Country of Metropolia is holding Olympiad of Metrpolises soon. It mean that all jury members of the olympiad should meet together in Metropolis (the capital of the country) for the problem preparation process.

There are n + 1 cities consecutively numbered from 0 to n. City 0 is Metropolis that is the meeting point for all jury members. For each city from 1 to n there is exactly one jury member living there. Olympiad preparation is a long and demanding process that requires k days of work. For all of these k days each of the n jury members should be present in Metropolis to be able to work on problems.

You know the flight schedule in the country (jury members consider themselves important enough to only use flights for transportation). All flights in Metropolia are either going to Metropolis or out of Metropolis. There are no night flights in Metropolia, or in the other words, plane always takes off at the same day it arrives. On his arrival day and departure day jury member is not able to discuss the olympiad. All flights in Megapolia depart and arrive at the same day.

Gather everybody for k days in the capital is a hard objective, doing that while spending the minimum possible money is even harder. Nevertheless, your task is to arrange the cheapest way to bring all of the jury members to Metrpolis, so that they can work together for k days and then send them back to their home cities. Cost of the arrangement is defined as a total cost of tickets for all used flights. It is allowed for jury member to stay in Metropolis for more than k days.


-----Input-----

The first line of input contains three integers n, m and k (1 ≤ n ≤ 10^5, 0 ≤ m ≤ 10^5, 1 ≤ k ≤ 10^6). 

The i-th of the following m lines contains the description of the i-th flight defined by four integers d_{i}, f_{i}, t_{i} and c_{i} (1 ≤ d_{i} ≤ 10^6, 0 ≤ f_{i} ≤ n, 0 ≤ t_{i} ≤ n, 1 ≤ c_{i} ≤ 10^6, exactly one of f_{i} and t_{i} equals zero), the day of departure (and arrival), the departure city, the arrival city and the ticket cost.


-----Output-----

Output the only integer that is the minimum cost of gathering all jury members in city 0 for k days and then sending them back to their home cities.

If it is impossible to gather everybody in Metropolis for k days and then send them back to their home cities, output "-1" (without the quotes).


-----Examples-----
Input
2 6 5
1 1 0 5000
3 2 0 5500
2 2 0 6000
15 0 2 9000
9 0 1 7000
8 0 2 6500

Output
24500

Input
2 4 5
1 2 0 5000
2 1 0 4500
2 1 0 3000
8 0 1 6000

Output
-1



-----Note-----

The optimal way to gather everybody in Metropolis in the first sample test is to use flights that take place on days 1, 2, 8 and 9. The only alternative option is to send jury member from second city back home on day 15, that would cost 2500 more.

In the second sample it is impossible to send jury member from city 2 back home from Metropolis.

Source: codeforces | Difficulty: MEDIUM_HARD
Tags: Sorting

Amortized analysis

Greedy algorithms


Solutions:
def main():
	(n, m, k) = list(map(int, input().split()))
	(ff, tt) = ([], [])
	for _ in range(m):
		(d, f, t, c) = list(map(int, input().split()))
		if f:
			ff.append((d, f, c))
		else:
			tt.append((-d, t, c))
	for ft in (ff, tt):
		(cnt, costs) = (n, [1000001] * (n + 1))
		ft.sort(reverse=True)
		while ft:
			(day, city, cost) = ft.pop()
			oldcost = costs[city]
			if oldcost > cost:
				costs[city] = cost
				if oldcost == 1000001:
					cnt -= 1
					if not cnt:
						break
		else:
			print(-1)
			return
		total = sum(costs) - 1000001
		l = [(day, total)]
		while ft:
			(day, city, cost) = ft.pop()
			oldcost = costs[city]
			if oldcost > cost:
				total -= oldcost - cost
				costs[city] = cost
				if l[-1][0] == day:
					l[-1] = (day, total)
				else:
					l.append((day, total))
		if ft is ff:
			ff = l
		else:
			tt = l
	(l, k) = ([], -k)
	(d, c) = tt.pop()
	try:
		for (day, cost) in ff:
			while d + day >= k:
				(d, c) = tt.pop()
			if d + day < k:
				l.append(c + cost)
	except IndexError:
		pass
	print(min(l, default=-1))

def __starting_point():
	main()
__starting_point()


import math
import heapq, bisect
import sys
from collections import deque, defaultdict
from fractions import Fraction
mod = 10 ** 9 + 7
mod1 = 998244353
import os
import sys
from io import BytesIO, IOBase
BUFSIZE = 8192

class FastIO(IOBase):
	newlines = 0

	def __init__(self, file):
		self._fd = file.fileno()
		self.buffer = BytesIO()
		self.writable = 'x' in file.mode or 'r' not in file.mode
		self.write = self.buffer.write if self.writable else None

	def read(self):
		while True:
			b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
			if not b:
				break
			ptr = self.buffer.tell()
			(self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr))
		self.newlines = 0
		return self.buffer.read()

	def readline(self):
		while self.newlines == 0:
			b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
			self.newlines = b.count(b'\n') + (not b)
			ptr = self.buffer.tell()
			(self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr))
		self.newlines -= 1
		return self.buffer.readline()

	def flush(self):
		if self.writable:
			os.write(self._fd, self.buffer.getvalue())
			(self.buffer.truncate(0), self.buffer.seek(0))

class IOWrapper(IOBase):

	def __init__(self, file):
		self.buffer = FastIO(file)
		self.flush = self.buffer.flush
		self.writable = self.buffer.writable
		self.write = lambda s: self.buffer.write(s.encode('ascii'))
		self.read = lambda : self.buffer.read().decode('ascii')
		self.readline = lambda : self.buffer.readline().decode('ascii')
(sys.stdin, sys.stdout) = (IOWrapper(sys.stdin), IOWrapper(sys.stdout))
input = lambda : sys.stdin.readline().rstrip('\r\n')

class TreeNode:

	def __init__(self, k, v):
		self.key = k
		self.value = v
		self.left = None
		self.right = None
		self.parent = None
		self.height = 1
		self.num_left = 1
		self.num_total = 1

class AvlTree:

	def __init__(self):
		self._tree = None

	def add(self, k, v):
		if not self._tree:
			self._tree = TreeNode(k, v)
			return
		node = self._add(k, v)
		if node:
			self._rebalance(node)

	def _add(self, k, v):
		node = self._tree
		while node:
			if k < node.key:
				if node.left:
					node = node.left
				else:
					node.left = TreeNode(k, v)
					node.left.parent = node
					return node.left
			elif node.key < k:
				if node.right:
					node = node.right
				else:
					node.right = TreeNode(k, v)
					node.right.parent = node
					return node.right
			else:
				node.value = v
				return

	@staticmethod
	def get_height(x):
		return x.height if x else 0

	@staticmethod
	def get_num_total(x):
		return x.num_total if x else 0

	def _rebalance(self, node):
		n = node
		while n:
			lh = self.get_height(n.left)
			rh = self.get_height(n.right)
			n.height = max(lh, rh) + 1
			balance_factor = lh - rh
			n.num_total = 1 + self.get_num_total(n.left) + self.get_num_total(n.right)
			n.num_left = 1 + self.get_num_total(n.left)
			if balance_factor > 1:
				if self.get_height(n.left.left) < self.get_height(n.left.right):
					self._rotate_left(n.left)
				self._rotate_right(n)
			elif balance_factor < -1:
				if self.get_height(n.right.right) < self.get_height(n.right.left):
					self._rotate_right(n.right)
				self._rotate_left(n)
			else:
				n = n.parent

	def _remove_one(self, node):
		replacement = node.left or node.right
		if node.parent:
			if AvlTree._is_left(node):
				node.parent.left = replacement
			else:
				node.parent.right = replacement
			replacement.parent = node.parent
			node.parent = None
		else:
			self._tree = replacement
			replacement.parent = None
		node.left = None
		node.right = None
		node.parent = None
		self._rebalance(replacement)

	def _remove_leaf(self, node):
		if node.parent:
			if AvlTree._is_left(node):
				node.parent.left = None
			else:
				node.parent.right = None
			self._rebalance(node.parent)
		else:
			self._tree = None
		node.parent = None
		node.left = None
		node.right = None

	def remove(self, k):
		node = self._get_node(k)
		if not node:
			return
		if AvlTree._is_leaf(node):
			self._remove_leaf(node)
			return
		if node.left and node.right:
			nxt = AvlTree._get_next(node)
			node.key = nxt.key
			node.value = nxt.value
			if self._is_leaf(nxt):
				self._remove_leaf(nxt)
			else:
				self._remove_one(nxt)
			self._rebalance(node)
		else:
			self._remove_one(node)

	def get(self, k):
		node = self._get_node(k)
		return node.value if node else -1

	def _get_node(self, k):
		if not self._tree:
			return None
		node = self._tree
		while node:
			if k < node.key:
				node = node.left
			elif node.key < k:
				node = node.right
			else:
				return node
		return None

	def get_at(self, pos):
		x = pos + 1
		node = self._tree
		while node:
			if x < node.num_left:
				node = node.left
			elif node.num_left < x:
				x -= node.num_left
				node = node.right
			else:
				return (node.key, node.value)
		raise IndexError('Out of ranges')

	@staticmethod
	def _is_left(node):
		return node.parent.left and node.parent.left == node

	@staticmethod
	def _is_leaf(node):
		return node.left is None and node.right is None

	def _rotate_right(self, node):
		if not node.parent:
			self._tree = node.left
			node.left.parent = None
		elif AvlTree._is_left(node):
			node.parent.left = node.left
			node.left.parent = node.parent
		else:
			node.parent.right = node.left
			node.left.parent = node.parent
		bk = node.left.right
		node.left.right = node
		node.parent = node.left
		node.left = bk
		if bk:
			bk.parent = node
		node.height = max(self.get_height(node.left), self.get_height(node.right)) + 1
		node.num_total = 1 + self.get_num_total(node.left) + self.get_num_total(node.right)
		node.num_left = 1 + self.get_num_total(node.left)

	def _rotate_left(self, node):
		if not node.parent:
			self._tree = node.right
			node.right.parent = None
		elif AvlTree._is_left(node):
			node.parent.left = node.right
			node.right.parent = node.parent
		else:
			node.parent.right = node.right
			node.right.parent = node.parent
		bk = node.right.left
		node.right.left = node
		node.parent = node.right
		node.right = bk
		if bk:
			bk.parent = node
		node.height = max(self.get_height(node.left), self.get_height(node.right)) + 1
		node.num_total = 1 + self.get_num_total(node.left) + self.get_num_total(node.right)
		node.num_left = 1 + self.get_num_total(node.left)

	@staticmethod
	def _get_next(node):
		if not node.right:
			return node.parent
		n = node.right
		while n.left:
			n = n.left
		return n
avl = AvlTree()

class SegmentTree1:

	def __init__(self, data, default='z', func=lambda a, b: min(a, b)):
		self._default = default
		self._func = func
		self._len = len(data)
		self._size = _size = 1 << (self._len - 1).bit_length()
		self.data = [default] * (2 * _size)
		self.data[_size:_size + self._len] = data
		for i in reversed(range(_size)):
			self.data[i] = func(self.data[i + i], self.data[i + i + 1])

	def __delitem__(self, idx):
		self[idx] = self._default

	def __getitem__(self, idx):
		return self.data[idx + self._size]

	def __setitem__(self, idx, value):
		idx += self._size
		self.data[idx] = value
		idx >>= 1
		while idx:
			self.data[idx] = self._func(self.data[2 * idx], self.data[2 * idx + 1])
			idx >>= 1

	def __len__(self):
		return self._len

	def query(self, start, stop):
		if start == stop:
			return self.__getitem__(start)
		stop += 1
		start += self._size
		stop += self._size
		res = self._default
		while start < stop:
			if start & 1:
				res = self._func(res, self.data[start])
				start += 1
			if stop & 1:
				stop -= 1
				res = self._func(res, self.data[stop])
			start >>= 1
			stop >>= 1
		return res

	def __repr__(self):
		return 'SegmentTree({0})'.format(self.data)

class SegmentTree:

	def __init__(self, data, default=0, func=lambda a, b: a + b):
		self._default = default
		self._func = func
		self._len = len(data)
		self._size = _size = 1 << (self._len - 1).bit_length()
		self.data = [default] * (2 * _size)
		self.data[_size:_size + self._len] = data
		for i in reversed(range(_size)):
			self.data[i] = func(self.data[i + i], self.data[i + i + 1])

	def __delitem__(self, idx):
		self[idx] = self._default

	def __getitem__(self, idx):
		return self.data[idx + self._size]

	def __setitem__(self, idx, value):
		idx += self._size
		self.data[idx] = value
		idx >>= 1
		while idx:
			self.data[idx] = self._func(self.data[2 * idx], self.data[2 * idx + 1])
			idx >>= 1

	def __len__(self):
		return self._len

	def query(self, start, stop):
		if start == stop:
			return self.__getitem__(start)
		stop += 1
		start += self._size
		stop += self._size
		res = self._default
		while start < stop:
			if start & 1:
				res = self._func(res, self.data[start])
				start += 1
			if stop & 1:
				stop -= 1
				res = self._func(res, self.data[stop])
			start >>= 1
			stop >>= 1
		return res

	def __repr__(self):
		return 'SegmentTree({0})'.format(self.data)

class Factorial:

	def __init__(self, MOD):
		self.MOD = MOD
		self.factorials = [1, 1]
		self.invModulos = [0, 1]
		self.invFactorial_ = [1, 1]

	def calc(self, n):
		if n <= -1:
			print('Invalid argument to calculate n!')
			print('n must be non-negative value. But the argument was ' + str(n))
			exit()
		if n < len(self.factorials):
			return self.factorials[n]
		nextArr = [0] * (n + 1 - len(self.factorials))
		initialI = len(self.factorials)
		prev = self.factorials[-1]
		m = self.MOD
		for i in range(initialI, n + 1):
			prev = nextArr[i - initialI] = prev * i % m
		self.factorials += nextArr
		return self.factorials[n]

	def inv(self, n):
		if n <= -1:
			print('Invalid argument to calculate n^(-1)')
			print('n must be non-negative value. But the argument was ' + str(n))
			exit()
		p = self.MOD
		pi = n % p
		if pi < len(self.invModulos):
			return self.invModulos[pi]
		nextArr = [0] * (n + 1 - len(self.invModulos))
		initialI = len(self.invModulos)
		for i in range(initialI, min(p, n + 1)):
			next = -self.invModulos[p % i] * (p // i) % p
			self.invModulos.append(next)
		return self.invModulos[pi]

	def invFactorial(self, n):
		if n <= -1:
			print('Invalid argument to calculate (n^(-1))!')
			print('n must be non-negative value. But the argument was ' + str(n))
			exit()
		if n < len(self.invFactorial_):
			return self.invFactorial_[n]
		self.inv(n)
		nextArr = [0] * (n + 1 - len(self.invFactorial_))
		initialI = len(self.invFactorial_)
		prev = self.invFactorial_[-1]
		p = self.MOD
		for i in range(initialI, n + 1):
			prev = nextArr[i - initialI] = prev * self.invModulos[i % p] % p
		self.invFactorial_ += nextArr
		return self.invFactorial_[n]

class Combination:

	def __init__(self, MOD):
		self.MOD = MOD
		self.factorial = Factorial(MOD)

	def ncr(self, n, k):
		if k < 0 or n < k:
			return 0
		k = min(k, n - k)
		f = self.factorial
		return f.calc(n) * f.invFactorial(max(n - k, k)) * f.invFactorial(min(k, n - k)) % self.MOD

def powm(a, n, m):
	if a == 1 or n == 0:
		return 1
	if n % 2 == 0:
		s = powm(a, n // 2, m)
		return s * s % m
	else:
		return a * powm(a, n - 1, m) % m

def sort_list(list1, list2):
	zipped_pairs = zip(list2, list1)
	z = [x for (_, x) in sorted(zipped_pairs)]
	return z

def product(l):
	por = 1
	for i in range(len(l)):
		por *= l[i]
	return por

def binarySearchCount(arr, n, key):
	left = 0
	right = n - 1
	count = 0
	while left <= right:
		mid = int((right + left) / 2)
		if arr[mid] <= key:
			count = mid + 1
			left = mid + 1
		else:
			right = mid - 1
	return count

def countdig(n):
	c = 0
	while n > 0:
		n //= 10
		c += 1
	return c

def countGreater(arr, n, k):
	l = 0
	r = n - 1
	leftGreater = n
	while l <= r:
		m = int(l + (r - l) / 2)
		if arr[m] >= k:
			leftGreater = m
			r = m - 1
		else:
			l = m + 1
	return n - leftGreater
(n, m, k) = map(int, input().split())
incom = defaultdict(list)
outgo = defaultdict(list)
for i in range(m):
	(d, f, t, cost) = map(int, input().split())
	if t == 0:
		incom[d].append((f, cost))
	else:
		outgo[d].append((t, cost))
cost = [9999999999999999999] * n
cou = 0
total_cost = 0
l = []
for i in sorted(incom.keys()):
	for j in range(len(incom[i])):
		if cost[incom[i][j][0] - 1] == 9999999999999999999:
			total_cost += incom[i][j][1]
			cou += 1
		else:
			total_cost += min(0, incom[i][j][1] - cost[incom[i][j][0] - 1])
		cost[incom[i][j][0] - 1] = min(cost[incom[i][j][0] - 1], incom[i][j][1])
		if cou == n:
			l.append((i, total_cost))
if max(cost) == 9999999999999999999:
	print(-1)
	sys.exit(0)
cost = [9999999999999999999] * n
cou = 0
total_cost = 0
l1 = []
for i in sorted(outgo.keys(), reverse=True):
	for j in range(len(outgo[i])):
		if cost[outgo[i][j][0] - 1] == 9999999999999999999:
			total_cost += outgo[i][j][1]
			cou += 1
		else:
			total_cost += min(0, outgo[i][j][1] - cost[outgo[i][j][0] - 1])
		cost[outgo[i][j][0] - 1] = min(cost[outgo[i][j][0] - 1], outgo[i][j][1])
		if cou == n:
			l1.append((i, total_cost))
if max(cost) == 9999999999999999999:
	print(-1)
	sys.exit(0)
l1.reverse()
mint = [0] * len(l1)
mint[-1] = l1[-1][1]
for i in range(len(l1) - 2, -1, -1):
	mint[i] = min(l1[i][1], mint[i + 1])
ans = 9999999999999999
t = 0
for i in range(len(l)):
	d = l[i][0] + k + 1
	f = 0
	if t == len(l1):
		break
	while d > l1[t][0]:
		t += 1
		if t == len(l1):
			f = 1
			break
	if f == 0:
		ans = min(ans, l[i][1] + mint[t])
if ans == 9999999999999999:
	print(-1)
else:
	print(ans)


g = lambda : map(int, input().split())
(n, m, k) = g()
(F, T) = ([], [])
e = int(300000000000.0)
for i in range(m):
	(d, f, t, c) = g()
	if f:
		F.append((d, f, c))
	else:
		T.append((-d, t, c))
for p in [F, T]:
	C = [e] * (n + 1)
	s = n * e
	q = []
	p.sort()
	for (d, t, c) in p:
		if C[t] > c:
			s += c - C[t]
			C[t] = c
			if s < e:
				q.append((s, d))
	p.clear()
	p += q
(s, t) = (e, (0, 0))
for f in F:
	while f:
		if t[1] + f[1] + k < 0:
			s = min(s, f[0] + t[0])
		elif T:
			t = T.pop()
			continue
		f = 0
print(s if s < e else -1)


(N, M, K) = map(int, input().split())
INF = 10 ** 6 + 1
from collections import defaultdict
incoming = defaultdict(list)
outgoing = defaultdict(list)
for _ in range(M):
	(d, f, t, c) = map(int, input().split())
	if t == 0:
		incoming[d].append((c, f - 1))
	if f == 0:
		outgoing[d].append((c, t - 1))
incoming_dates = sorted(incoming.keys())
outgoing_dates = sorted(outgoing.keys(), reverse=True)
Li = []
mark = [False] * N
cnt = 0
costs = [0] * N
total_cost = 0
for d in incoming_dates:
	for (c, x) in incoming[d]:
		if mark[x]:
			if costs[x] > c:
				total_cost += c - costs[x]
				costs[x] = c
		else:
			mark[x] = True
			cnt += 1
			costs[x] = c
			total_cost += c
	if cnt == N:
		Li.append((d, total_cost))
Lo = []
mark = [False] * N
cnt = 0
costs = [0] * N
total_cost = 0
for d in outgoing_dates:
	for (c, x) in outgoing[d]:
		if mark[x]:
			if costs[x] > c:
				total_cost += c - costs[x]
				costs[x] = c
		else:
			mark[x] = True
			cnt += 1
			costs[x] = c
			total_cost += c
	if cnt == N:
		Lo.append((d, total_cost))
Lo.reverse()
if not Li or not Lo:
	print(-1)
	exit()
from bisect import bisect
best = float('inf')
for (d, c) in Li:
	i = bisect(Lo, (d + K + 1, 0))
	if i >= len(Lo):
		break
	else:
		best = min(best, c + Lo[i][1])
if best == float('inf'):
	print(-1)
else:
	print(best)


from bisect import *
from sys import *
(n, m, k) = [int(i) for i in input().split()]
pln = []
if m == 0:
	print(-1)
	exit(0)
for i in range(m):
	pln.append([int(i) for i in input().split()])
pln.sort()
grp = [[pln[0]]]
gt = 0
for i in range(1, m):
	if pln[i][0] != pln[i - 1][0]:
		gt = gt + 1
		grp.append([])
	grp[gt].append(pln[i])
xx = []
for i in range(len(grp)):
	xx.append(grp[i][0][0])
from math import inf
pre = [0] * len(xx)
ct = 0
mincost = [inf] * (n + 1)
sumcost = inf
for (i, x) in enumerate(grp):
	for (di, fi, ti, ci) in x:
		if ti == 0:
			if mincost[fi] == inf:
				ct += 1
			if sumcost == inf:
				mincost[fi] = min(mincost[fi], ci)
			else:
				sumcost = sumcost - mincost[fi]
				mincost[fi] = min(mincost[fi], ci)
				sumcost = sumcost + mincost[fi]
	if ct == n and sumcost == inf:
		sumcost = sum(mincost[1:])
	pre[i] = sumcost
sa = [0] * len(xx)
ct = 0
mincost = [inf] * (n + 1)
sumcost = inf
grp.reverse()
for (i, x) in enumerate(grp):
	for (di, fi, ti, ci) in x:
		if fi == 0:
			if mincost[ti] == inf:
				ct += 1
			if sumcost == inf:
				mincost[ti] = min(mincost[ti], ci)
			else:
				sumcost = sumcost - mincost[ti]
				mincost[ti] = min(mincost[ti], ci)
				sumcost = sumcost + mincost[ti]
	if ct == n and sumcost == inf:
		sumcost = sum(mincost[1:])
	sa[i] = sumcost
sa.reverse()
ans = inf
for (l, xxi) in enumerate(xx):
	r = bisect_right(xx, xxi + k)
	ansl = pre[l]
	ansr = inf if r == len(xx) else sa[r]
	ans = min(ans, ansl + ansr)
print(ans) if ans != inf else print(-1)


R = lambda : map(int, input().split())
(n, m, k) = R()
(F, T) = ([], [])
ans = int(1000000000000.0)
for i in range(m):
	(d, f, t, c) = R()
	if f:
		F.append((d, f, c))
	else:
		T.append((-d, t, c))
for p in [F, T]:
	cost = [ans] * (n + 1)
	s = n * ans
	q = []
	p.sort()
	for (d, t, c) in p:
		if c < cost[t]:
			s += c - cost[t]
			cost[t] = c
			if s < ans:
				q.append((s, d))
	p.clear()
	p += q
(s, t) = (ans, (0, 0))
for f in F:
	while f:
		if f[1] + t[1] + k < 0:
			s = min(s, f[0] + t[0])
		elif T:
			t = T.pop()
			continue
		f = 0
print(s if s < ans else -1)