2021. Moving Pebbles
Two players play the following game. At the beginning of the game they start with n (1<=n<=100000) piles of stones. At each step of the game, the player chooses a pile and remove at least one stone from this pile and move zero or more stones from this pile to any other pile that still has stones. A player loses if he has no more possible moves. Given the initial piles, determine who wins: the first player, or the second player, if both play perfectly.
Each line of input has integers 0 < n <= 100000, followed by n positive integers denoting the initial piles.
For each line of input, output "first player" if first player can force a win, or "second player", if the second player can force a win.