Gym - 101350E-Competitive Seagulls（对称博弈）

Competitive Seagulls

time limit per test

1.0 s

memory limit per test

256 MB

input

standard input

output

standard output

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?

Input

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).

Output

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.

Example

input

Copy

2
2
5

output

Copy

second
first

博弈总结点这里

原题链接点这里

题意：

        有n个格子排成一排，每次能在任意一片区域取连续的一个数x（前提是能取），且x为素数&&x最大为最长区域的1/2（向上取整），如果不存在满足上面两个条件的x，则取1。

所以我们只需要第一次取了之后，让左边的格子数等于右边的格子数即可（第一次从中间取），这样second无论取哪里，我们都能取得对应的那一边。

        所以第一次我们必须要能取到2或者3（这样才能满足无论如何都能使左右相等）

        所以需要对5以下特判（5/2向上取整等于3,此时first一定能赢）

        1->first    2->second  3->second  4->first;

    所以只要n不为2或者3,则first赢

#include <iostream>
#include <cstdio>
#include <algorithm>
using namespace std;
int main()
{
    int t,n;
    cin >> t;
    while(t--){
        scanf("%d",&n);
        printf((n!=2&&n!=3)?"first\n":"second\n");
    }
    return 0;
}