The numbers $1$, $3$, $6$, $10$, $15$, $21$, $28$, $36$, $45$ and t_i=\frac{1}{2}i(i+1)t​i​​=​2​​1​​i(i+1), are called half-consecutive.

For given $N$, find the smallest $r$ which is no smaller than $N$ such that t_rt​r​​ is square.

Input Format

The input contains multiple test cases.

The first line of a multiple input is an integer T

Each line contains an integer N~(1\le N\le 10^{16})N(1≤N≤10​16​​).

Output Format

For each test case, output the case number first.

Then for given $N$, output the smallest $r$.

If this half-consecutive number does not exist, output $-1$.

樣例輸入

4
1
2
9
50

樣例輸出

Case #1: 1
Case #2: 8
Case #3: 49
Case #4: 288

題目來源

打表找規律

import java.io.BufferedReader;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.math.BigInteger;
import java.util.HashSet;
import java.util.Set;
import java.util.StringTokenizer;


public class Main {
    
    public static void main(String[] args) {
        new Task().solve();
    }
}

class Task {
    InputReader in = new InputReader(System.in) ;
    PrintWriter out = new PrintWriter(System.out) ;
    
    void solve(){
    	/*for(long i = 1 ; i <= 100000000L ; i++){
	    	long x =  i*(i+1)/2 ;
	    	long y = (long)Math.sqrt(x + 0.5) ;
	    	if(y * y == x){
	    		System.out.println(i + " " + x + " " + y) ;
	    	}
      	}*/
    	long[] a = new long[26] ;
    	long[] b = new long[26] ;
    	long[] r = new long[26] ;
    	a[0] = 1 ;
    	b[0] = 1 ;
    	r[0] = 1 ;
    	for(int i = 1 ; i < 26 ; i++){
    		a[i] = a[i-1] + b[i-1] ;
    		b[i] = a[i-1] + a[i] ;
    		r[i] = b[i] * b[i] + ((i%2==0) ? 0 : -1) ;
    	}

    	int cas = 1 ;
    	int t = in.nextInt() ;
    	while(t-- > 0){
    		long n = in.nextLong() ; 
    		for(int i = 0 ; i < 26 ; i++){
    			if(r[i] >= n){
    				out.println("Case #" + (cas++) + ": " + r[i]) ;
    				break ;
    			}
    		}
    	}
    	out.flush() ; 
    }
    
}


class InputReader {    
    public BufferedReader reader;    
    public StringTokenizer tokenizer;    
    
    public InputReader(InputStream stream) {    
        reader = new BufferedReader(new InputStreamReader(stream), 32768);    
        tokenizer = new StringTokenizer("");    
    }    
    private void eat(String s) {    
        tokenizer = new StringTokenizer(s);    
    }    
    
    public String nextLine() {     
        try {    
            return reader.readLine();    
        } catch (Exception e) {    
            return null;    
        }    
    }    
    
    public boolean hasNext() {    
        while (!tokenizer.hasMoreTokens()) {    
            String s = nextLine();    
            if (s == null)    
                return false;    
            eat(s);    
        }    
        return true;    
    }    
    
    public String next() {    
        hasNext();    
        return tokenizer.nextToken();    
    }    
    
    public int nextInt() {    
        return Integer.parseInt(next());    
    }    
    
    public int[] nextInts(int n) {    
        int[] nums = new int[n];    
        for (int i = 0; i < n; i++) {    
            nums[i] = nextInt();    
        }    
        return nums;    
    }    
    
    public long nextLong() {    
        return Long.parseLong(next());    
    }    
    
    public double nextDouble() {    
        return Double.parseDouble(next());    
    }    
    
    public BigInteger nextBigInteger() {    
        return new BigInteger(next());    
    }    
    
}