Language: C++

#include <stdio.h>
#include <sstream>
#include <string.h>
#include <vector>
#include <map>
#include <algorithm>
#include <utility>
#include <set>
#include <cctype>
#include <queue>
#include <stack>
#include <cstdio>
#include <cstdlib>
#include <cmath>
#include <deque>
#include <limits>
#include <iomanip>
#include <ctype.h>
#include <unordered_map>
#include <random>
#include <numeric>
#include <iostream>
#include <array>

#define _USE_MATH_DEFINES
#include <iostream>
#include <math.h>

using namespace std;

typedef long long ll;
typedef pair<int, int> pii;
typedef pair<ll, ll> pll;
typedef pair<ll, double> pld;
typedef pair<double, double> pdd;
typedef pair<double, ll> pdl;
typedef pair<int, char> pic;
typedef vector<ll> vl;
typedef vector<int> vi;
typedef priority_queue<ll, vector<ll>, greater<ll>> llgreaterq;
typedef priority_queue<pll, vector<pll>, greater<pll>> pllgreaterq;
typedef priority_queue<pair<ll, pll>, vector<pair<ll, pll>>, greater<pair<ll, pll>>> plpllgreaterq;
typedef priority_queue<vi, vector<vi>, greater<vi>> vigreaterq;
typedef priority_queue<vl, vector<vl>, greater<vl >> vlgreaterq;

template <class o, class p, class q>
using tuple3q = priority_queue<tuple<o, p, q>, vector<tuple<o, p, q>>, greater<tuple<o, p, q>>>;

template <class o, class p, class q, class r>
using tuple4q = priority_queue<tuple<o, p, q, r>, vector<tuple<o, p, q, r>>, greater<tuple<o, p, q, r>>>;

template <class o, class p, class q, class r, class s>
using tuple5q = priority_queue<tuple<o, p, q, r, s>, vector<tuple<o, p, q, r, s>>, greater<tuple<o, p, q, r, s>>>;

int dx[] = { -1,0,1,0 };
int dy[] = { 0,-1,0,1 };

#define bit(x,v) ((ll)x << v)
#define rep(x,n) for(ll x = 0;x < n;x++)
#define rep2(x,f,v) for(ll x=f;x<v;x++)
#define repe(v,x) for(auto v : x)

/* Allowable error: ε */
#define EPS (1e-10)

/* Two scalars are equal */
#define EQ(a,b) (std::abs(a-b) < EPS)

/* Two vector are equal */
#define EQV(a,b) ( EQ((a).real(), (b).real()) && EQ((a).imag(), (b).imag()) )

#define all(a) a.begin(),a.end()
#define all0(a) memset(a,0,sizeof(a))
#define allm1(a) memset(a,-1,sizeof(a))

#define put_float(v) 	cout << fixed << setprecision(10); \
						cout << v << endl
#define put(v) cout << v << endl

#define vinsert(v,p,x) v.insert(v.begin() + p,x)
#define vsort(v) sort(all(v));
#define vdesc(v) vsort(v); \
				 reverse(all(v))

#define dup(v) v.erase(unique(all(v)),v.end())
#define ion(i,j) ((i & (1LL << j)) > 0)
#define next(i) i++;i%=2
#define Len size()
#define ull unsignd long long

#define psp(a,b) push_back(make_pair(a,b))
#define psp2(a,b) push(make_pair(a,b))

#define cini(a) a; cin >> a

#define infa(a,b) (a + b) % INF
#define infm(a,b) (a * b) % INF
#define infd(a,b) (a * modinv(b)) % INF
#define infs(a,b) (a + INF - b) % INF
#define inf(a) (a) %= INF
#define inff(a) ((a) % INF)

#define No cout << "No" << endl
#define Yes cout << "Yes" << endl
#define NO cout << "NO" << endl
#define YES cout << "YES" << endl

#define smal -INF*INF
#define big INF*INF

const ll INF = 1000000007;
const int MAX = 2000010;
const int MOD = 1000000007;

long long fac[MAX], finv[MAX], inv[MAX];

void COMinit() {
	fac[0] = fac[1] = 1;
	finv[0] = finv[1] = 1;
	inv[1] = 1;

	for (int i = 2; i < MAX; i++) {

		fac[i] = fac[i - 1] * i % MOD;
		inv[i] = MOD - inv[MOD % i] * (MOD / i) % MOD;
		finv[i] = finv[i - 1] * inv[i] % MOD;
	}
}

/* Binomial coefficient calculation */
long long COM(int n, int k) { 

	if (n < k) return 0;
	if (n < 0 || k < 0) return 0;

	return fac[n] * (finv[k] * finv[n - k] % MOD) % MOD;
}

ll getpow(ll b, ll x, ll md) {

	ll t = b;
	ll res = 1;

	while (x > 0)
	{
		if (x & 1) {
			res *= t;
			res %= md;
		}

		x >>= 1;
		t *= t;
		t %= md;
	}
	return res;
}
ll getpow(ll b, ll x) {

	return getpow(b, x, INF);
}
ll modinv(ll x) {
	return getpow(x, INF - 2);
}
ll gcd(ll a, ll b) {

	if (b == 0) return a;
	return gcd(b, a % b);
}

class mint {
	int md = 1000000007;

public:
	long long x;
	mint(ll x, ll md) {
		this->md = md;
		this->x = (x % md + md) % md;
	}

	mint(long long x = 0) : x((x% md + md) % md) {}
	mint operator-() const {
		return mint(-x);
	}

	mint& operator+=(const mint& a) {
		if ((x += a.x) >= md) x -= md;
		return *this;
	}

	mint& operator-=(const mint& a) {
		if ((x += md - a.x) >= md) x -= md;
		return *this;
	}

	mint& operator*=(const  mint& a) {
		(x *= a.x) %= md;
		return *this;
	}

	mint operator+(const mint& a) const {
		mint res(*this);
		return res += a;
	}

	mint operator-(const mint& a) const {
		mint res(*this);
		return res -= a;
	}

	mint operator*(const mint& a) const {
		mint res(*this);
		return res *= a;
	}

	mint pow(ll t) const {
		if (!t) return 1;
		mint a = pow(t >> 1);
		a *= a;
		if (t & 1) a *= *this;
		return a;
	}

	/* for prime mod */
	mint inv() const {
		return pow(md - 2);
	}

	mint& operator/=(const mint& a) {
		return (*this) *= a.inv();
	}

	mint operator/(const mint& a) const {
		mint res(*this);
		return res /= a;
	}

	friend ostream& operator<<(ostream& os, const mint& m) {
		os << m.x;
		return os;
	}
};

int pr[100010];
int lank[100010];

void uini(int n) {

	for (size_t i = 0; i <= n; i++)
	{
		pr[i] = i;
		lank[i] = 1;
	}
}

int parent(int x) {

	if (x == pr[x]) return x;
	return pr[x] = parent(pr[x]);
}

int same(int x, int y) {
	return parent(x) == parent(y);
}

bool unit(int x, int y) {

	int px = parent(x);
	int py = parent(y);

	if (px == py) return false;
	if (lank[py] < lank[px]) {

		pr[py] = px;
		lank[px] += lank[py];
	}
	else {
		pr[px] = py;
		lank[py] += lank[px];
	}

	return true;
}

ll n, m;
int ci = 0;

struct Node {
	int key;
	int priority;

	Node* parent, *left, *right;
	Node(int key, int priority);
	Node() {}
};

Node NIL;
Node::Node(int key, int priority) : key(key), priority(priority) {

	left = &NIL;
	right = &NIL;
}

Node* root = new Node();

void cenrec(Node* k) {

	if (k->key == NIL.key) return;
	cenrec(k->left);

	cout << " " << k->key;
	cenrec(k->right);
}
void fastrec(Node* k) {
 
	if (k->key == NIL.key) return;

	cout << " " << k->key;
	fastrec(k->left);
	fastrec(k->right);
}

void insert(Node* v) {

	Node* y = &NIL;
	Node* x = root;

	while (x->key != NIL.key) {
		y = x;

		if (v->key < x->key) {
			x = x->left;
		}

		else {
			x = x->right;
		}
	}

	v->parent = y;
	if (y->key == NIL.key) {
		root = v;
	}

	else if (v->key < y->key) {
		y->left = v;
	}

	else {
		y->right = v;
	}

}

Node* find(Node* k, ll v) {

	if (k->key == NIL.key) return &NIL;
	if (k->key == v) return k;
	if (v < k->key) return find(k->left, v);

	return find(k->right, v);
}

void delp12(Node* x) {

	if (x->key == NIL.key)  return;
	Node* l = x->left;
	Node* r = x->right;
	Node* pr = x->parent;

	if (l->key == NIL.key
		&& r->key == NIL.key) {

		if (pr->left == x) {
			pr->left = &NIL;
		}

		else pr->right = &NIL;
	}

	else if (l->key != NIL.key) {

		if (pr->left == x) {
			pr->left = l;
		}

		else pr->right = l;
		l->parent = pr;
	}

	else if (r->key != NIL.key) {

		if (pr->left == x) {

			pr->left = r;
		}

		else pr->right = r;
		r->parent = pr;
	}
}

Node* get_next(Node* k) {

	if (k->key == NIL.key) return &NIL;
	Node* res = get_next(k->left);

	if (res->key != NIL.key) return res;
	return k;
}

void del(Node* x) {

	if (x->key == NIL.key) return;
	Node* l = x->left;
	Node* r = x->right;
	Node* pr = x->parent;

	if (l->key != NIL.key && r->key != NIL.key) {

		Node* nex = get_next(r);
		x->key = nex->key;
		delp12(nex);
	}

	else {
		delp12(x);
	}
}

Node* rightRotate(Node* t) {

	Node* s = t->left;
	t->left = s->right;
	s->right = t;

	return s;
}

Node* leftRotate(Node* t) {

	Node* s = t->right;
	t->right = s->left;
	s->left = t;

	return s;
}

Node* _insert(Node* t, int key, int priority) {

	if (t->key == NIL.key) {
		return new Node(key, priority);
	}

	if (key == t->key) {
		return t;
	}

	if (key < t->key) {

		t->left = _insert(t->left, key, priority);
		if (t->priority < t->left->priority) {
			t = rightRotate(t);
		}
	}

	else {
		t->right = _insert(t->right, key, priority);

		if (t->priority < t->right->priority) {
			t = leftRotate(t);
		}
	}

	return t;
}

Node* delete1(Node* t, int key);
Node* _delete(Node* t, int key) {

	if (t->left->key == NIL.key && t->right->key == NIL.key) {
		return &NIL;
	}

	else if (t->left->key == NIL.key) {
		t = leftRotate(t);
	}

	else if (t->right->key == NIL.key) {
		t = rightRotate(t);
	}

	else {

		if (t->left->priority > t->right->priority) {
			t = rightRotate(t);
		}

		else
			t = leftRotate(t);
	}

	return delete1(t, key);
}

Node* delete1(Node* t, int key) {

	if (t->key == NIL.key) {
		return &NIL;
	}

	if (key < t->key) {
		t->left = delete1(t->left, key);
	}

	else if (key > t->key) {
		t->right = delete1(t->right, key);
	}

	else return _delete(t, key);
	return t;

int H;

int left(int i) {
	return i * 2 + 1;
}

int right(int i) {
	return i * 2 + 2;
}

class edge {

public:

	int from, to, i;
	ll val;
	edge() {}
	edge(ll to) : to(to) {}
	edge(ll to, ll i) : to(to), i(i) {}
	edge(ll from, ll to, ll val) : from(from), to(to), val(val) {}
};

class LCA {

private:

	vector<vector<edge>> v;
	vector<vector<int>> parent;
	vector<int> depth;

	void dfs(int n, int m, int d) {
		parent[0][n] = m;
		depth[n] = d;

		for (auto x : v[n]) {
			if (x.to != m) dfs(x.to, n, d + 1);
		}
	}

public:

	LCA(ll N, ll root, vector<vector<edge>>& tree) {
		v = tree;

		parent = vector<vector<int>>(21, vector<int>(N + 1, 0));
		depth = vector<int>(N + 1, 0);
		dfs(root, -1, 0);

		for (int j = 0; j + 1 < 20; j++) {
			for (int i = 1; i <= N; i++) {
				if (parent[j][i] < 0) parent[j + 1][i] = -1;
				else parent[j + 1][i] = parent[j][parent[j][i]];
			}
		}
	}

	int lca(int n, int m) {

		if (depth[n] > depth[m]) swap(n, m);

		for (int j = 0; j < 20; j++) {

			if ((depth[m] - depth[n]) >> j & 1) m = parent[j][m];
		}

		if (n == m) return n;

		for (int j = 19; j >= 0; j--) {

			if (parent[j][n] != parent[j][m]) {
				n = parent[j][n];
				m = parent[j][m];
			}
		}

		return parent[0][n];

	}

	int dep(int n) { return depth[n]; }
};

ll k;
int _rank[1010];
int temp[1010];

bool compare_sa(int i, int j) {

	if (_rank[i] != _rank[j]) return _rank[i] < _rank[j];

	else {
		int ri = i + k <= n ? _rank[i + k] : -1;
		int rj = j + k <= n ? _rank[j + k] : -1;

		return ri < rj;
	}
}

void construct_sa(string S, int* sa) {
	n = S.length();

	for (size_t i = 0; i <= n; i++) {
		sa[i] = i;
		_rank[i] = i < n ? S[i] : -1;
	}

	for (k = 1; k <= n; k *= 2) {
		sort(sa, sa + n + 1, compare_sa);

		/* "sa" is Prefix order after sorting, "rank" is Updated with the original position index preserved */
		/* ? */
		temp[sa[0]] = 0;

		for (size_t i = 1; i <= n; i++)
		{
			temp[sa[i]] = temp[sa[i - 1]] + (compare_sa(sa[i - 1], sa[i]) ? 1 : 0);
		}

		for (size_t i = 0; i <= n; i++)
		{
			_rank[i] = temp[i];
		}
	}
}

bool contain(string S, int* sa, string T) {

	int a = 0, b = S.length();
	/* "sa" is The prefixes are arranged in dictionary order, index for that position inside */

	while (b - a > 1) {

		int c = (a + b) / 2;
		if (S.compare(sa[c], T.length(), T) < 0) a = c;
		else b = c;
	}

	return S.compare(sa[b], T.length(), T) == 0;
}


#define bit(x,v) ((ll)x << v)

class BIT {

	static const int MAX_N = 500010;
public:

	BIT() { memset(bit, 0, sizeof(bit)); }

	ll bit[MAX_N + 1], n;
	ll sum(int i) {
		ll s = 0;

		while (i > 0)
		{
			s += bit[i];
			i -= i & -i;
		}
		return s;
	}

	void add(int i, int x) {

		while (i <= n)
		{
			bit[i] += x;
			i += i & -i;
		}
	}


};

struct UnionFind {

	vector<int> A;
	UnionFind(int n) : A(n, -1) {}

	int find(int x) {

		if (A[x] < 0) return x;
		return A[x] = find(A[x]);
	}

	void unite(int x, int y) {
		x = find(x), y = find(y);

		if (x == y) return;
		if (A[x] > A[y]) swap(x, y);
		A[x] += A[y];
		A[y] = x;
	}

	int ngroups() {

		int ans = 0;
		for (auto a : A) if (a < 0) ans++;
		return ans;
	}
};

vector<ll> getp(ll n) {

	vector<ll> res;
	ll a = 2;

	if (n % 2 == 0) {
		res.push_back(2);
		while (n % 2 == 0)n /= 2;
	}

	for (ll i = 3; i * i <= n; i += 2) {

		if (n % i == 0) {
			res.push_back(i);
			while (n % i == 0)n /= i;
		}
	}

	if (n != 1) res.push_back(n);
	return res;
}

vector<ll> getp2(ll n) {

	vector<ll> res;
	ll a = 2;

	if (n % 2 == 0) {

		while (n % 2 == 0) { n /= 2; res.push_back(2); }
	}

	for (ll i = 3; i * i <= n; i += 2) {

		if (n % i == 0) {

			while (n % i == 0) { n /= i; res.push_back(i); }
		}
	}

	if (n != 1) res.push_back(n);
	return res;
}

vector<pll> getp3(ll n) {
	vector<pll> res;
	ll a = 2;

	int si = 0;
	if (n % 2 == 0) {

		res.push_back(make_pair(2, 0));
		while (n % 2 == 0) { n /= 2; res[si].second++; }
		si++;
	}

	for (ll i = 3; i * i <= n; i += 2) {

		if (n % i == 0) {
			res.push_back(make_pair(i, 0));
			while (n % i == 0) { n /= i; res[si].second++; }
			si++;
		}
	}

	if (n != 1) { res.push_back(make_pair(n, 1)); }
	return res;
}

vector<ll> getDivisors(ll n) {

	vector<ll> res;
	ll a = 2;

	res.push_back(1);
	for (ll i = 2; i * i <= n; i++) {

		if (n % i == 0) {
			res.push_back(i);
			if (n / i != i)
				res.push_back(n / i);
		}
	}
	return res;
}

struct ve {
public:

	vector<ve> child;
	int _t = INF;
	ve(int t) :_t(t) {}
	ve(ve _left, ve _right) {
		_t = _left._t + _right._t;
		child.push_back(_left);
		child.push_back(_right);
	}

	bool operator<(const ve& t) const {
		return _t > t._t;
	}
};

vector<bool> elas(ll n) {
	vector<bool> r(n);
	fill(r.begin(), r.end(), 1);

	r[0] = 0;
	r[1] = 0;

	for (ll i = 2; i * i < n; i++) {

		if (!r[i]) continue;
		ll ti = i * 2;
		while (ti < n)
		{
			r[ti] = false;
			ti += i;
		}
	}
	return r;
}

bool isPrime(ll v) {

	for (ll i = 2; i * i <= v; i++) {

		if (v % i == 0) return false;
	}
	return true;
}


class SegTree {

public:
	const static int MAX_N = 100010;
	const static int DAT_SIZE = (1 << 18) - 1;
	int N, Q;
	int A[MAX_N];


	ll data[DAT_SIZE], datb[DAT_SIZE];
	void init(int _n) {

		N = 1;
		while (N < _n) N <<= 1;
		memset(data, 0, sizeof(data));
		memset(datb, 0, sizeof(datb));
	}

	void init(int _n, ll iv) {

		N = 1;
		while (N < _n) N <<= 1;
		rep(i, DAT_SIZE) {
			data[i] = iv;
			datb[i] = iv;
		}
	}

	void add(int a, int b, int x) {
		add(a, b + 1, x, 0, 0, N);
	}

	void add(int a, int b, int x, int k, int l, int r) {

		if (a <= l && r <= b) {
			data[k] += x;
		}
		else if (l < b && a < r) {
			datb[k] += (min(b, r) - max(a, l)) * x;
			add(a, b, x, k * 2 + 1, l, (l + r) / 2);
			add(a, b, x, k * 2 + 2, (l + r) / 2, r);
		}
	}

	void change(int a, int b, int x) {
		change(a, b + 1, x, 0, 0, N);
	}

	void change(int a, int b, int x, int k, int l, int r) {

		if (a <= l && r <= b) {
			data[k] = x;
		}
		else if (l < b && a < r) {
			datb[k] = x;
			change(a, b, x, k * 2 + 1, l, (l + r) / 2);
			change(a, b, x, k * 2 + 2, (l + r) / 2, r);
		}
	}

	ll sum(int a, int b) {
		return sum(a, b + 1, 0, 0, N);
	}

	ll sum(int a, int b, int k, int l, int r) {
		if (b <= l || r <= a) {
			return 0;
		}

		if (a <= l && r <= b) {
			return data[k] * (r - l) + datb[k];
		}

		ll res = (min(b, r) - max(a, l)) * data[k];
		res += sum(a, b, k * 2 + 1, l, (l + r) / 2);
		res += sum(a, b, k * 2 + 2, (l + r) / 2, r);
		return res;
	}
};

class Segment;
class Circle;

class Point {
public:

	double x, y;

	Point(double x = 0, double y = 0) :x(x), y(y) {}

	Point operator + (Point p) { return Point(x + p.x, y + p.y); }
	Point operator - (Point p) { return Point(x - p.x, y - p.y); }
	Point operator * (double a) { return Point(a * x, a * y); }
	Point operator / (double a) { return Point(x / a, y / a); }

	double abs() { return sqrt(norm()); }
	double norm() { return x * x + y * y; }

	bool operator < (const Point& p)const {
		return x != p.x ? x < p.x : y < p.y;
	}

	bool operator == (const Point& p) const {
		return fabs(x - p.x) < EPS && fabs(y - p.y) < EPS;
	}

	static double dot(Point a, Point b) {
		return a.x * b.x + a.y * b.y;
	}

	static double cross(Point a, Point b) {
		return a.x * b.y - a.y * b.x;
	}

	static bool isOrthogonal(Point a, Point b) {
		return EQ(dot(a, b), 0.0);
	}

	static bool isOrthogonal(Point a1, Point a2, Point b1, Point b2) {
		return isOrthogonal(a1 - a2, b1 - b2);
	}

	static bool isOrthogonal(Segment s1, Segment s2);

	static bool isPalallel(Point a, Point b) {
		return EQ(cross(a, b), 0.0);
	}

	static bool isPalallel(Point a1, Point a2, Point b1, Point b2) {
		return isPalallel(a1 - a2, b1 - b2);
	}

	static bool isPalallel(Segment s1, Segment s2);

	static const int COUNTER_CLOCKWISE = 1;
	static const int CLOCKWISE = -1;
	static const int ONLINE_BACK = 2;
	static const int ONLINE_FRONT = -2;
	static const int ON_SEGMENT = 0;
	static int ccw(Point p0, Point p1, Point p2) {

		/* Line segment is p0& p1.    find out where p2 is */
		Point a = p1 - p0;
		Point b = p2 - p0;

		if (cross(a, b) > EPS) return COUNTER_CLOCKWISE;
		if (cross(a, b) < -EPS) return CLOCKWISE;
		if (dot(a, b) < -EPS) return ONLINE_BACK;
		if (a.norm() < b.norm()) return ONLINE_FRONT;
		return ON_SEGMENT;
	}

	static bool intersect(Point p1, Point p2, Point p3, Point p4) {

		return (ccw(p1, p2, p3) * ccw(p1, p2, p4) <= 0
			&& ccw(p3, p4, p1) * ccw(p3, p4, p2) <= 0);
	}

	static bool intersect(Segment s1, Segment s2);
	static Point project(Segment s, Point p);
	static Point reflect(Segment s, Point p);
	static Point getDistance(Point a, Point b) {
		return (a - b).abs();
	}

	static double getDistanceLP(Segment s, Point p);
	static double getDistanceSP(Segment s, Point p);
	static double getDistance(Segment s1, Segment s2);
	static Point getIntersection(Segment s1, Segment s2);
	static pair<Point, Point> crossPoints(Circle c, Segment s);
	static int contains(vector<Point> g, Point p) {

		int n = g.size();
		bool x = false;

		rep(i, n) {
			Point a = g[i] - p, b = g[(i + 1) % n] - p;
			// On the line

			if (std::abs(cross(a, b)) < EPS && dot(a, b) < EPS) return 1;

			// Whether it is above or below "p"
			// Cross product is positive

			if (a.y > b.y) swap(a, b);
			if (a.y < EPS && EPS < b.y && cross(a, b) > EPS) x = !x;
		}

		return x ? 2 : 0;
	}

	static vector<Point> andrewScan(vector<Point> s) {
		vector<Point> u, l;

		if (s.size() < 3) return s;
		sort(all(s));
		u.push_back(s[0]);
		u.push_back(s[1]);
		l.push_back(s[s.size() - 1]);
		l.push_back(s[s.size() - 2]);

		for (int i = 2; i < s.size(); i++) {

			for (int _n = u.size(); _n >= 2 && ccw(u[_n - 2], u[_n - 1], s[i]) > CLOCKWISE; _n--) {
				u.pop_back();
			}
			u.push_back(s[i]);
		}

		for (int i = s.size() - 3; i >= 0; i--) {

			for (int _n = l.size(); _n >= 2 && ccw(l[_n - 2], l[_n - 1], s[i]) > CLOCKWISE; _n--) {
				l.pop_back();
			}
			l.push_back(s[i]);
		}

		reverse(all(l));
		for (int i = u.size() - 2; i >= 1; i--)
		{
			l.push_back(u[i]);
		}

		return l;
	}
	void get_cin() {
		cin >> x >> y;
	}
};

class Segment {
public:

	Point p1, p2;
	Segment() {}
	Segment(Point p1, Point p2) :p1(p1), p2(p2) {}

	void get_cin() {
		cin >> p1.x >> p1.y >> p2.x >> p2.y;
	}

	Point p1tp2() {
		return p2 - p1;
	}

	Point p2tp1() {
		return p1 - p2;
	}

	double abs() {
		return std::abs(norm());
	}

	double norm() {
		return (p2 - p1).norm();
	}
};

bool Point::isOrthogonal(Segment s1, Segment s2) {
	return EQ(dot(s1.p2 - s1.p1, s2.p2 - s2.p1), 0.0);
}

bool Point::isPalallel(Segment s1, Segment s2) {
	return EQ(cross(s1.p2 - s1.p1, s2.p2 - s2.p1), 0.0);
}

bool Point::intersect(Segment s1, Segment s2) {
	return intersect(s1.p1, s1.p2, s2.p1, s2.p2);
}

Point Point::project(Segment s, Point p) {

	Point base = s.p2 - s.p1;
	double r = Point::dot(p - s.p1, base) / base.norm();
	return s.p1 + base * r;
}

Point Point::reflect(Segment s, Point p) {
	return (project(s, p) * 2) - p;
}

double Point::getDistanceLP(Segment s, Point p) {
	return std::abs(cross(s.p2 - s.p1, p - s.p1) / (s.p2 - s.p1).abs());
}

double Point::getDistanceSP(Segment s, Point p) {

	if (dot(s.p2 - s.p1, p - s.p1) < 0.0) return (p - s.p1).abs();
	if (dot(s.p1 - s.p2, p - s.p2) < 0.0) return (p - s.p2).abs();
	return getDistanceLP(s, p);
}

double Point::getDistance(Segment s1, Segment s2) {

	if (intersect(s1, s2)) return 0.0;
	return min({ getDistanceSP(s1,s2.p1),getDistanceSP(s1,s2.p2)
		,getDistanceSP(s2,s1.p1),getDistanceSP(s2,s1.p2) });
}

Point Point::getIntersection(Segment s1, Segment s2) {

	// (s1.p1 - s2.p1).norm()
	auto bs = s1.p2 - s1.p1;
	auto n1 = s2.p1 - s1.p1;
	auto n2 = s2.p2 - s1.p1;
	auto c1 = std::abs(cross(n1, bs)) / bs.norm();
	auto c2 = std::abs(cross(n2, bs)) / bs.norm();
	return s2.p1 + (s2.p2 - s2.p1) * (c1 / (c1 + c2));

	// c1:c2=t:1-t
	// c2t=(1-t)c1
	// t/(1-t)=c1/(c1+c2)
}

double arg(Point p) { return atan2(p.y, p.x); }
Point polar(double a, double r) { return Point(cos(r) * a, sin(r) * a); }

class Circle {
public:

	Point c;
	double r;
	Circle(Point c = Point(), double r = 0.0) : c(c), r(r) {}

	void get_cin() {
		cin >> c.x >> c.y >> r;
	}

	static pair<Point, Point> getCrossPoints(Circle c1, Circle c2) {

		double d = (c1.c - c2.c).abs(); // Center point distance
		double a = acos((c1.r * c1.r + d * d - c2.r * c2.r) / (2 * c1.r * d));
		double t = arg(c2.c - c1.c);
		return make_pair(c1.c + polar(c1.r, t + a), c1.c + polar(c1.r, t - a));

	}
};

pair<Point, Point> Point::crossPoints(Circle c, Segment s) {

	auto pp = project(s, c.c);
	auto f = (pp - c.c).norm();
	auto mu = sqrt(c.r * c.r - f);
	auto e = s.p1tp2() / s.p1tp2().abs();
	return make_pair(pp + e * mu, pp - e * mu);

}

ll divRm(string s, ll x) {

	ll r = 0;
	for (ll i = 0; i < s.size(); i++) {
		r *= 10;
		r += s[i] - '0';
		r %= x;
	}
	return r;
}

ll cmbi(ll x, ll b) {

	ll res = 1;
	for (size_t i = 0; i < b; i++) {
		res *= x - i;
		res %= INF;
		res *= inv[b - i];
		res %= INF;
	}
	return res;
}

double digsum(ll x) {

	ll res = 0;
	while (x > 0) {
		res += x % 10;
		x /= 10;
	}

	return res;
}

bool check_parindrome(string s) {

	int n = s.size();
	rep(i, n / 2) {
		if (s[i] != s[n - i - 1]) {
			return false;
		}

	}
	return true;
}

ll npr(ll n, ll r) {

	if (r == 0)
		return 1;
	return inff(fac[n] * modinv(fac[n - r]));
}

vl zalgo(string s) {

	ll c = 0;
	vl a(s.size());
	ll si = s.size();
	rep2(i, 1, s.size()) {
		if (i + a[i - c] < c + a[c]) {
			a[i] = a[i - c];
		}

		else {
			ll j = max(0LL, a[c] - (i - c));
			while (i + j < si && s[j] == s[i + j])
			{
				j++;
			}

			a[i] = j;
			c = i;
		}

	}

	a[0] = s.size();
	return a;
}
string decStrNum(string s) {

	ll si = s.size();
	for (int i = si - 1; i >= 0; i--) {

		if (s[i] == '0') {
			s[i] = '9';
			continue;
		}

		s[i] = s[i] - 1;
		break;
	}
	return s;
}

//　Up to this library
// Code from here

void solv() {

	cin >> n;
	vector<ll> es[200010];
	rep(i, n - 1) {
		ll a, b;
		cin >> a >> b;
		es[a].push_back(b);
		es[b].push_back(a);
	}

	ll sum = 0;
	ll t = 0;

	rep2(i, 1, n + 1) {
		vsort(es[i]);
		auto p = lower_bound(all(es[i]), i) - es[i].begin();
		// If comes out, bottom element will increase by one
		if (p == 0)
			t++;
		else
			t -= (p - 1);
		sum += t;
	}

	ll res = sum;

	rep2(i, 1, n) {

		// element disappears from set
		// subtract appeared independently from sum
		auto p = lower_bound(all(es[i]), i) - es[i].begin();
		ll si = es[i].size();

		if (p < si) {
			sum -= es[i][p] - i;
		}

		else {
			sum -= n + 1 - i;
		}

		// num of divisions increases 2 or more are connected
		// Check AC subtracting from n+ 1
		// "2" both 2 and 4 n= 5
		// Is the AC

		rep2(j, p + 1, si) {
			sum += n + 1 - es[i][j];
		}

		res += sum;
	}

	cout << res << endl;
}


int main() {
	COMinit();
	solv();
	return 0;
}


Compiler output:
a.cc: In function 'Node* delete1(Node*, int)':
a.cc:524:17: error: a function-definition is not allowed here before '{' token
  524 | int left(int i) {
      |                 ^
a.cc:528:18: error: a function-definition is not allowed here before '{' token
  528 | int right(int i) {
      |                  ^
a.cc:608:31: error: a function-definition is not allowed here before '{' token
  608 | bool compare_sa(int i, int j) {
      |                               ^
a.cc:620:38: error: a function-definition is not allowed here before '{' token
  620 | void construct_sa(string S, int* sa) {
      |                                      ^
a.cc:647:43: error: a function-definition is not allowed here before '{' token
  647 | bool contain(string S, int* sa, string T) {
      |                                           ^
a.cc:667:26: error: local class 'class delete1(Node*, int)::BIT' shall not have static data member 'const int delete1(Node*, int)::BIT::MAX_N' [-fpermissive]
  667 |         static const int MAX_N = 500010;
      |                          ^~~~~
a.cc:724:23: error: a function-definition is not allowed here before '{' token
  724 | vector<ll> getp(ll n) {
      |                       ^
a.cc:746:24: error: a function-definition is not allowed here before '{' token
  746 | vector<ll> getp2(ll n) {
      |                        ^
a.cc:768:25: error: a function-definition is not allowed here before '{' token
  768 | vector<pll> getp3(ll n) {
      |                         ^
a.cc:793:30: error: a function-definition is not allowed here before '{' token
  793 | vector<ll> getDivisors(ll n) {
      |                              ^
a.cc:827:25: error: a function-definition is not allowed here before '{' token
  827 | vector<bool> elas(ll n) {
      |                         ^
a.cc:847:20: error: a function-definition is not allowed here before '{' token
  847 | bool isPrime(ll v) {
      |                    ^
a.cc:860:26: error: local class 'class delete1(Node*, int)::SegTree' shall not have static data member 'const int delete1(Node*, int)::SegTree::MAX_N' [-fpermissive]
  860 |         const static int MAX_N = 100010;
      |                          ^~~~~
a.cc:861:26: error: local class 'class delete1(Node*, int)::SegTree' shall not have static data member 'const int delete1(Node*, int)::SegTree::DAT_SIZE' [-fpermissive]
  861 |         const static int DAT_SIZE = (1 << 18) - 1;
      |                          ^~~~~~~~
a.cc:991:26: error: local class 'class delete1(Node*, int)::Point' shall not have static data member 'const int delete1(Node*, int)::Point::COUNTER_CLOCKWISE' [-fpermissive]
  991 |         static const int COUNTER_CLOCKWISE = 1;
      |                          ^~~~~~~~~~~~~~~~~
a.cc:992:26: error: local class 'class delete1(Node*, int)::Point' shall not have static data member 'const int delete1(Node*, int)::Point::CLOCKWISE' [-fpermissive]
  992 |         static const int CLOCKWISE = -1;
      |                          ^~~~~~~~~
a.cc:993:26: error: local class 'class delete1(Node*, int)::Point' shall not have static data member 'const int delete1(Node*, int)::Point::ONLINE_BACK' [-fpermissive]
  993 |         static const int ONLINE_BACK = 2;
      |                          ^~~~~~~~~~~
a.cc:994:26: error: local class 'class delete1(Node*, int)::Point' shall not have static data member 'const int delete1(Node*, int)::Point::ONLINE_FRONT' [-fpermissive]
  994 |         static const int ONLINE_FRONT = -2;
      |                          ^~~~~~~~~~~~
a.cc:995:26: error: local class 'class delete1(Node*, int)::Point' shall not have static data member 'const int delete1(Node*, int)::Point::ON_SEGMENT' [-fpermissive]
  995 |         static const int ON_SEGMENT = 0;
      |                          ^~~~~~~~~~
a.cc:1115:25: error: qualified-id in declaration before '(' token
 1115 | bool Point::isOrthogonal(Segment s1, Segment s2) {
      |                         ^
a.cc:1119:23: error: qualified-id in declaration before '(' token
 1119 | bool Point::isPalallel(Segment s1, Segment s2) {
      |                       ^
a.cc:1123:22: error: qualified-id in declaration before '(' token
 1123 | bool Point::intersect(Segment s1, Segment s2) {
      |                      ^
a.cc:1127:21: error: qualified-id in declaration before '(' token
 1127 | Point Point::project(Segment s, Point p) {
      |                     ^
a.cc:1134:21: error: qualified-id in declaration before '(' token
 1134 | Point Point::reflect(Segment s, Point p) {
      |                     ^
a.cc:1138:28: error: qualified-id in declaration before '(' token
 1138 | double Point::getDistanceLP(Segment s, Point p) {
      |                            ^
a.cc:1142:28: error: qualified-id in declaration before '(' token
 1142 | double Point::getDistanceSP(Segment s, Point p) {
      |                            ^
a.cc:1149:26: error: qualified-id in declaration before '(' token
 1149 | double Point::getDistance(Segment s1, Segment s2) {
      |                          ^
a.cc:1156:29: error: qualified-id in declaration before '(' token
 1156 | Point Point::getIntersection(Segment s1, Segment s2) {
      |                             ^
a.cc:1171:21: error: a function-definition is not allowed here before '{' token
 1171 | double arg(Point p) { return atan2(p.y, p.x); }
      |                     ^
a.cc:1172:33: error: a function-definition is not allowed here before '{' token
 1172 | Point polar(double a, double r) { return Point(cos(r) * a, sin(r) * a); }
      |                                 ^
a.cc: In static member function 'static std::pair<delete1(Node*, int)::Point, delete1(Node*, int)::Point> delete1(Node*, int)::Circle::getCrossPoints(delete1(Node*, int)::Circle, delete1(Node*, int)::Circle)':
a.cc:1189:28: error: 'arg' was not declared in this scope
 1189 |                 double t = arg(c2.c - c1.c);
      |                            ^~~
a.cc:1190:41: error: 'polar' was not declared in this scope
 1190 |                 return make_pair(c1.c + polar(c1.r, t + a), c1.c + polar(c1.r, t - a));
      |                                         ^~~~~
a.cc: In function 'Node* delete1(Node*, int)':
a.cc:1195:38: error: qualified-id in declaration before '(' token
 1195 | pair<Point, Point> Point::crossPoints(Circle c, Segment s) {
      |                                      ^
a.cc:1205:26: error: a function-definition is not allowed here before '{' token
 1205 | ll divRm(string s, ll x) {
      |                          ^
a.cc:1216:21: error: a function-definition is not allowed here before '{' token
 1216 | ll cmbi(ll x, ll b) {
      |                     ^
a.cc:1228:21: error: a function-definition is not allowed here before '{' token
 1228 | double digsum(ll x) {
      |                     ^
a.cc:1239:33: error: a function-definition is not allowed here before '{' token
 1239 | bool check_parindrome(string s) {
      |                                 ^
a.cc:1251:20: error: a function-definition is not allowed here before '{' token
 1251 | ll npr(ll n, ll r) {
      |                    ^
a.cc:1258:20: error: a function-definition is not allowed here before '{' token
 1258 | vl zalgo(string s) {
      |                    ^
a.cc:1284:28: error: a function-definition is not allowed here before '{' token
 1284 | string decStrNum(string s) {
      |                            ^
a.cc:1303:13: error: a function-definition is not allowed here before '{' token
 1303 | void solv() {
      |             ^
a.cc:1361:9: warning: empty parentheses were disambiguated as a function declaration [-Wvexing-parse]
 1361 | int main() {
      |         ^~
a.cc:1361:9: note: remove parentheses to default-initialize a variable
 1361 | int main() {
      |         ^~
      |         --
a.cc:1361:9: note: or replace parentheses with braces to value-initialize a variable
a.cc:1361:12: error: a function-definition is not allowed here before '{' token
 1361 | int main() {
      |            ^
a.cc:1365:2: error: expected '}' at end of input
 1365 | }
      |  ^
a.cc:505:33: note: to match this '{'
  505 | Node* delete1(Node* t, int key) {
      |                                 ^