Problem: Let us denote by d(n) the sum of all divisors of the number n, i.e. d(n) = ∑_{k | n} k.

For example, d(1) = 1, d(4) = 1+2+4=7, d(6) = 1+2+3+6=12.

For a given number c, find the minimum n such that d(n) = c.

Input

The first line contains one integer t (1 ≤ t ≤ 10^4). Then t test cases follow.

Each test case is characterized by one integer c (1 ≤ c ≤ 10^7).

Output

For each test case, output: 

  * "-1" if there is no such n that d(n) = c; 
  * n, otherwise. 

Example

Input


12
1
2
3
4
5
6
7
8
9
10
39
691


Output


1
-1
2
3
-1
5
4
7
-1
-1
18
-1

Solution (in JAVA):

Solution:
import java.util.*;
import java.io.*;
public class MyClass
{
    static class FastReader 
    { 
        BufferedReader br; 
        StringTokenizer st; 
  
        public FastReader() 
        { 
            br = new BufferedReader(new
                     InputStreamReader(System.in)); 
        } 
  
        String next() 
        { 
            while (st == null || !st.hasMoreElements()) 
            { 
                try
                { 
                    st = new StringTokenizer(br.readLine()); 
                } 
                catch (IOException  e) 
                { 
                    e.printStackTrace(); 
                } 
            } 
            return st.nextToken(); 
        } 
  
        int nextInt() 
        { 
            return Integer.parseInt(next()); 
        } 
  
        long nextLong() 
        { 
            return Long.parseLong(next()); 
        } 
  
        double nextDouble() 
        { 
            return Double.parseDouble(next()); 
        } 
  
        String nextLine() 
        { 
            String str = ""; 
            try
            { 
                str = br.readLine(); 
            } 
            catch (IOException e) 
            { 
                e.printStackTrace(); 
            } 
            return str; 
        } 
    }
    static class Pair implements Comparable<Pair>
    {
        int f,s;
        Pair(int f,int s)
        {
            this.f=f;
            this.s=s;
        }
        public int compareTo(Pair p)
        {
            return this.f-p.f;
        }
    }
    public static void main(String args[])
    {
        FastReader fs=new FastReader();
        PrintWriter pw=new PrintWriter(System.out);
        int prime[]=new int[(int)1e7+1];
        prime[1]=1;
        for(int i=2;i*i<prime.length;i++)
        {
            if(prime[i]==0)
            {
                for(int j=i*i;j<prime.length;j+=i)
                {
                    if(prime[j]==0)
                    prime[j]=i;
                }
            }
        }
        long s[]=new long[(int)1e7+1];
        s[1]=1;
        for(int i=2;i<s.length;i++)
        {
            if(prime[i]==0)
            {
                prime[i]=i;
                s[i]=prime[i]+1;
            }
            else
            {
                s[i]=1;
                int j=i;
                while(j%prime[i]==0)
                {
                    j/=prime[i];
                    s[i]=s[i]*prime[i]+1;
                }
                s[i]*=s[j];
            }
        }
        long ans[]=new long[(int)1e7+10];
        Arrays.fill(ans,-1);
        for(int i=s.length-1;i>0;i--)
        {
            if(s[i]<=(int)1e7)
            ans[(int)s[i]]=i;
        }
        int tc=fs.nextInt();
        while(tc-->0)
        pw.println(ans[fs.nextInt()]);
        pw.flush();
        pw.close();
    }
}