403874: GYM101350 E Competitive Seagulls

There are two seagulls playing a very peculiar game. First they line up N unit squares in a line, all originally colored white.

Let L be the length of the longest continuous sub-segment of white unit squares. Let P be any prime that satisfies the condition that . The player can choose any P if it satisfies the conditions but if there is no value of P that does, then P is set to 1.

The current player then proceeds to choose any continuous sub-segment of white unit squares of length P and paint them black. The player who can’t make a move loses.

If both players play optimally and the first player starts, which player is going to win the game?

The first line of input is T – the number of test cases.

Each test case contains a line with a single integer N (1 ≤ N ≤ 10⁷).

For each test case, output on a single line "first" (without quotes) if the first player would win the game, or "second" if the second would win.

2
2
5

second
first