You are given NN points on a plane. These points are precisely the set of vertices of some regular NN-gon. Koosaga, an extreme villain, is challenging you with a game using these points. You and Koosaga alternatively take turns, and in each turn, the player
- chooses two of the given points, then
- draws the line segment connecting the two chosen points.
Also, the newly drawn line segment must not intersect with any of the previously drawn line segments in the interior. It is possible for two segments to meet at their endpoints. If at any point of the game, there exists a convex polygon consisting of the drawn line segments, the game ends and the last player who made the move wins.
Given the integer NN, Koosaga is letting you decide who will move first. Your task is decide whether you need to move first or the second so that you can win regardless of Koosaga's moves.
Input
The input consists of many test cases. The first line contains an integer TT (1≤T≤50001≤T≤5000), the number of test cases. Each of the following TTtest cases is consisted of one line containing the integer NN (3≤N≤50003≤N≤5000).
Output
For each test case, print one line containing the string First if you need to move first or Secondif you need to move second so that you can win regardless of Koosaga's moves.
Example
235
FirstSecond
1 #include <bits/stdc++.h>
2
3 using namespace std;
4
5 int sg[5005], vis[5005];
6
7 void find_sg(int n)
8 {
9 int i, j;
10 memset(sg, 0, sizeof(sg));
11 for(i=1;i<=n;i++)
12 {
13 memset(vis, 0, sizeof(vis));
14 for(j=0;j<=i-2;j++)
15 {
16 vis[sg[j] ^ sg[i-j-2]] = 1;
17 }
18 for(j=0;j<=n;j++)
19 {
20 if(vis[j]==0)
21 {
22 sg[i] = j;
23 break;
24 }
25 }
26 }
27 }
28
29 int main()
30 {
31 int t, n;
32 find_sg(5005);
33 cin >> t;
34 while(t--)
35 {
36 cin >> n;
37 if(sg[n]) cout << "First" << endl;
38 else cout << "Second" << endl;
39 }
40 return 0;
41 }