While exploring the old caves, researchers found a book, or more precisely, a stash of mixed pages from a book. Luckily, all of the original pages are present and each page contains its number. Therefore, the researchers can reconstruct the book.

After taking a deeper look into the contents of these pages, linguists think that this may be some kind of dictionary. What's interesting is that this ancient civilization used an alphabet which is a subset of the English alphabet, however, the order of these letters in the alphabet is not like the one in the English language.

Given the contents of pages that researchers have found, your task is to reconstruct the alphabet of this ancient civilization using the provided pages from the dictionary.


-----Input-----

First-line contains two integers: $n$ and $k$ ($1 \le n, k \le 10^3$) — the number of pages that scientists have found and the number of words present at each page. Following $n$ groups contain a line with a single integer $p_i$ ($0 \le n \lt 10^3$) — the number of $i$-th page, as well as $k$ lines, each line containing one of the strings (up to $100$ characters) written on the page numbered $p_i$.


-----Output-----

Output a string representing the reconstructed alphabet of this ancient civilization. If the book found is not a dictionary, output "IMPOSSIBLE" without quotes. In case there are multiple solutions, output any of them.


-----Example-----
Input
3 3
2
b
b
bbac
0
a
aca
acba
1
ab
c
ccb

Output
acb

Difficulty: MEDIUM

Starter code:

Solutions:
from bisect import bisect_left as bl
from bisect import bisect_right as br
from heapq import heappush, heappop
import math
from collections import *
from functools import reduce, cmp_to_key, lru_cache
import io, os
input = io.BytesIO(os.read(0, os.fstat(0).st_size)).readline
M = mod = 10 ** 9 + 7

def factors(n):
	return sorted(set(reduce(list.__add__, ([i, n // i] for i in range(1, int(n ** 0.5) + 1) if n % i == 0))))

def inv_mod(n):
	return pow(n, mod - 2, mod)

def li():
	return [int(i) for i in input().rstrip().split()]

def st():
	return str(input().rstrip())[2:-1]

def val():
	return int(input().rstrip())

def li2():
	return [str(i)[2:-1] for i in input().rstrip().split()]

def li3():
	return [int(i) for i in st()]
graph = defaultdict(set)
(n, k) = li()
l = []
allwords = set()
for i in range(n):
	p = val()
	l1 = []
	for j in range(k):
		l1.append(st())
	allwords |= set(l1[-1])
	l.append([p, l1[:]])
l.sort(key=lambda x: x[0])
l = [i[1] for i in l]
if n == k == 1:
	print(''.join(set(l[0][0])))
	return
ingraph = defaultdict(int)

def match(a, b):
	for j in range(min(len(a), len(b))):
		if a[j] == b[j]:
			continue
		elif b[j] in graph[a[j]]:
			return
		else:
			graph[a[j]].add(b[j])
			ingraph[b[j]] += 1
			return
	if len(a) > len(b):
		print('IMPOSSIBLE')
		return
finl = []
for i in l:
	finl.extend(i)
l = finl
for i in range(1, len(l)):
	match(l[i - 1], l[i])
if min([ingraph[j] for j in graph]) != 0:
	print('IMPOSSIBLE')
	return
ans = ''
d = deque()
for j in graph:
	if ingraph[j] == 0:
		d.append(j)
while d:
	node = d.popleft()
	ans += node
	for j in graph[node]:
		ingraph[j] -= 1
		if not ingraph[j]:
			d.append(j)
if len(ans) != len(allwords):
	print('IMPOSSIBLE')
	return
print(ans)


import os
import io
from collections import deque, defaultdict
input = io.BytesIO(os.read(0, os.fstat(0).st_size)).readline

def li():
	return [int(i) for i in input().rstrip().split()]

def st():
	return str(input().rstrip())[2:-1]

def val():
	return int(input().rstrip())
(n, k) = li()
words = [''] * n * k
abc = set()
for i in range(n):
	p = val()
	page = []
	for j in range(k):
		word = st()
		words[p * k + j] = word
	abc |= set(word)

def match(w1, w2):
	for i in range(min(len(w1), len(w2))):
		if w1[i] == w2[i]:
			continue
		else:
			return (w1[i], w2[i])
	if len(w1) > len(w2):
		print('IMPOSSIBLE')
		return
g = {c: set() for c in abc}
indeg = {c: 0 for c in abc}
for i in range(len(words) - 1):
	out = match(words[i], words[i + 1])
	if out is not None:
		(c1, c2) = out
		if c2 not in g[c1]:
			g[c1].add(c2)
			indeg[c2] += 1
ts = []
zero = deque()
for u in g:
	if indeg[u] == 0:
		zero.append(u)
while len(ts) != len(abc):
	if len(zero) == 0:
		print('IMPOSSIBLE')
		return
	u = zero.popleft()
	ts.append(u)
	for v in g[u]:
		indeg[v] -= 1
		if indeg[v] == 0:
			zero.append(v)
print(''.join(ts))


import io
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))

def input():
	return sys.stdin.readline().rstrip('\r\n')
(n, m) = map(int, input().split())
inc = {}
l = [None for i in range(n * m)]
for i in range(n):
	t = int(input())
	for j in range(m):
		ipt = input()
		l[t * m + j] = ipt
		if len(inc) == 26:
			continue
		for q in ipt:
			inc.setdefault(q, 0)
d = {}

def ae(u, v):
	t = d.setdefault(u, set())
	if v not in t:
		t.add(v)
		inc[v] = inc.get(v, 0) + 1
for (p, i) in enumerate(l[1:]):
	for j in range(min(len(l[p]), len(i))):
		if l[p][j] != i[j]:
			ae(i[j], l[p][j])
			break
		if len(i) - 1 == j and len(l[p]) - 1 > j:
			print('IMPOSSIBLE')
			return
ans = []
dq = []
ptr = 0
ninc = {}
for (k, v) in inc.items():
	if v == 0:
		dq.append(k)
	else:
		ninc[k] = v
inc = ninc
while ptr != len(dq):
	fst = dq[ptr]
	ans.append(fst)
	for i in d.get(fst, []):
		inc[i] -= 1
		if inc[i] == 0:
			dq.append(i)
			inc.pop(i)
	ptr += 1
if len(inc):
	print('IMPOSSIBLE')
	return
print(*reversed(ans), sep='')


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()

def RL():
	return map(int, sys.stdin.readline().split())

def RLL():
	return list(map(int, sys.stdin.readline().split()))

def N():
	return int(input())

def print_list(l):
	print(' '.join(map(str, l)))
from collections import defaultdict as dc
(n, k) = RL()
dic = [[] for _ in range(1000)]
for _ in range(n):
	page = N()
	for _ in range(k):
		dic[page].append(input().strip())
dic = [word for page in dic for word in page]
nw = len(dic)
ingress = dc(int)
edges = dc(list)
chars = set()
chars |= set(dic[0])
F = True
for i in range(1, nw):
	(a, b) = (dic[i - 1], dic[i])
	if len(chars) < 26:
		chars |= set(b)
	flag = False
	for (i, j) in zip(a, b):
		if i != j:
			ingress[j] += 1
			edges[i].append(j)
			flag = True
			break
	if not flag and len(b) < len(a):
		F = False
		break
if not F:
	print('IMPOSSIBLE')
else:
	res = ''
	now = []
	for c in chars:
		ingress[c] = max(0, ingress[c])
		if ingress[c] == 0:
			now.append(c)
	while now:
		a = now.pop()
		res += a
		for b in edges[a]:
			ingress[b] -= 1
			if ingress[b] == 0:
				now.append(b)
	if len(res) == len(chars):
		print(res)
	else:
		print('IMPOSSIBLE')


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')
from math import gcd, ceil

def prod(a, mod=10 ** 9 + 7):
	ans = 1
	for each in a:
		ans = ans * each % mod
	return ans

def lcm(a, b):
	return a * b // gcd(a, b)

def binary(x, length=16):
	y = bin(x)[2:]
	return y if len(y) >= length else '0' * (length - len(y)) + y
for _ in range(int(input()) if not True else 1):
	(n, k) = map(int, input().split())
	di = {}
	present = [False] * 26
	for i in range(n):
		page = int(input())
		di[page] = []
		for __ in range(k):
			s = input()
			for i in s:
				present[ord(i) - 97] = True
			di[page] += [s]
	words = []
	for u in sorted((k for k in di)):
		words += di[u]
	graph = [set() for i in range(26)]
	pos = True
	for i in range(1, len(words)):
		j = 0
		while j < min(len(words[i]), len(words[i - 1])):
			if words[i][j] == words[i - 1][j]:
				j += 1
				continue
			(l1, l2) = (ord(words[i - 1][j]) - 97, ord(words[i][j]) - 97)
			if l1 in graph[l2]:
				pos = False
				break
			graph[l1].add(l2)
			break
		if len(words[i - 1]) > len(words[i]) and words[i - 1][:len(words[i])] == words[i]:
			print('IMPOSSIBLE')
			quit()
		if not pos:
			break
	if not pos:
		print('IMPOSSIBLE')
		quit()
	graph = [list(k) for k in graph]
	edges = [i for i in range(26) if present[i]]
	order = []
	vis = [False] * 26
	while True:
		lo = len(order)
		for e in edges:
			if not graph[e] and e not in order:
				order += [e]
				vis[e] = True
		for i in range(26):
			for j in order:
				if j in graph[i]:
					graph[i].remove(j)
		if lo == len(order):
			break
	order = order[::-1]
	if not order:
		print('IMPOSSIBLE')
		quit()
	pos = True
	for i in range(26):
		for j in graph[i]:
			if order.index(i) > order.index(j):
				pos = False
				break
		if not pos:
			break
	if not pos:
		print('IMPOSSIBLE')
	else:
		print(''.join((chr(97 + k) for k in order)))