Hey guys I was learning python and I was stuck on this one problem. I have attempted it but my output does not meet the correct answer. Any reasons why and how to fix it?

Problem: The game of Assassin is a simple game played on university campuses where each player is assigned a target to assassinate by simply saying "you’re dead" to them. Of course with thousands of people on campus and only a few dozen in the game you never know who is looking to assassinate you. Once you assassinate someone you take on the target they were looking for. If this happens to be you then you are the winner. To ensure that this works properly the targets must form a continuous "chain." Write a program that allows the user to enter their target assignments and output whether it is valid or not based on if there is a continuous "chain." Each person in the list is represented by position in the list. The value at the position is their target.

My code:

total=0
list_of_players=[]
player=raw_input("Enter a player (end to stop): ")
while player !="end":
 list_of_players.append(int(player))
 player=raw_input("Enter a player (end to stop): ")
for x in range(len(list_of_players)):
 total+=1
 if list_of_players[x]==0 and len(list_of_players)==total:
 print "The game is valid."
if list_of_players[x]!=0 or len(list_of_players)!=total:
 print "The game is not valid. "

The problem states that if I enter players 4,3,0,5,6,2,1: It should be valid. My program displays this as invalid. Any ideas how I can improve my program? I got this practice question from programmersheaven.com if anyone is curious! Thanks!