#include <bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/rope>
using namespace std;
using namespace __gnu_pbds;
using namespace __gnu_cxx;
// /*
// //////////**DEFINES - START**//////////
#define ret return
#define fi first
#define se second
#define mp make_pair
#define all(x) x.begin(), x.end()
#define be(x) x.begin()
#define en(x) x.end()
#define sz(x) ll(x.size())
#define for0(i, n) for (ll i = 0; i < (n); ++i)
#define for1(i, n) for (ll i = 1; i < (n); ++i)
#define rfor0(i, n) for (ll i = (n) - 1; i >= 0; --i)
#define rfor1(i, n) for (ll i = (n) - 1; i >= 1; --i)
#define rep(i, a, n) for (ll i = a; i < ll(n); ++i)
#define rrep(i, a, n) for (ll i = a - 1; i >= ll(n); --i)
#define popcount __builtin_popcount
#define popcountll __builtin_popcountll
#define fastIO() ios::sync_with_stdio(0); cin.tie(0); cout.tie(0);
#define con continue
#define pb push_back
#define pob pop_back
#define deb(x) cout << (#x) << " is " << (x) << endl
#define ins insert
#define len(s) (s).length()
#define gi greater<int>()
#define gll greater<ll >()
#define gstr greater<string>()
#define gpll greater<pair<ll , ll >>()
#define rast(x1, y1, x2, y2) sqrt((x1-x2)*(x1-x2)+(y1-y2)*(y1-y2))
#define rev reverse
#define ub upper_bound
#define lb lower_bound
#define bs binary_search
#define rs resize
#define last(a) a.back()
#define co count
#define ba(a) a.back()
#define um unordered_map
#define rsun(a) a.resize(unique(a.begin(), a.end())-a.begin())
#define endl '\n'
#ifdef OG_Matveychick1
bool local = true;
#else
bool local = false;
#endif
// \\\\\\\\\\**DEFINES - END**\\\\\\\\\\
// */
// /*
// //////////**TYPEDEFS - START**//////////
typedef vector<int> vi;
typedef vector<vi> vvi;
typedef vector<char> vc;
typedef pair<int, int> pii;
typedef vector<pii> vpii;
typedef vector<string> vs;
typedef long long ll;
typedef unsigned long long ull;
typedef vector<ull> vull;
typedef pair<ll, ll> pll;
typedef vector<ll> vll;
typedef vector<pll> vpll;
typedef pair<double, double> pdd;
typedef double ld;
typedef double D;
typedef vector<ld> vld;
typedef vector<pair<ld, ld>>
vpld;
typedef string str;
typedef set<ll> sll;
typedef set<int> si;
typedef set<str> ss;
typedef set<pii> spii;
typedef multiset<int> msi;
typedef multiset<ll> msll;
typedef multiset<str> mss;
typedef multiset<pii> mspii;
typedef multiset<pll> mspll;
typedef map<str, str> mps;
typedef map<int, int> mpi;
typedef map<ll, ll> mpll;
typedef map<int, vi> mpvi;
typedef map<int, vll> mpvll;
typedef map<char, int> mpci;
typedef multimap<ll, ll> mmpll;
typedef multimap<str, str> mmps;
typedef multimap<int, int> mmpi;
typedef vector<vector<int>> vvi;
typedef vector<vector<ll>> vvll;
typedef vector<vector<long double>> vvld;
typedef vector<vvi> vvvi;
typedef vector<vector<char>> vvc;
typedef vector<vs> vvs;
typedef vector<D> vD;
typedef set<pair<ll, ll>>
spll;
typedef pair<ull, ull> pull;
typedef vector<pull> vpull;
typedef vector<bool> vb;
typedef vector<vb> vvb;
typedef set<char> sc;
typedef queue<int> qi;
typedef queue<ll> qll;
typedef queue<bool> qb;
typedef vector<sll> vsll;
typedef queue<pair<ll, ll>>
qpll;
typedef vector<vector<pair<int, int>>>
vvpii;
typedef vector<vector<pair<ll, ll>>>
vvpll;
typedef vector<spll> vspll;
typedef multiset<char> msc;
typedef queue<str> qs;
typedef vector<set<int>> vsi;
typedef priority_queue<ll> pqll;
typedef vector<vsll> vvsll;
typedef pair<ld, ld> pld;
typedef vector<vvll> vvvll;
typedef set<ld> sld;
typedef vector<vpld> vvpld;
typedef tree<ll, null_type, less<ll>, rb_tree_tag, tree_order_statistics_node_update>
ordered_set;
typedef tree<ll, null_type, less_equal<ll>, rb_tree_tag, tree_order_statistics_node_update>
ordered_multiset;
// \\\\\\\\\\**TYPEDEFS - END**\\\\\\\\\\
// */
// /*
// //////////**CONSTANTS - START**//////////
const ld pi = acosl(-1);
const ll mod1 = 1e9 + 7;
const ll mod2 = 998244353;
const ll MAXLL = 9223372036854775807;
//const ll MAXINT = 2147483647;
const ld eps = 1e-6;
// \\\\\\\\\\**CONSTANTS - END**\\\\\\\\\\
// */
// /*
// //////////**TEMPLATES - START**//////////
template<typename T>
istream &operator>>(istream &in, vector<T> &a) {
for (T &i: a) in >> i;
return in;
}
template<typename T1, typename T2>
istream &operator>>(istream &in, pair<T1, T2> &a) {
in >> a.fi >> a.se;
return in;
}
template<typename T1, typename T2>
ostream &operator<<(ostream &out, pair<T1, T2> a) {
out << a.fi << " " << a.se;
return out;
}
template<typename T1, typename T2>
istream &operator>>(istream &in, vector<pair<T1, T2>>
&a) {
for (
pair<T1, T2> &i
: a)
in >> i.fi >> i.
se;
return
in;
}
template<typename T>
ostream &operator<<(ostream &out, const vector<T> &a) {
for (auto i: a) {
out << i << " ";
}
return out;
}
template<typename T1, typename T2>
ostream &operator<<(ostream &out, vector<pair<T1, T2>>
&a) {
for (
pair<T1, T2> i
: a)
out << i.fi << " " << i.se <<
endl;
return
out;
}
template<typename T1>
ostream &operator<<(ostream &out, vector<vector<T1>> &a) {
for (vector<T1> i: a) {
for (T1 j: i) out << j << " ";
out << endl;
}
return out;
}
template<typename T1, typename T2>
inline T1 min(T1 a, T2 b) {
b = (T1) b;
return a > b ? b : a;
}
template<typename T1, typename T2>
inline T1 max(T1 a, T2 b) {
b = (T1) b;
return a > b ? a : b;
}
template<typename T1, typename T2>
inline void amin(T1 &a, T2 b) {
a = min(a, b);
}
template<typename T1, typename T2>
inline void amax(T1 &a, T2 b) {
a = max(a, b);
}
// \\\\\\\\\\**TEMPLATES - END**\\\\\\\\\\
// */
// This bear is a good alternative to duck!!!
/*
???? ??????
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??? ???????????? ??
??????????????????
??????????????? ?
?????????????????
??????? ??? ??
???? ??????????
???? ?? ???
???????????? ?????
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???????? ?? ???????
??????? ?????
*/
ld getTime() {
return (ld) clock() / (ld) CLOCKS_PER_SEC;
}
mt19937_64 rn(chrono::steady_clock::now().time_since_epoch().count());
//mt19937_64 rn(4);
ll rnd(ll l, ll r) {
ll a = rn() % (r - l + 1) + l;
return a;
}
void solve();
ll T = 1;
signed main(int argc, char **argv) {
// setlocale(LC_ALL, "RUS");
fastIO()
cout.precision(12);
cout << fixed;
if (local && argc == 1) {
freopen("input.txt", "r", stdin);
// freopen("output.txt", "w", stdout);
}
// cin >> T;
while (T--) {
solve();
}
if (local && argc == 1) {
cout << endl << fixed << "time = " << getTime();
}
return 0;
}
/*
___ __ __ ______ __ _____ __ __ __ __
/ | _____/ /___ ______ _/ / / ____/___ ____/ /__ / ___// /_____ ______/ /______ / / / /__ ________
/ /| |/ ___/ __/ / / / __ `/ / / / / __ \/ __ / _ \ \__ \/ __/ __ `/ ___/ __/ ___/ / /_/ / _ \/ ___/ _ \
/ ___ / /__/ /_/ /_/ / /_/ / / / /___/ /_/ / /_/ / __/ ___/ / /_/ /_/ / / / /_(__ ) / __ / __/ / / __/
/_/ |_\___/\__/\__,_/\__,_/_/ \____/\____/\__,_/\___/ /____/\__/\__,_/_/ \__/____/ /_/ /_/\___/_/ \___/
*/
struct ST {
vll t;
ll n;
ST(ll n) : n(n), t(4 * n, -1) {}
void update(ll l, ll r, ll x) {
update(1, 0, n, l, r, x);
}
void push(ll v) {
if (t[v] != -1) t[v * 2] = t[v * 2 + 1] = t[v], t[v] = -1;
}
void update(ll v, ll l, ll r, ll L, ll R, ll x) {
if (l >= R || r <= L) ret;
if (l >= L && r <= R) {
t[v] = x;
ret;
}
push(v);
ll m = (l + r) / 2;
update(v * 2, l, m, L, R, x);
update(v * 2 + 1, m, r, L, R, x);
}
ll get(ll p) {
ret get(1, 0, n, p);
}
ll get(ll v, ll l, ll r, ll p) {
if (l > p || r <= p) ret -1;
if (l + 1 == r) ret t[v];
ll m = (l + r) / 2;
push(v);
ll rt = max(get(v * 2, l, m, p), get(v * 2 + 1, m, r, p));
if (rt == -1) ret t[v];
else
ret rt;
}
};
const ll N = 1e5 + 5, K = 20;
ll n, a[N], s[N], up[K][N], in[N], ou[N], ti, hd[N], d[N], f[N];
pll e[N];
vll g[N];
void dfs1(ll v, ll p) {
up[0][v] = p;
for0(i, K - 1) up[i + 1][v] = up[i][up[i][v]];
if (p != v) g[v].erase(find(all(g[v]), p));
s[v] = 1;
for (auto x: g[v]) {
if (x == p) con;
d[x] = d[v] + 1;
dfs1(x, v);
s[v] += s[x];
}
sort(all(g[v]), [&](ll x, ll y) { ret s[x] > s[y]; });
}
void dfs2(ll v, ll h) {
in[v] = ti++;
hd[v] = h;
for (auto x: g[v]) dfs2(x, (x == g[v][0] ? h : x));
ou[v] = ti;
}
bool is_p(ll u, ll v) {
ret in[u] <= in[v] && ou[u] >= ou[v];
}
ll lca(ll u, ll v) {
if (u == v) ret u;
if (in[u] > in[v]) swap(u, v);
rfor0(i, K) if (!is_p(up[i][v], u)) v = up[i][v];
ret up[0][v];
}
void update(ll p, ll x) {
for (; p < N; p += p & -p) f[p] += x;
}
ll get(ll p) {
ll ans = 0;
for (; p; p -= p & -p) ans += f[p];
ret ans;
}
ll get(ll l, ll r) {
ret get(r) - get(l - 1);
}
ll la(ll v, ll k) {
for0(i, K) if ((k >> i) & 1) v = up[i][v];
ret v;
}
void solve() {
cin >> n;
for0(i, n) cin >> a[i];
vll _a;
for0(i, n) _a.pb(a[i]);
sort(all(_a));
rsun(_a);
for0(i, n) a[i] = lb(all(_a), a[i]) - be(_a) + 1;
for1(i, n) {
ll u, v;
cin >> u >> v;
u--;
v--;
e[i - 1] = {u, v};
g[u].pb(v);
g[v].pb(u);
}
dfs1(0, 0);
dfs2(0, 0);
ST t(n);
t.update(0, 1, 0);
for0(i, n - 1) {
auto [u, v] = e[i];
ll w = 0;
ll lst = -1;
ll ans = 0;
vpll pl;
while (1) {
ll nxt = lca(u, t.get(in[w]));
ll cnt = d[nxt] - lst;
ans += cnt * get(a[t.get(in[w])] + 1, N - 1);
update(a[t.get(in[w])], cnt);
pl.pb({a[t.get(in[w])], cnt});
lst = d[nxt];
if (nxt == u) break;
w = la(u, d[u] - d[nxt] - 1);
}
cout << ans << endl;
for (auto [p, x]: pl) update(p, -x);
w = v;
while (1) {
t.update(in[hd[w]], in[w] + 1, v);
if (hd[w] == 0) break;
w = up[0][hd[w]];
}
}
}
