Problem: Gotou just received a dictionary. However, he doesn't recognize the language used in the dictionary. He did some analysis on the dictionary and realizes that the dictionary contains all possible **diverse** words in lexicographical order.  A word is called **diverse** if and only if it is a nonempty string of English lowercase letters and all letters in the word are distinct. For example, `atcoder`, `zscoder` and `agc` are diverse words while `gotou` and `connect` aren't diverse words.  Given a diverse word S, determine the next word that appears after S in the dictionary, i.e. the lexicographically smallest diverse word that is lexicographically larger than S, or determine that it doesn't exist.  Let X = x_{1}x_{2}...x_{n} and Y = y_{1}y_{2}...y_{m} be two distinct strings. X is lexicographically larger than Y if and only if Y is a prefix of X or x_{j} > y_{j} where j is the smallest integer such that x_{j} \neq y_{j}.

Submission attempts (in order):
# encoding:utf-8
 
import fractions
 
def check(l):
	l = list(map(int, l.split()))
 
	if max(l) >= 30001:
		return False
	tmp = l[0]
 
	for i in range(len(l) - 1):
		tmp = fractions.gcd(tmp, l[i+1])
	if tmp != 1:
		return False 
 
	for i in range(len(l)):
		if fractions.gcd(l[i], sum(l) - l[i]) == 1:
			return False
 
	return True
 
 
def main(n):
	if n == 3:
		return "2 5 63"
	if n <= 5003:
		sub = [i * 3 for i in range(1, 10001) if i % 2 == 1]
		if n % 2 == 0:
			s = "2 4 " + " ".join([str(x) for x in sub[0:(n-2)]])
			return(s)
		else:
			s = "2 4 6 " + " ".join([str(x) for x in sub[0:(n-3)]])
			return(s)
	else:
		sub = [i * 3 for i in range(1, 10001) if i % 2 == 1]
		if n % 2 == 0:
			s = " ".join([str(i) for i in range(1, 30000) if i % 2 == 0 and i % 3 != 0][0:(n-5000)]) + " " +  " ".join([str(x) for x in sub])
			return(s)
		else:
			s = " ".join([str(i) for i in range(1, 30000) if i % 2 == 0 and i % 3 != 0][0:(n-5001)]) + " 6 " +  " ".join([str(x) for x in sub])
			return(s)
if __name__ == '__main__':
	n = int(input())
	print(main(n))
	
	

# encoding:utf-8


def main(s):
	alphabet = "abcdefghijklmnopqrstuvwxyz"
	d = {alphabet[i]:i for i in range(26)}
	if s == "zyxwvutsrqponmlkjihgfedcba":
		print("-1")
	elif len(s) < 26:
		for i in range(26):
			if alphabet[i] not in s:
				print(s + alphabet[i])
				break
	else:
		tail = [d[s[25]]]
		for i in range(0, 25):
			if d[s[24 - i]] >= max(tail):
				tail.append(d[s[24 - i]])
				continue
			else:
				tmp = min([x for x in tail if x >= d[s[24-i]]])
				print(s[0:(24-i)] + alphabet[tmp])
				break


if __name__ == '__main__':
	#s = input()
	main("abc")
	main("adc")
	main("zyawvutsrqponmlkjihgfedcbx")
	main("abcdefghijklmnopqrstuvwzyx")

# encoding:utf-8

import fractions

def check(l):
	l = list(map(int, l.split()))
	print(len(l), len([x for x in l if x % 2 == 0]), len([x for x in l if x % 2 == 1]))
	if max(l) >= 30001:
		print("max >= 30001")
		return False

	if len(set(l)) != len(l):
		print("not unique")
		return False

	tmp = l[0]


	for i in range(len(l) - 1):
		tmp = fractions.gcd(tmp, l[i+1])
	if tmp != 1:
		print("gcd is 1")
		return False 

	for i in range(len(l)):
		if fractions.gcd(l[i], sum(l) - l[i]) == 1:
			print("not special")
			return False

	return True


def main(n):
	if n == 3:
		return "2 5 63"

	sub1 = [str(i * 3) for i in range(1, 10001) if i % 2 == 1]
	sub2 = [str(i) for i in range(1, 30000) if i % 2 == 0 and i % 3 != 0]
	sub3 = [str(i) for i in range(1, 30001) if i % 6 == 0]
	if n <= 5003:
		if n % 2 == 0:
			s = "2 4 " + " ".join([str(x) for x in sub1[0:(n-2)]])
			return(s)
		else:
			s = "2 4 6 " + " ".join([str(x) for x in sub1[0:(n-3)]])
			return(s)
	elif n <= 15000:
		if n % 2 == 0:
			s = " ".join(sub2[0:(n-5000)]) + " " +  " ".join(sub1)
			return(s)
		else:
			s = " ".join(sub2[0:(n-5001)]) + " 6 " +  " ".join(sub1)
			return(s)
	else:
		s = " ".join(sub2) + " " +  " ".join(sub1) + " " + " ".join(sub3[0:(n-15000)]) 
		return(s)

if __name__ == '__main__':
	n = int(input())
	#print(check(main(n)))
	#print(main(20000))
	print(main(n))
	#print(check("2 4 3 20001"))
	
	
	
	

# encoding:utf-8


def main(s):
	alphabet = "abcdefghijklmnopqrstuvwxyz"
	d = {alphabet[i]:i for i in range(26)}
	if s == "zyxwvutsrqponmlkjihgfedcba":
		print("-1")
	elif len(s) < 26:
		for i in range(26):
			if alphabet[i] not in s:
				print(s + alphabet[i])
				break
	else:
		tail = [d[s[25]]]
		for i in range(0, 25):
			if d[s[24 - i]] >= max(tail):
				tail.append(d[s[24 - i]])
				continue
			else:
				tmp = min([x for x in tail if x >= d[s[24-i]]])
				print(s[0:(24-i)] + alphabet[tmp])
				break


if __name__ == '__main__':
	s = input()
	main(s)

Verdicts: Runtime Error

Wrong Answer

Runtime Error

Accepted