You are given n integer numbers a_1, a_2, ..., a_n. Consider graph on n nodes, in which nodes i, j (i≠ j) are connected if and only if, a_i AND a_j≠ 0, where AND denotes the [bitwise AND operation](https://en.wikipedia.org/wiki/Bitwise_operation#AND).

Find the length of the shortest cycle in this graph or determine that it doesn't have cycles at all.

Input

The first line contains one integer n (1 ≤ n ≤ 10^5) — number of numbers.

The second line contains n integer numbers a_1, a_2, ..., a_n (0 ≤ a_i ≤ 10^{18}).

Output

If the graph doesn't have any cycles, output -1. Else output the length of the shortest cycle.

Examples

Input


4
3 6 28 9


Output


4

Input


5
5 12 9 16 48


Output


3

Input


4
1 2 4 8


Output


-1

Note

In the first example, the shortest cycle is (9, 3, 6, 28).

In the second example, the shortest cycle is (5, 12, 9).

The graph has no cycles in the third example.
import java.io.*; 
import java.util.*; 
//import javafx.util.*; 
import java.math.*;
//import java.lang.*;
public class untitled 
{ 
  //  static int n;static ArrayList<Integer> arr[];
   // int ans[];
    public static void main(String[] args) throws IOException { 
    //    Scanner sc=new Scanner(System.in);
        PrintWriter pw = new PrintWriter(new BufferedWriter(new OutputStreamWriter(System.out)));
    //    br = new BufferedReader(new InputStreamReader(System.in));
        Reader s=new Reader();
        int n=s.nextInt();
        long arr[]=new long[n];
        for(int i=0;i<n;i++){
            arr[i]=s.nextLong();
        }
        ArrayList<Integer> bit[]=new ArrayList[60];
        for(int i=0;i<60;i++){
            bit[i]=new ArrayList<Integer>();
        }
        for(int j=0;j<60;j++){
            for(int i=0;i<n;i++){
                if((arr[i] & (1L << j)) >0){
        //            pw.println(j+" "+i);
                    bit[j].add(i);
                }
            }
        }
        for(int i=0;i<60;i++){
            if(bit[i].size()>2){
                pw.println("3");
                pw.close();
                return;
            }
        }
        HashSet<Integer> g[]=new HashSet[n];
        for(int i=0;i<n;i++){
            g[i]=new HashSet();
        }
        for(int i=0;i<60;i++){
            for (int j : bit[i]) {
                for (int k : bit[i]) {
                    if (j != k) {
                      //  out.println(i+" "+j+" "+k);
                        g[j].add(k);
                    }
                }
            }
        }
        //  for(int i=0;i<n;i++){
        //     Iterator itr =g[i].iterator();
        //     pw.println(i);
        //     while(itr.hasNext()){
        //         pw.print(itr.next()+" ");
        //     }
        //     pw.println();
        // }
        int min=10000000;
        for(int i=0;i<n;i++){
            //boolean visited[]=new boolean[n];
            if(g[i].size()<=1){
                continue;
            }
        
             //   pw.println(i);
                int ans=fun(g,i,n);
             //   pw.println(ans+" "+i);
                if(ans<min){
                    min=ans;
                }
            
        }
        if(min==10000000){
            pw.println("-1");
        }
        else{
            pw.println(min);
        }
        pw.close();
    }
    static int fun(HashSet<Integer> g[],int i,int n){
        int pre[]=new int[n];
        int dis[]=new int[n];
        Arrays.fill(pre,-1);
        Arrays.fill(dis,-1);
        ArrayDeque<Integer> q=new ArrayDeque<Integer>();
        q.add(i);
        dis[i]=0;
        int min = Integer.MAX_VALUE;
        while(!q.isEmpty()){

            int v=q.remove();
        //    System.out.println(v);
            Iterator itr =g[v].iterator();
            while(itr.hasNext()){
                int u=(Integer)itr.next();
                if(dis[u]<0){
                    dis[u]=dis[v]+1;
                    pre[u]=v;
                    q.add(u);
                }
                else if(pre[v]!=u){
                    min=Math.min(dis[u]+dis[v]+1,min);
                }
            }
        }
        return min;
    }


    public static BufferedReader br;
    public static StringTokenizer st;
    public static String next() {
        while (st == null || !st.hasMoreTokens()) {
            try {
                st = new StringTokenizer(br.readLine());
            } catch (Exception e) {
                throw new RuntimeException(e);
            }
        }
        return st.nextToken();
    }
 
    public static Integer nextInt() {
        return Integer.parseInt(next());
    }
 
    public static Long nextLong() {
        return Long.parseLong(next());
    }
 
    public static Double nextDouble() {
        return Double.parseDouble(next());
    }
    static class Pair{
        int x;int y;
        Pair(int x,int y){
            this.x=x;
            this.y=y;
          //  this.i=i;
        }
    }
    static class sorting implements Comparator<Pair>{
        public int compare(Pair a,Pair b){
            //return (a.y)-(b.y);
            return (a.x-b.x);
        }
    }
    public static int[] na(int n)throws IOException{
        int[] a = new int[n];
        for(int i = 0;i < n;i++)a[i] = nextInt();
        return a;
    }
    static class query implements Comparable<query>{
        int l,r,idx,block;
        static int len;
        query(int l,int r,int i){
            this.l=l;
            this.r=r;
            this.idx=i;
            this.block=l/len;
        }   
        public int compareTo(query a){
            return block==a.block?r-a.r:block-a.block;
        }
    }
    static boolean isPrime(int n) { 
        if (n <= 1) 
            return false; 
        if (n <= 3) 
            return true; 
        if (n % 2 == 0 ||  
            n % 3 == 0) 
            return false; 
      
        for (int i = 5; 
                 i * i <= n; i = i + 6) 
            if (n % i == 0 || 
                n % (i + 2) == 0) 
                return false; 
      
        return true; 
    } 
    static long gcd(long a, long b) { 
      if (b == 0) 
        return a; 
      return gcd(b, a % b);  
    }  
    static long modInverse(long a, long m) { 
        long g = gcd(a, m); 
        if (g != 1) 
            return -1; 
        else{ 
            // If a and m are relatively prime, then modulo inverse 
            // is a^(m-2) mode m 
            return (power(a, m - 2, m)); 
        } 
    } 
      
    // To compute x^y under modulo m 
    static long power(long x, long y, long m){ 
        if (y == 0) 
            return 1;      
        long p = power(x, y / 2, m) % m; 
        p = (p * p) % m; 
      
        if (y % 2 == 0) 
            return p; 
        else
            return (x * p) % m; 
    }
    static long fast_pow(long base,long n,long M){
        if(n==0)
           return 1;
        if(n==1)
        return base;
        long halfn=fast_pow(base,n/2,M);
        if(n%2==0)
            return ( halfn * halfn ) % M;
        else
            return ( ( ( halfn * halfn ) % M ) * base ) % M;
    }
       static long modInverse(long n,int M){
        return fast_pow(n,M-2,M);
    }
        static class Reader 
    { 
        final private int BUFFER_SIZE = 1 << 16; 
        private DataInputStream din; 
        private byte[] buffer; 
        private int bufferPointer, bytesRead; 
  
        public Reader() 
        { 
            din = new DataInputStream(System.in); 
            buffer = new byte[BUFFER_SIZE]; 
            bufferPointer = bytesRead = 0; 
        } 
  
        public Reader(String file_name) throws IOException 
        { 
            din = new DataInputStream(new FileInputStream(file_name)); 
            buffer = new byte[BUFFER_SIZE]; 
            bufferPointer = bytesRead = 0; 
        } 
  
        public String readLine() throws IOException 
        { 
            byte[] buf = new byte[1000000]; // line length 
            int cnt = 0, c; 
            while ((c = read()) != -1) 
            { 
                if (c == '\n') 
                    break; 
                buf[cnt++] = (byte) c; 
            } 
            return new String(buf, 0, cnt); 
        } 
  
        public int nextInt() throws IOException 
        { 
            int ret = 0; 
            byte c = read(); 
            while (c <= ' ') 
                c = read(); 
            boolean neg = (c == '-'); 
            if (neg) 
                c = read(); 
            do
            { 
                ret = ret * 10 + c - '0'; 
            }  while ((c = read()) >= '0' && c <= '9'); 
  
            if (neg) 
                return -ret; 
            return ret; 
        } 
  
        public long nextLong() throws IOException 
        { 
            long ret = 0; 
            byte c = read(); 
            while (c <= ' ') 
                c = read(); 
            boolean neg = (c == '-'); 
            if (neg) 
                c = read(); 
            do { 
                ret = ret * 10 + c - '0'; 
            } 
            while ((c = read()) >= '0' && c <= '9'); 
            if (neg) 
                return -ret; 
            return ret; 
        } 
  
        public double nextDouble() throws IOException 
        { 
            double ret = 0, div = 1; 
            byte c = read(); 
            while (c <= ' ') 
                c = read(); 
            boolean neg = (c == '-'); 
            if (neg) 
                c = read(); 
  
            do { 
                ret = ret * 10 + c - '0'; 
            } 
            while ((c = read()) >= '0' && c <= '9'); 
  
            if (c == '.') 
            { 
                while ((c = read()) >= '0' && c <= '9') 
                { 
                    ret += (c - '0') / (div *= 10); 
                } 
            } 
  
            if (neg) 
                return -ret; 
            return ret; 
        } 
  
        private void fillBuffer() throws IOException 
        { 
            bytesRead = din.read(buffer, bufferPointer = 0, BUFFER_SIZE); 
            if (bytesRead == -1) 
                buffer[0] = -1; 
        } 
  
        private byte read() throws IOException 
        { 
            if (bufferPointer == bytesRead) 
                fillBuffer(); 
            return buffer[bufferPointer++]; 
        } 
  
        public void close() throws IOException 
        { 
            if (din == null) 
                return; 
            din.close(); 
        } 
    } 
} 