[c] <= k[0]) {
        for(auto [i, v] : enumerate(vs[c])) {
            ans[v] = 3 * (i + 1);
        }
        int j = 1;
        for(int v : vs[1 - c]) {
            if(j % 3 == 0) ++j;
            ans[v] = j;
        }
    } else {
        int x = 1, y = 2, z = 3;
        for(int v : vs[c]) {
            if(y <= N) {
                ans[v] = y;
                y += 3;
            } else {
                ans[v] = z;
                z += 3;
            }
        }
        for(int v : vs[1 - c]) {
            if(x <= N) {
                ans[v] = x;
                x += 3;
            } else {
                ans[v] = z;
                z += 3;
            }
        }
    }
    for(int i : printer(range(1, N + 1))) {
        print_1(ans[i]);
    }
}

int main() {
    int t = 1;
    //cin >> t;
    for(int i = 0; i < t; ++i) {
        solve();
    }
    return 0;
}


Compiler output:
In file included from /usr/include/c++/14/string:43,
                 from /usr/include/c++/14/bitset:52,
                 from /usr/include/x86_64-linux-gnu/c++/14/bits/stdc++.h:52,
                 from a.cc:6:
/usr/include/c++/14/bits/allocator.h: In destructor 'std::_Vector_base<int, std::allocator<int> >::_Vector_impl::~_Vector_impl()':
/usr/include/c++/14/bits/allocator.h:182:7: error: inlining failed in call to 'always_inline' 'std::allocator< <template-parameter-1-1> >::~allocator() noexcept [with _Tp = int]': target specific option mismatch
  182 |       ~allocator() _GLIBCXX_NOTHROW { }
      |       ^
In file included from /usr/include/c++/14/vector:66,
                 from /usr/include/c++/14/functional:64,
                 from /usr/include/x86_64-linux-gnu/c++/14/bits/stdc++.h:53:
/usr/include/c++/14/bits/stl_vector.h:132:14: note: called from here
  132 |       struct _Vector_impl
      |              ^~~~~~~~~~~~