Problem: You are given n integers. You need to choose a subset and put the chosen numbers in a beautiful rectangle (rectangular matrix). Each chosen number should occupy one of its rectangle cells, each cell must be filled with exactly one chosen number. Some of the n numbers may not be chosen.

A rectangle (rectangular matrix) is called beautiful if in each row and in each column all values are different.

What is the largest (by the total number of cells) beautiful rectangle you can construct? Print the rectangle itself.

Input

The first line contains n (1 ≤ n ≤ 4⋅10^5). The second line contains n integers (1 ≤ a_i ≤ 10^9).

Output

In the first line print x (1 ≤ x ≤ n) — the total number of cells of the required maximum beautiful rectangle. In the second line print p and q (p ⋅ q=x): its sizes. In the next p lines print the required rectangle itself. If there are several answers, print any.

Examples

Input


12
3 1 4 1 5 9 2 6 5 3 5 8


Output


12
3 4
1 2 3 5
3 1 5 4
5 6 8 9


Input


5
1 1 1 1 1


Output


1
1 1
1

Solution (in JAVA):

Solution:
import java.io.*;
import java.math.BigDecimal;
import java.util.*;
import java.util.Map.Entry;
public class Contest1 {
    ////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
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////////                                                                                                               /////////
////////                                                                                                               /////////
////////   HHHH        HHHH  EEEEEEEEEEEEE   MMMM          MMMM         OOOOOO             SSSSSSS      EEEEEEEEEEEEE  /////////
////////   HHHH        HHHH  EEEEEEEEEEEEE   MMMMMM      MMMMMM      OOO      OOO        SSSS   SSS     EEEEEEEEEEEEE  /////////
////////   HHHH        HHHH  EEEEE           MMMM MMM  MMM MMMM    OOO          OOO    SSSS       SSS   EEEEE          /////////
////////   HHHH        HHHH  EEEEE           MMMM  MMMMMM  MMMM   OOO            OOO   SSSS             EEEEE          /////////
////////   HHHH        HHHH  EEEEE           MMMM          MMMM  OOO              OOO   SSSSSSS         EEEEE          /////////
////////   HHHHHHHHHHHHHHHH  EEEEEEEEEEE     MMMM          MMMM  OOO              OOO      SSSSSS       EEEEEEEEEEE    /////////
////////   HHHHHHHHHHHHHHHH  EEEEEEEEEEE     MMMM          MMMM  OOO              OOO         SSSSSSS   EEEEEEEEEEE    /////////
////////   HHHH        HHHH  EEEEE           MMMM          MMMM   OOO            OOO              SSSS  EEEEE          /////////
////////   HHHH        HHHH  EEEEE           MMMM          MMMM    OOO          OOO     SSS       SSSS  EEEEE          /////////
////////   HHHH        HHHH  EEEEEEEEEEEEE   MMMM          MMMM      OOO      OOO        SSS    SSSS    EEEEEEEEEEEEE  /////////
////////   HHHH        HHHH  EEEEEEEEEEEEE   MMMM          MMMM         OOOOOO             SSSSSSS      EEEEEEEEEEEEE  /////////
////////                                                                                                               /////////
////////                                                                                                               /////////
////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
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    public static void main(String[] args) throws IOException, InterruptedException {
        Scanner sc = new Scanner(System.in);
        PrintWriter pw = new PrintWriter(System.out);
        int n = sc.nextInt();
        Integer[]a = new Integer[n];
        HashMap<Integer,Integer>hm= new HashMap<>();
        for (int i =0;i<n;i++){
            a[i]=sc.nextInt();
            hm.put(a[i],hm.getOrDefault(a[i],0)+1);
        }
        int[]occless= new int[n+1];
        int[]occgrt= new int[n+2];
        for (int x:hm.keySet()){
            occless[hm.get(x)]+=hm.get(x);
            occgrt[hm.get(x)]++;
        }
        for (int i =1;i<=n;i++)occless[i]+=occless[i-1];
        for (int i =n;i>=1;i--)occgrt[i]+=occgrt[i+1];
        int d1=1;
        int d2=1;
        for (int i =1;i<=n;i++){
//            int j =2;
//            while (1l*j*j<=i){
//                if (i%j==0){
//                    md=Math.max(md,Math.min(j,i/j));
//                }
//                j++;
//            }
            int x= occless[i-1];
            x+=occgrt[i]*i;
            if (x/i>=i&&(i*(x/i))>d1*d2){
                d1=i;
                d2=x/i;
            }
        }
        int[][]sol= new int[d1][d2];
        int i =0;
        int j =0;
        Arrays.sort(a);
        Arrays.sort(a,(cc,vv)->hm.get(vv)-hm.get(cc));
        Queue<Integer>q= new LinkedList<>();
        int ll=0;
        int occ=0;
        int all=0;
        for (int l=0;all<d1*d2&&l<n;l++){
            if (ll==a[l]){
                if (occ==d1)continue;
                occ++;
                ((LinkedList<Integer>) q).add(a[l]);
                all++;
            }
            else {
                all++;
                occ=1;
                ll=a[l];
                ((LinkedList<Integer>) q).add(a[l]);
            }
        }
        int c=0;
        while (c<d1*d2){
            if (sol[i][j]!=0){
                i=i+1;
                i%=d1;
                continue;
            }
            sol[i][j]=q.poll();
            i++;
            j++;
            i%=d1;
            j%=d2;
            c++;
        }
        pw.println(d1*d2);
        pw.println(d1+" "+d2);
        for (int []x:sol){
            for (int z:x)pw.print(z+" ");
            pw.println();
        }


        pw.flush();
    }

    static class Scanner {
        StringTokenizer st;
        BufferedReader br;

        public Scanner(FileReader r) {
            br = new BufferedReader(r);
        }

        public Scanner(InputStream s) {
            br = new BufferedReader(new InputStreamReader(s));
        }

        public String next() throws IOException {
            while (st == null || !st.hasMoreTokens())
                st = new StringTokenizer(br.readLine());
            return st.nextToken();
        }

        public int nextInt() throws IOException {
            return Integer.parseInt(next());
        }

        public long nextLong() throws IOException {
            return Long.parseLong(next());
        }

        public String nextLine() throws IOException {
            return br.readLine();
        }

        public double nextDouble() throws IOException {
            String x = next();
            StringBuilder sb = new StringBuilder("0");
            double res = 0, f = 1;
            boolean dec = false, neg = false;
            int start = 0;
            if (x.charAt(0) == '-') {
                neg = true;
                start++;
            }
            for (int i = start; i < x.length(); i++)
                if (x.charAt(i) == '.') {
                    res = Long.parseLong(sb.toString());
                    sb = new StringBuilder("0");
                    dec = true;
                } else {
                    sb.append(x.charAt(i));
                    if (dec)
                        f *= 10;
                }
            res += Long.parseLong(sb.toString()) / f;
            return res * (neg ? -1 : 1);
        }

        public boolean ready() throws IOException {
            return br.ready();
        }
    }

}