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.awt.*;
import java.io.*;
import java.sql.Array;
import java.util.*;
import java.util.List;

public class Main {
    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 final int N=10000005;
    static final int mod=1000000007;
    static final int INF=1000000009;
    static final int numBit=17;
    static FastReader r=new FastReader();
    static PrintWriter pw = new PrintWriter(System.out);

    static int factor[]=new int[N];

    public static void sieve(){
        for(int i=2;i<N;++i){
            if(factor[i]==0){
                factor[i]=i;
                for(long j=1l*i*i;j<N;j+=i){
                    factor[(int)j]=i;
                }
            }
        }
    }

    public static void main(String[] args) throws IOException {
        sieve();
        int []ans=new int[N];
        for(int i=1;i<=10000000;++i){
            int x=i;
            long cur=1;
            while(x>1){
                int f=factor[x];
                long q=1;
                while(x%f==0){
                    x/=f;
                    q*=f;
                }
                q*=f;
                cur*=(q-1)/(f-1);
            }
            if(cur<=10000000){
                if(ans[(int)cur]==0) ans[(int)cur]=i;
            }
        }
        int t=r.nextInt();
        while(t-->0){
            int x=r.nextInt();
            if(ans[x]==0) pw.println(-1);
            else pw.println(ans[x]);
        }
        pw.close();
    }
}