Let's consider a simplified version of order book of some stock. The order book is a list of orders (offers) from people that want to buy or sell one unit of the stock, each order is described by direction (BUY or SELL) and price.

At every moment of time, every SELL offer has higher price than every BUY offer. 

In this problem no two ever existed orders will have the same price.

The lowest-price SELL order and the highest-price BUY order are called the best offers, marked with black frames on the picture below. [Image] The presented order book says that someone wants to sell the product at price $12$ and it's the best SELL offer because the other two have higher prices. The best BUY offer has price $10$. 

There are two possible actions in this orderbook:  Somebody adds a new order of some direction with some price. Somebody accepts the best possible SELL or BUY offer (makes a deal). It's impossible to accept not the best SELL or BUY offer (to make a deal at worse price). After someone accepts the offer, it is removed from the orderbook forever.

It is allowed to add new BUY order only with prices less than the best SELL offer (if you want to buy stock for higher price, then instead of adding an order you should accept the best SELL offer). Similarly, one couldn't add a new SELL order with price less or equal to the best BUY offer. For example, you can't add a new offer "SELL $20$" if there is already an offer "BUY $20$" or "BUY $25$" — in this case you just accept the best BUY offer.

You have a damaged order book log (in the beginning the are no orders in book). Every action has one of the two types: "ADD $p$" denotes adding a new order with price $p$ and unknown direction. The order must not contradict with orders still not removed from the order book.  "ACCEPT $p$" denotes accepting an existing best offer with price $p$ and unknown direction.

The directions of all actions are lost. Information from the log isn't always enough to determine these directions. Count the number of ways to correctly restore all ADD action directions so that all the described conditions are satisfied at any moment. Since the answer could be large, output it modulo $10^9 + 7$. If it is impossible to correctly restore directions, then output $0$.


-----Input-----

The first line contains an integer $n$ ($1 \le n \le 363\,304$) — the number of actions in the log.

Each of the next $n$ lines contains a string "ACCEPT" or "ADD" and an integer $p$ ($1 \le p \le 308\,983\,066$), describing an action type and price. 

All ADD actions have different prices. For ACCEPT action it is guaranteed that the order with the same price has already been added but has not been accepted yet.


-----Output-----

Output the number of ways to restore directions of ADD actions modulo $10^9 + 7$.


-----Examples-----
Input
6
ADD 1
ACCEPT 1
ADD 2
ACCEPT 2
ADD 3
ACCEPT 3

Output
8

Input
4
ADD 1
ADD 2
ADD 3
ACCEPT 2

Output
2

Input
7
ADD 1
ADD 2
ADD 3
ADD 4
ADD 5
ACCEPT 3
ACCEPT 5

Output
0



-----Note-----

In the first example each of orders may be BUY or SELL.

In the second example the order with price $1$ has to be BUY order, the order with the price $3$ has to be SELL order.

Source: codeforces | Difficulty: HARD
Tags: Combinatorics

Data structures

Greedy algorithms


Solutions:
import math
import random
import heapq, bisect
import sys
from collections import deque, defaultdict
from fractions import Fraction
import sys
from collections import defaultdict
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

class SegmentTree2:

	def __init__(self, data, default=3000006, 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 SegmentTree1:

	def __init__(self, data, default=10 ** 10, 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 binary(x, length):
	y = bin(x)[2:]
	return y if len(y) >= length else '0' * (length - len(y)) + y

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

class TrieNode:

	def __init__(self):
		self.children = [None] * 26
		self.isEndOfWord = False

class Trie:

	def __init__(self):
		self.root = self.getNode()

	def getNode(self):
		return TrieNode()

	def _charToIndex(self, ch):
		return ord(ch) - ord('a')

	def insert(self, key):
		pCrawl = self.root
		length = len(key)
		for level in range(length):
			index = self._charToIndex(key[level])
			if not pCrawl.children[index]:
				pCrawl.children[index] = self.getNode()
			pCrawl = pCrawl.children[index]
		pCrawl.isEndOfWord = True

	def search(self, key):
		pCrawl = self.root
		length = len(key)
		for level in range(length):
			index = self._charToIndex(key[level])
			if not pCrawl.children[index]:
				return False
			pCrawl = pCrawl.children[index]
		return pCrawl != None and pCrawl.isEndOfWord

class Node:

	def __init__(self, data):
		self.data = data
		self.count = 0
		self.left = None
		self.right = None

class BinaryTrie:

	def __init__(self):
		self.root = Node(0)

	def insert(self, pre_xor, t):
		self.temp = self.root
		for i in range(31, -1, -1):
			val = pre_xor & 1 << i
			if val:
				if not self.temp.right:
					self.temp.right = Node(0)
				self.temp = self.temp.right
				self.temp.count += t
			if not val:
				if not self.temp.left:
					self.temp.left = Node(0)
				self.temp = self.temp.left
				self.temp.count += t
		self.temp.data = pre_xor

	def query(self, p, l):
		ans = 0
		self.temp = self.root
		for i in range(31, -1, -1):
			val = p & 1 << i
			val1 = l & 1 << i
			if val1 == 0:
				if val == 0:
					if self.temp.left and self.temp.left.count > 0:
						self.temp = self.temp.left
					else:
						return ans
				elif self.temp.right and self.temp.right.count > 0:
					self.temp = self.temp.right
				else:
					return ans
			elif val != 0:
				if self.temp.right:
					ans += self.temp.right.count
				if self.temp.left and self.temp.left.count > 0:
					self.temp = self.temp.left
				else:
					return ans
			else:
				if self.temp.left:
					ans += self.temp.left.count
				if self.temp.right and self.temp.right.count > 0:
					self.temp = self.temp.right
				else:
					return ans
		return ans
n = int(input())
l = []
w = []
for i in range(n):
	(typ, a) = map(str, input().split())
	l.append((typ, a))
	w.append(a)
w.sort()
ind = defaultdict(int)
for i in range(len(w)):
	ind[w[i]] = i
nex = -1
ne = [-1] * n
for i in range(n - 1, -1, -1):
	(typ, a) = l[i]
	if typ == 'ACCEPT':
		nex = int(a)
	else:
		ne[i] = nex
ans = 1
buy = []
sell = []
heapq.heapify(buy)
heapq.heapify(sell)
t = 0
for i in range(n):
	(typ, a) = l[i]
	a = int(a)
	nex = ne[i]
	if typ == 'ADD':
		if nex == -1:
			if len(buy) > 0 and buy[0] * -1 > a:
				heapq.heappush(buy, -a)
			elif len(sell) > 0 and sell[0] < a:
				heapq.heappush(sell, a)
			else:
				t += 1
			continue
		if nex > a:
			heapq.heappush(buy, -a)
		elif nex < a:
			heapq.heappush(sell, a)
		elif len(buy) > 0 and buy[0] * -1 > a:
			heapq.heappush(buy, -a)
		elif len(sell) > 0 and sell[0] < a:
			heapq.heappush(sell, a)
		else:
			heapq.heappush(buy, -a)
			heapq.heappush(sell, a)
			ans *= 2
			ans %= mod
	else:
		w = 0
		w1 = 308983067
		if len(buy) > 0:
			w = heapq.heappop(buy)
		if len(sell) > 0:
			w1 = heapq.heappop(sell)
		w *= -1
		if a != w and a != w1:
			ans = 0
			break
		else:
			if a != w and w != 0:
				heapq.heappush(buy, -w)
			if a != w1 and w1 != 308983067:
				heapq.heappush(sell, w1)
ans *= t + 1
ans %= mod
print(ans)


from sys import stdin
from heapq import heappush, heappop

def main():
	(n, r, m) = (int(input()), 0, 1000000007)
	(bb, ss, bs) = ([0], [m], [])
	for s in stdin.read().splitlines():
		if s[1] == 'D':
			p = int(s[4:])
			if ss and ss[0] < p:
				heappush(ss, p)
			elif bb and -bb[0] > p:
				heappush(bb, -p)
			else:
				bs.append(p)
		else:
			p = int(s[7:])
			if -bb[0] < p < ss[0]:
				r += 1
			elif p == ss[0]:
				heappop(ss)
			elif p == -bb[0]:
				heappop(bb)
			else:
				print(0)
				return
			for x in bs:
				if x < p:
					heappush(bb, -x)
				elif x > p:
					heappush(ss, x)
			bs = []
	print((len(bs) + 1) * pow(2, r, m) % m)
main()


import heapq
n = int(input())
ans = 1
mod = 10 ** 9 + 7
(buy, undefined, sell) = ([], [], [])
for i in range(n):
	(cmd, str_p) = input().split()
	p = int(str_p)
	if cmd == 'ADD':
		if buy and p < -buy[0]:
			heapq.heappush(buy, -p)
		elif sell and p > sell[0]:
			heapq.heappush(sell, p)
		else:
			undefined.append(p)
	else:
		if buy and p < -buy[0] or (sell and p > sell[0]):
			ans = 0
			break
		elif buy and p == -buy[0]:
			heapq.heappop(buy)
		elif sell and p == sell[0]:
			heapq.heappop(sell)
		else:
			ans = (ans << 1) % mod
		for x in undefined:
			if x < p:
				heapq.heappush(buy, -x)
			elif x > p:
				heapq.heappush(sell, x)
		undefined = []
ans = ans * (len(undefined) + 1) % mod
print(ans)


from sys import exit
from heapq import heapify, heappush, heappop
n = int(input())
low = []
high = []
pos = 0
mid = set()
for i in range(n):
	s = input().split()
	x = int(s[1])
	s = s[0]
	if s == 'ADD':
		if len(low) and x < -1 * low[0]:
			heappush(low, -x)
		elif len(high) and x > high[0]:
			heappush(high, x)
		else:
			mid.add(x)
	else:
		if len(low) and x == -low[0]:
			heappop(low)
		elif len(high) and x == high[0]:
			heappop(high)
		elif x in mid:
			pos += 1
		else:
			print(0)
			exit()
		for j in mid:
			if j > x:
				heappush(high, j)
			elif j < x:
				heappush(low, -j)
		mid = set()
mod = int(1000000000.0 + 7)
print(pow(2, pos, mod) * (len(mid) + 1) % mod)


import heapq
n = int(input())
buy = []
sell = []
unknown = []
res = 1
for i in range(n):
	(cmd, amount) = input().strip().split()
	amount = int(amount)
	if cmd == 'ADD':
		if sell and sell[0] < amount:
			heapq.heappush(sell, amount)
		elif buy and -buy[0] > amount:
			heapq.heappush(buy, -amount)
		else:
			unknown.append(amount)
	else:
		if sell and amount > sell[0] or (buy and amount < -buy[0]):
			print(0)
			return
		if sell and amount == sell[0]:
			heapq.heappop(sell)
		elif buy and amount == -buy[0]:
			heapq.heappop(buy)
		else:
			res = res * 2 % 1000000007
		for x in unknown:
			if x < amount:
				heapq.heappush(buy, -x)
			elif x > amount:
				heapq.heappush(sell, x)
		unknown = []
res = res * (len(unknown) + 1) % 1000000007
print(res)


from sys import stdin
import heapq
MOD = pow(10, 9) + 7
n = int(stdin.readline())
a = []
for i in range(n):
	x = stdin.readline().split()
	if x[0] == 'ADD':
		a.append((0, int(x[1])))
	else:
		a.append((1, int(x[1])))
next_accept = [-1] * n
accept = -1
for i in range(n - 1, -1, -1):
	if a[i][0] == 1:
		accept = i
	next_accept[i] = accept
top = []
bottom = []
buysell_n = 0
last_n = 0
invalid = False
for i in range(n):
	if a[i][0] == 0:
		if next_accept[i] != -1:
			if a[i][1] > a[next_accept[i]][1]:
				heapq.heappush(top, a[i][1])
			elif a[i][1] < a[next_accept[i]][1]:
				heapq.heappush(bottom, -a[i][1])
		elif (len(top) == 0 or a[i][1] < top[0]) and (len(bottom) == 0 or a[i][1] > -bottom[0]):
			last_n += 1
	elif len(top) > 0 and a[i][1] == top[0]:
		heapq.heappop(top)
	elif len(bottom) > 0 and a[i][1] == -bottom[0]:
		heapq.heappop(bottom)
	else:
		if len(top) > 0 and a[i][1] > top[0] or (len(bottom) > 0 and a[i][1] < -bottom[0]):
			invalid = True
			break
		buysell_n += 1
if invalid:
	ans = 0
else:
	ans = pow(2, buysell_n, MOD) * (last_n + 1) % MOD
print(ans)