【Description】

Jessie and Justin want to participate in e-sports. E-sports contain many games, but
they don't know which one to choose, so they use a way to make decisions.

They have several boxes of candies, and there are iii candies in the ithi^{th}ith 
box, each candy is wrapped in a piece of
 
 candy paper. Jessie opens the candy boxes
in turn from the first box. Every time a box is opened, Jessie will take out all 
the candies inside, finish it, and hand all the candy papers to Justin.

When Jessie takes out the candies in the NthN^{th}Nth box and hasn't eaten yet, if 
the amount of candies in
 
 Jessie's hand and the amount of candy papers in Justin's 
hand are both perfect square numbers, they will choose Arena of Valor. If only the 
amount of candies in Jessie's hand is a perfect square number, they will choose 
Hearth Stone. If only the amount of candy papers in Justin's hand is a perfect 
square number
 
, they will choose Clash Royale. Otherwise they will choose League of
Legends.

Now tell you the value of NNN, please judge which game they will choose.

【Input】

The first line contains an integer T(1≤T≤800)T(1 \le T \le 800)T(1≤T≤800) , which 
is the number of test cases.

Each test case contains one line with a single integer: N(1≤N≤10^200)N(1 \le N \le 
10^{200})N(1≤N≤10200) .

【Output】

 For each test case, output one line containing the answer.

【Examples】

Sample Input

4
1
2
3
4

Sample Output

Arena of Valor
Clash Royale
League of Legends
Hearth Stone

【Problem Description】

就判斷n和sum(n-1)是否是完全平方數. sum(n-1)=1+2+3+..+n-1

【Solution】

用java大數二分判斷兩次即可。

【Code】

import java.util.*;

import java.math.BigInteger;

public class Main {
    static Scanner s=new Scanner(System.in);
    public static  BigInteger binary_find(BigInteger n){
        BigInteger l = new BigInteger("1");
        BigInteger two = new BigInteger("2");
        BigInteger r = new BigInteger("100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000");
        BigInteger mid;
        while (l.compareTo(r) != 1) {
            mid = l.add(r);
            mid = mid.shiftRight(1);
//                System.out.println(mid);
            BigInteger ss = mid.multiply(mid);
            if (ss.compareTo(n) == -1) {
                l = mid.add(BigInteger.ONE);
            } else {
                r = mid.subtract(BigInteger.ONE);
            }
        }
        return l;
    }
    public static void main(String[] args){
        int T=s.nextInt();
        while (T>0) {
            T--;
            BigInteger n = s.nextBigInteger();
            if(n.equals(BigInteger.ONE)){
                System.out.println("Arena of Valor");
                continue;
            }
//            System.out.println(l);
            boolean e=false,f=false;
            BigInteger i=binary_find(n);
            if(i.multiply(i).equals(n)) e=true;
            i=binary_find(n.multiply(n.subtract(BigInteger.ONE)).divide(BigInteger.valueOf(2)));
            if(i.multiply(i).equals(n.multiply(n.subtract(BigInteger.ONE)).divide(BigInteger.valueOf(2)))) f=true;
            if(e && f) {
                System.out.println("Arena of Valor");
            } else if (e) {
                System.out.println("Hearth Stone");
            } else if (f) {
                System.out.println("Clash Royale");
            } else {
                System.out.println("League of Legends");
            }
        }
    }
}