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//Konrad Paluszek,University of Warsaw(former XIV LO Staszic)
//#STAY AT HOME
#ifndef LOCAL
#pragma GCC optimize("O3")
#endif
#define TIME (chrono::steady_clock::now().time_since_epoch().count())
#include<bits/stdc++.h>
#include<ext/pb_ds/assoc_container.hpp>
#include<ext/pb_ds/tree_policy.hpp>
#define xfm(a,b)a##b
#define xwb(a,b)xfm(a,b)
#define _ xwb(nvj,__LINE__)
#define __ xwb(kjy,__LINE__)
#define ___ xwb(cjm,__LINE__)
#define REP(i,n)for(urs(n)i=0;i<(n);++i)
#define PER(r...)for(bool _=1;_||next_permutation(r);_=false)
#define FS(r)r.first,r.second
#define ALL(r)(r).begin(),(r).end()
#define M0(r) memset(r,0,sizeof(r))
#define sim template<class c
#define forbits(i,m)if(m)for(urs(m)i=ctz(m),i##nvj=m;i##nvj;i##nvj^=((urs(m))1<<i),i=i##nvj?ctz(i##nvj):0)
#define fordbits(i,m)if(m)for(urs(m)i=8*sizeof(m)-clz(m)-1,i##nxd=m;i##nxd;i##nxd^=((urs(m))1<<i),i=i##nxd?8*sizeof(m)-clz(i##nxd)-1:0)
#define ksets(t, m, k, n)for(t m=(((t)1<<(k))-1);m<((t)1<<(n));m=nux(m))
#define urs(r...)typename decay<decltype(r)>::type
#define hur(f,g)sim>int f(c a){if(sizeof(c)==8)return g##ll(a);return g(a);}
using namespace __gnu_pbds;using namespace std;using ll=long long;using ld=long double;using ull=unsigned long long;using vi=vector<int>;using vll=vector<ll>;using pii=pair<int,int>;using pll=pair<ll,ll>;using vpii=vector<pii>;using unt=unsigned int;sim>using min_queue=priority_queue<c,vector<c>,greater<c>>;sim,class b,class cmp=less<c>>using ordered_map=tree<c,b,cmp,rb_tree_tag,tree_order_statistics_node_update>;sim,class cmp=less<c>>using ordered_set=ordered_map<c,null_type,cmp>;hur(popc,__builtin_popcount)hur(ctz,__builtin_ctz)hur(clz,__builtin_clz)sim,class N>bool mini(c&o,const N&h){if(o>h)return o=h,1;return 0;}sim,class N>bool maxi(c&o,const N&h){if(o<h)return o=h,1;return 0;}
#ifdef LOCAL
#include </home/kjp/headers/debuglib.hpp>
#else
#define loc(...)
#define onl(r...)r
#define debug(...)
#define print_stack(...)
#define mark_stack(...)
#define set_pre(...)
#define reg_it(...)
#define def_op(...) struct _{};
#define mask_set(...)
#define exit my_exit
void my_exit(int x) {fflush(stdout);_Exit(x);}
#endif
#define next nexT
#define prev preV
#define tree trEE
#define left lefT
#define right righT
#define div diV
#define y1 y_1
#define pow don't'
ull mix(ull o){o+=0x9e3779b97f4a7c15;o=(o^(o>>30))*0xbf58476d1ce4e5b9;o=(o^(o>>27))*0x94d049bb133111eb;return o^(o>>31);}ull SALT=0x7a14a4b0881ebf9,tqu=0x7a14a4b0881ebf9;ull my_rand(){return tqu=mix(tqu);}void my_srand(ull x){SALT=tqu=x;}const int inf=1023400000;const ll llinf=1234567890000000000ll;ll fix(ll o, ll m){o%=m;if(o<0)o+=m;return o;}
#define rand my_rand
#define srand my_srand
#define random_shuffle(r...)random_shuffle(r,[](int _){return my_rand()%_;})
sim>inline c nux(c m){if(!m)return numeric_limits<c>::max();c A=m&-m;c B=~((A-1)^m);c C=B&-B;c D=(C>>(1+ctz(A)))-1;return C|(m&~(C-1))|D;}sim>void unq(c&x){x.resize(unique(ALL(x))-x.begin());}
//#STAY AT HOME
using res_t = vector <vector <pll> >;
res_t make(int x) {
	return {{make_pair(x * 1ll * x, x)}};
}
pll if_cut(pll top, pll bot) {
	auto [s1, t1] = top;
	auto [s2, t2] = bot;
	return {s1 + s2, t1};
}
pll if_noncut(pll top, pll bot) {
	auto [s1, t1] = top;
	auto [s2, t2] = bot;
	return {s1 + s2 + 2 * t1 * t2, t1 + t2};
}
__attribute__((no_sanitize_undefined)) ll det(pll a, pll b, pll c) {
	a.first -= c.first;
	a.second -= c.second;
	b.first -= c.first;
	b.second -= c.second;
	ld ret = (a.first * (ld)b.second - a.second * (ld)b.first);
	if (ret > 1e18) return 1;
	if (ret < -1e18) return -1;
	return a.first * b.second - a.second * b.first;
}
void clear(vector <pll> &x) {
	sort(x.begin(), x.end());
	unq(x);
	// return;
	vector <pll> ans;
	for (pll p : x) {
		while (ans.size() >= 2u && det(p, ans.end()[-1], ans.end()[-2]) >= 0) ans.pop_back();
		if (ans.empty() || ans.back().second > p.second) ans.push_back(p);
	}
	assert(x.size() >= ans.size());
	if (ans.size() < x.size()) debug(imie(x), imie(ans));
	x = move(ans);
}
res_t merge(const res_t &me, const res_t &child) {//Called n - 1 times per testcase
	res_t ans(me.size() + child.size());
	REP(i, me.size()) REP(j, child.size()) {
		//cut
		for (auto a : me[i]) for (auto b : child[j]) ans[i + j].push_back(if_noncut(a, b));
		//noncut
		for (auto a : me[i]) for (auto b : child[j]) ans[i + j + 1].push_back(if_cut(a, b));
	}
	for (auto &x : ans) clear(x);
	return ans;
}
vector <ll> extract(const res_t &r) {
	vector <ll> ans(r.size(), numeric_limits<ll>::max());
	REP(i, r.size()) for (auto &x : r[i]) mini(ans[i], x.first);
	return ans;
}
struct solve {
	vi a;
	vector <vi> graph;
	res_t dfs(int x, int y = -1) {
		res_t ans = make(a[x]);
		for (int v : graph[x])
			if (v != y)
				ans = merge(ans, dfs(v, x));
		return ans;
	}
	void run() {
		int n;
		scanf("%d", &n);
		a.resize(n + 1);
		for (int i = 1; i <= n; ++i) scanf("%d", &a[i]);
		graph.resize(n + 1);
		REP(_, n - 1) {
			int x, y;
			scanf("%d%d", &x, &y);
			graph[x].push_back(y);
			graph[y].push_back(x);
		}
		debug(draw_tree(1, graph, node_arrays(a)));
		auto get = extract(dfs(1));
		assert((int) get.size() == n);
		for (ll c : get) printf("%lld ", c);
		printf("\n");
	}
};
int main() {
	// unt seed = TIME; debug(imie(seed));srand(seed);
	int t = 1;
	scanf("%d", &t);
	REP(_, t) solve().run();
	exit(0);
}
//#STAY AT HOME