Shared code

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

#define rep(i, a, b) for(int i = a; i < (b); ++i)
#define all(x) begin(x), end(x)
#define sz(x) (int)(x).size()
#define F first
#define S second
#define pb push_back
typedef long long ll;
typedef pair<int, int> pii;
typedef pair<ll, ll> pll;
typedef vector<int> vi;


typedef pair<ll,ll> T;
struct AllRoots {
	int n;
	vector<vi> adj;
	vector<vector<T>> pre, suf;
	const T unit = {0, 0};
	AllRoots(int n) : n(n), adj(n), pre(n), suf(n) {}
	// !!!
	T merge(const T& v1, const T& v2) {
		return {v1.F + v2.F, v1.S + v2.S};
	}
	T promote(const T& v1) {
		return {v1.F + v1.S, v1.S + 1};
	}
	T get(int x, int i = 0){
		return promote(merge(pre[x][i], suf[x][i+1]));
	};
	void addEdge(int u, int v){
		adj[u].pb(v);
		adj[v].pb(u);
	}
	T down(int x, int p = -1) {
		for(auto& c : adj[x]) if(c == p) swap(c, adj[x][0]);
		for(int i = adj[x].size()-1; i > -(p<0); --i)
			suf[x][i] = merge(down(adj[x][i], x), suf[x][i+1]);
		return get(x);
	}
	void up(int x, int p = -1) {
		rep(i, p != -1, adj[x].size()) {
			pre[x][i+1] = merge(pre[x][i], get(adj[x][i]));
			pre[adj[x][i]][1] = get(x, i);
			up(adj[x][i], x);
		}
	}
	vector<T> calc(int root = 0) {
		rep(i,0,n) {
			pre[i].assign(adj[i].size() + 1, unit);
			suf[i].assign(adj[i].size() + 1, unit);
		}
		down(root);
		if(sz(adj[root]))
			pre[root][1] = get(adj[root][0]);
		up(root);
		vector<T> res(n);
		rep(i,0,n) res[i] = promote(pre[i].back());
		return res;
	}
};
 
int main() {
	cin.tie(nullptr)->sync_with_stdio(false);
	int n; cin >> n;
	AllRoots ar(n);

	rep(i,0,n-1) {
		int u,v; cin >> u >> v;
		ar.addEdge(u-1, v-1);
	}

	auto res = ar.calc();
	rep(i,0,n) cout << res[i].F << ' ';
	cout<<endl;
}