// #pragma GCC optimize("O3,unroll-loops")
#include <bits/stdc++.h>
// #include <x86intrin.h>
using namespace std;
#if __cplusplus >= 202002L
using namespace numbers;
#endif

template<class T>
struct graph{
	using Weight_t = T;
	struct Edge_t{
		int from, to;
		T cost;
	};
	int n;
	vector<Edge_t> edge;
	vector<vector<int>> adj;
	function<bool(int)> ignore;
	graph(int n = 1): n(n), adj(n){
		assert(n >= 1);
	}
	graph(const vector<vector<int>> &adj, bool undirected = true): n((int)adj.size()), adj(n){
		assert(n >= 1);
		if(undirected){
			for(auto u = 0; u < n; ++ u) for(auto v: adj[u]) if(u < v) link(u, v);
		}
		else for(auto u = 0; u < n; ++ u) for(auto v: adj[u]) orient(u, v);
	}
	graph(const vector<vector<pair<int, T>>> &adj, bool undirected = true): n((int)adj.size()), adj(n){
		assert(n >= 1);
		if(undirected){
			for(auto u = 0; u < n; ++ u) for(auto [v, w]: adj[u]) if(u < v) link(u, v, w);
		}
		else for(auto u = 0; u < n; ++ u) for(auto [v, w]: adj[u]) orient(u, v, w);
	}
	graph(int n, vector<array<int, 2>> &edge, bool undirected = true): n(n), adj(n){
		assert(n >= 1);
		for(auto [u, v]: edge) undirected ? link(u, v) : orient(u, v);
	}
	graph(int n, vector<tuple<int, int, T>> &edge, bool undirected = true): n(n), adj(n){
		assert(n >= 1);
		for(auto [u, v, w]: edge) undirected ? link(u, v, w) : orient(u, v, w);
	}
	int operator()(int u, int id) const{
		#ifdef LOCAL
		assert(0 <= id && id < (int)edge.size());
		assert(edge[id].from == u || edge[id].to == u);
		#endif
		return u ^ edge[id].from ^ edge[id].to;
	}
	int link(int u, int v, T w = {}){ // insert an undirected edge
		int id = (int)edge.size();
		adj[u].push_back(id), adj[v].push_back(id), edge.push_back({u, v, w});
		return id;
	}
	int orient(int u, int v, T w = {}){ // insert a directed edge
		int id = (int)edge.size();
		adj[u].push_back(id), edge.push_back({u, v, w});
		return id;
	}
	void clear(){
		for(auto [u, v, w]: edge){
			adj[u].clear();
			adj[v].clear();
		}
		edge.clear();
		ignore = {};
	}
	graph transposed() const{ // the transpose of the directed graph
		graph res(n);
		for(auto &e: edge) res.orient(e.to, e.from, e.cost);
		res.ignore = ignore;
		return res;
	}
	int degree(int u) const{ // the degree (outdegree if directed) of u (without the ignoration rule)
		return (int)adj[u].size();
	}
	// The adjacency list is sorted for each vertex.
	vector<vector<int>> get_adjacency_list() const{
		vector<vector<int>> res(n);
		for(auto u = 0; u < n; ++ u) for(auto id: adj[u]){
			if(ignore && ignore(id)) continue;
			res[(*this)(u, id)].push_back(u);
		}
		return res;
	}
	void set_ignoration_rule(const function<bool(int)> &f){
		ignore = f;
	}
	void reset_ignoration_rule(){
		ignore = nullptr;
	}
	friend ostream &operator<<(ostream &out, const graph &g){
		for(auto id = 0; id < (int)g.edge.size(); ++ id){
			if(g.ignore && g.ignore(id)) continue;
			auto &e = g.edge[id];
			out << "{" << e.from << ", " << e.to << ", " << e.cost << "}\n";
		}
		return out;
	}
};

// Requires graph
template<class T>
struct dfs_forest{
	int n;
	T base_dist;
	vector<T> dist;
	vector<int> pv;
	vector<int> pe;
	vector<int> order;
	vector<int> pos;
	vector<int> end;
	vector<int> size;
	vector<int> root_of;
	vector<int> root;
	vector<int> depth;
	vector<int> min_depth;
	vector<int> min_depth_origin;
	vector<int> min_depth_spanning_edge;
	// extra_edge[u]: adjacent edges of u which is not part of the spanning forest found during the last dfs-like run.
	vector<vector<int>> extra_edge;
	vector<int> was;
	dfs_forest(T base_dist = 0): base_dist(base_dist){ }
	void init(int n){
		this->n = n;
		pv.assign(n, -1);
		pe.assign(n, -1);
		order.clear();
		pos.assign(n, -1);
		end.assign(n, -1);
		size.assign(n, 0);
		root_of.assign(n, -1);
		root.clear();
		depth.assign(n, -1);
		min_depth.assign(n, -1);
		min_depth_origin.assign(n, -1);
		min_depth_spanning_edge.assign(n, -1);
		dist.assign(n, base_dist);
		extra_edge.assign(n, {});
		was.assign(n, -2);
		attempt = -1;
	}
	int attempt;
	// O(# of nodes reachable from u)
	template<class U, class F = plus<>>
	void _dfs(const graph<U> &g, int u, F UT = plus<>()){
		depth[u] = 0;
		dist[u] = base_dist;
		root_of[u] = u;
		root.push_back(u);
		pv[u] = pe[u] = -1;
		auto recurse = [&](auto self, int u)->void{
			was[u] = attempt;
			pos[u] = (int)order.size();
			order.push_back(u);
			size[u] = 1;
			min_depth[u] = depth[u];
			min_depth_origin[u] = u;
			min_depth_spanning_edge[u] = -1;
			for(auto id: g.adj[u]){
				if(id == pe[u] || g.ignore && g.ignore(id)) continue;
				int v = g(u, id);
				if(was[v] == attempt){
					if(min_depth[u] > depth[v]){
						min_depth[u] = depth[v];
						min_depth_spanning_edge[u] = id;
					}
					if(pe[u] != id) extra_edge[u].push_back(id);
					continue;
				}
				depth[v] = depth[u] + 1;
				dist[v] = UT(g.edge[id].cost, dist[u]);
				pv[v] = u;
				pe[v] = id;
				root_of[v] = root_of[u];
				self(self, v);
				size[u] += size[v];
				if(min_depth[u] > min_depth[v]){
					min_depth[u] = min_depth[v];
					min_depth_origin[u] = min_depth_origin[v];
					min_depth_spanning_edge[u] = min_depth_spanning_edge[v];
				}
			}
			end[u] = (int)order.size();
		};
		recurse(recurse, u);
	}
	// O(# of nodes reachable from src)
	template<class U, class F = plus<>>
	void dfs(const graph<U> &g, const vector<int> &src, F UT = plus<>()){
		assert(g.n <= n);
		root.clear(), order.clear();
		++ attempt;
		for(auto u: src){
			assert(0 <= u && u < g.n);
			if(was[u] != attempt) _dfs(g, u, UT);
		}
	}
	// O(n + m)
	template<class U, class F = plus<>>
	void dfs_all(const graph<U> &g, F UT = plus<>()){
		assert(g.n <= n);
		root.clear(), order.clear();
		++ attempt;
		for(auto u = 0; u < g.n; ++ u) if(was[u] != attempt) _dfs(g, u, UT);
	}
	// Check if u is visited during the last dfs-like call.
	bool visited(int u) const{
		assert(0 <= u && u < n);
		return was[u] == attempt;
	}
	// Check if u is an ancestor of v in some spanning tree.
	bool ancestor_of(int u, int v) const{
		assert(visited(u) && visited(v));
		return pos[u] <= pos[v] && end[v] <= end[u];
	}
	// Check if any cycle is found during the last dfs-like call.
	// If must_contain_root = true, the sought cycle is forced to contain one of the root of the trees.
	template<class U>
	optional<pair<int, vector<int>>> find_any_cycle(const graph<U> &g, bool must_contain_root = false) const{
		for(auto u: order) for(auto id: extra_edge[u]){
			int v = g(u, id);
			if(!ancestor_of(v, u) || must_contain_root && root_of[v] != v) continue;
			vector<int> cycle_edge;
			while(u != v) cycle_edge.push_back(pe[u]), u = pv[u];
			reverse(cycle_edge.begin(), cycle_edge.end());
			cycle_edge.push_back(id);
			return pair{v, cycle_edge};
		}
		return {};
	}
};

template<int h = 20>
struct binary_lifting{
	int n = 0;
	vector<int> depth;
	vector<array<int, h>> lift;
	binary_lifting(){ }
	// pv: parent vertex (-1 if root of an arborescence)
	binary_lifting(const vector<int> &pv): n((int)pv.size()), depth(n, numeric_limits<int>::max()), lift(n){
		for(auto u = 0; u < n; ++ u) lift[u][0] = ~pv[u] ? pv[u] : u;
		for(auto bit = 1; bit < h; ++ bit) for(auto u = 0; u < n; ++ u) lift[u][bit] = lift[lift[u][bit - 1]][bit - 1];
	}
	// Requires graph
	template<class Graph>
	binary_lifting(const Graph &g, const vector<int> &roots){
		vector<int> pv(g.n, -1), depth(g.n);
		auto dfs = [&](auto self, int u, int pe)->void{
			for(auto id: g.adj[u]){
				if(id == pe || g.ignore && g.ignore(id)) continue;
				auto &e = g.edge[id];
				int v = u ^ e.from ^ e.to;
				depth[v] = depth[u] + 1;
				pv[v] = u;
				self(self, v, id);
			}
		};
		for(auto u: roots) assert(!depth[u]), pv[u] = u, dfs(dfs, u, -1);
		*this = binary_lifting(pv, depth);
	}
	// pv: parent vertex (-1 if root of an arborescence)
	binary_lifting(const vector<int> &pv, const vector<int> &depth): n((int)pv.size()), depth(depth){
		lift.resize(n);
		for(auto u = 0; u < n; ++ u) lift[u][0] = ~pv[u] ? pv[u] : u;
		for(auto d = 1; d < h; ++ d) for(auto u = 0; u < n; ++ u) lift[u][d] = lift[lift[u][d - 1]][d - 1];
	}
	// Index becomes the current number of nodes
	// O(log n)
	int add_root(){
		int u = n ++;
		depth.push_back(0);
		lift.emplace_back();
		fill(lift.back().begin(), lift.back().end(), u);
		return u;
	}
	// Index becomes the current number of nodes
	// O(log n)
	int add_child(int p){
		assert(0 <= p && p < n);
		int u = n ++;
		depth.push_back(depth[p] + 1);
		lift.emplace_back();
		lift[u][0] = p;
		for(auto d = 1; d < h; ++ d) lift[u][d] = lift[lift[u][d - 1]][d - 1];
	}
	// Get the k-th ancestor of u
	// O(log n)
	int ancestor(int u, int k) const{
		for(auto d = 0; d < h; ++ d) if(k & 1 << d) u = lift[u][d];
		return u;
	}
	// Assumes u and v lies on the same arboresence
	// O(log n)
	int lca(int u, int v) const{
		if(depth[u] < depth[v]) swap(u, v);
		u = ancestor(u, depth[u] - depth[v]);
		if(u == v) return u;
		for(auto d = h - 1; d >= 0; -- d) if(lift[u][d] != lift[v][d]) u = lift[u][d], v = lift[v][d];
		return lift[u][0];
	}
	// Get # of edges between u and v
	// Assumes u and v lies on the same arboresence
	// O(log n)
	int steps(int u, int v, int w = -1) const{
		return depth[u] + depth[v] - 2 * depth[~w ? w : lca(u, v)];
	}
	// For an ancestor p of u, pred(p) is T, ..., T, F, ..., F in decreasing order of depth. Returns the highest p with T
	// O(log n)
	int find_highest(int u, auto pred) const{
		assert(pred(u));
		for(auto d = h - 1; d >= 0; -- d) if(pred(lift[u][d])) u = lift[u][d];
		return u;
	}
};

int main(){
	cin.tie(0)->sync_with_stdio(0);
	cin.exceptions(ios::badbit | ios::failbit);
	int n;
	cin >> n;
	map<int, vector<int>> mp;
	for(auto u = 0; u < n; ++ u){
		int x;
		cin >> x;
		mp[x].push_back(u);
	}
	graph<int> g(n);
	for(auto i = 0; i < n - 1; ++ i){
		int u, v;
		cin >> u >> v, -- u, -- v;
		g.link(u, v, 1);
	}
	binary_lifting lift(g, {0});
	dfs_forest<int> df;
	df.init(n);
	df.dfs(g, {0});
	int x = -1, y = -1;
	vector<int> active(n);
	auto color_path = [&](int u, int v)->void{
		assert(!active[u] && active[v]);
		while(!active[u] && !df.ancestor_of(u, v)){
			active[u] = true;
			u = df.pv[u];
		}
		if(active[u]){
			return;
		}
		v = lift.find_highest(v, [&](int v){ return active[v]; });
		while(v != u){
			v = df.pv[v];
			active[v] = true;
		}
	};
	vector<int> res(n, -1);
	for(auto [_, a]: mp | ranges::views::reverse){
		int i = 0;
		if(!~x){
			x = y = a[i ++];
			active[x] = true;
		}
		for(; i < (int)a.size(); ++ i){
			int u = a[i];
			if(active[u]){
				continue;
			}
			color_path(u, x);
			if(lift.steps(x, y) < lift.steps(x, u)){
				swap(y, u);
			}
			if(lift.steps(x, y) < lift.steps(y, u)){
				swap(x, u);
			}
		}
		for(auto u: a){
			res[u] = max(lift.steps(x, u), lift.steps(y, u));
		}
	}
	ranges::copy(res, ostream_iterator<int>(cout, " "));
	cout << "\n";
	return 0;
}

/*

*/