Accidental Victory

A championship is held in Berland, in which $$$n$$$ players participate. The player with the number $$$i$$$ has $$$a_i$$$ ($$$a_i \ge 1$$$) tokens.

The championship consists of $$$n-1$$$ games, which are played according to the following rules:

• in each game, two random players with non-zero tokens are selected;
• the player with more tokens is considered the winner of the game (in case of a tie, the winner is chosen randomly);
• the winning player takes all of the loser's tokens;

The last player with non-zero tokens is the winner of the championship.

All random decisions that are made during the championship are made equally probable and independently.

For example, if $$$n=4$$$, $$$a = [1, 2, 4, 3]$$$, then one of the options for the game (there could be other options) is:

• during the first game, the first and fourth players were selected. The fourth player has more tokens, so he takes the first player's tokens. Now $$$a = [0, 2, 4, 4]$$$;
• during the second game, the fourth and third players were selected. They have the same number of tokens, but in a random way, the third player is the winner. Now $$$a = [0, 2, 8, 0]$$$;
• during the third game, the second and third players were selected. The third player has more tokens, so he takes the second player's tokens. Now $$$a = [0, 0, 10, 0]$$$;
• the third player is declared the winner of the championship.

Championship winners will receive personalized prizes. Therefore, the judges want to know in advance which players have a chance of winning, i.e have a non-zero probability of winning the championship. You have been asked to find all such players.