**Time limit:**1.00 s**Memory limit:**512 MB

There is a heap of n coins and two players who move alternately. On each move, a player chooses a heap and divides into two nonempty heaps that have a different number of coins. The player who makes the last move wins the game.

Your task is to find out who wins if both players play optimally.

# Input

The first input line contains an integer t: the number of tests.

After this, there are t lines that describe the tests. Each line has an integer n: the number of coins in the initial heap.

# Output

For each test case, print "first" if the first player wins the game and "second" if the second player wins the game.

# Constraints

- 1 \le t \le 10^5
- 1 \le n \le 10^6

# Example

Input:

3 6 7 8

Output:

first second first