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 CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
const double pi = acos(-1.0);
const double eps = 1e-11;
template <class T>
inline void checkmin(T &a, T b) {
  if (b < a) a = b;
}
template <class T>
inline void checkmax(T &a, T b) {
  if (b > a) a = b;
}
template <class T>
inline T sqr(T x) {
  return x * x;
}
template <class T>
inline string bin(T n, int pos = 62) {
  string s;
  T i, one = 1, two = 2;
  for (i = (one << (pos - 1)); i > 0; i = (i >> 1)) s += ((n & i) ? "1" : "0");
  return s;
}
int lsb(unsigned int v) {
  int r;
  static const int MultiplyDeBruijnBitPosition[32] = {
      0,  1,  28, 2,  29, 14, 24, 3, 30, 22, 20, 15, 25, 17, 4,  8,
      31, 27, 13, 23, 21, 19, 16, 7, 26, 12, 18, 6,  11, 5,  10, 9};
  r = MultiplyDeBruijnBitPosition[((uint32_t)((v & -v) * 0x077CB531U)) >> 27];
  return r + 1;
}
template <class T>
inline int msb(T n) {
  return (n == 0) ? 0 : (1 + msb(n >> 1));
}
template <class T>
inline T getbit(T n, int pos) {
  return ((n & (1 << pos)) ? 1 : 0);
}
template <class T>
inline int countbit(T n) {
  return (n == 0) ? 0 : (1 + countbit(n & (n - 1)));
}
template <class T>
inline void setbit(T &n, int p) {
  n = n | (1LL << p);
}
template <class T>
inline T gcd(T a, T b) {
  if (a < 0) return gcd(-a, b);
  if (b < 0) return gcd(a, -b);
  return (b == 0) ? a : gcd(b, a % b);
}
bool isequal(vector<int> a, vector<int> b) {
  for (int i = 0; i < (a.size()); i++)
    if (a[i] != b[i]) return false;
  return true;
}
template <class T>
bool allequal(vector<T> a) {
  sort(a.begin(), a.end());
  return a[0] == a[a.size() - 1];
}
template <class T1, class T2>
void printpairs(vector<pair<T1, T2>> p) {
  for (auto t : p) {
    cout << "(" << t.first << " " << t.second << ")  ";
  }
  cout << endl;
}
template <class T>
void printvec(vector<T> a) {
  for (int i = 0; i < (a.size()); i++) cout << a[i] << " ";
  cout << endl;
}
void printarray(int *a, int n) {
  for (int i = 0; i < (n); i++) cout << *(a + i) << " ";
  cout << endl;
}
template <typename T>
void printmatrix(vector<vector<T>> a, int n, int m, int width = 5) {
  for (int i = 0; i < n; i++) {
    for (int j = 0; j < m; j++) {
      cout << a[i][j] << " ";
    }
    cout << endl;
  }
}
template <typename T>
void readmatrix(vector<vector<T>> &a, int n, int m) {
  for (int i = 0; i < n; i++) {
    for (int j = 0; j < m; j++) {
      cin >> a[i][j];
    }
  }
}
template <class T>
void printsubarray(vector<T> a, int start, int end) {
  if (start < 0 or end > a.size() - 1) cout << "Out of bounds" << endl;
  for (int i = start; i <= end; i++) cout << a[i] << " ";
  cout << endl;
}
bool isprime(int n) {
  if (n < 2) return false;
  if (n == 2) return true;
  for (int i = 2; i * i <= n; i++) {
    if (n % i == 0) return false;
  }
  return true;
}
void split(const string &s, char c, vector<string> &result) {
  stringstream ss(s);
  string x;
  while (getline(ss, x, c)) result.push_back(x);
}
void err(vector<string>::iterator it) {}
template <typename T, typename... Args>
void err(vector<string>::iterator it, T a, Args... args) {
  cerr << it->substr((*it)[0] == ' ', it->length()) << " = " << a << ' ';
  err(++it, args...);
}
void yup() { cout << "Yes" << endl; }
void nope() { cout << "No" << endl; }
void Yup() { cout << "YES" << endl; }
void Nope() { cout << "NO" << endl; }
template <typename T>
void readvec(vector<T> &a, int size) {
  T tmp;
  a.clear();
  for (int i = 0; i < (size); i++) {
    cin >> tmp;
    a.push_back(tmp);
  }
}
int best(int x, vector<int> a, int n) {
  long long s = 0;
  for (int i = 0; i < n; i++) {
    s += min(a[i], x);
  }
  int k = s / (long long)x;
  if (k >= x)
    return k;
  else
    return 0;
}
vector<pair<int, int>> c;
void printboard(int r, int c, vector<pair<int, int>> p) {
  for (pair<int, int> &x : p)
    if (x.first > r) x.first = r;
  int s = 0;
  int j = 0;
  for (pair<int, int> &x : p) {
    j++;
    s += x.first;
    if (s >= r * c) {
      x.first = x.first - s + r * c;
      p.erase(p.begin() + j, p.end());
      break;
    }
  }
  int m = p.size();
  int offset = 0;
  vector<vector<int>> g(r, vector<int>(c, 0));
  int curx = 0, cury = 0;
  for (int i = 0; i < m; i++) {
    auto &x = p[i];
    while (x.first > 0) {
      g[curx][cury] = x.second;
      curx++;
      cury++;
      if (curx == r) {
        cury = ++offset;
      }
      curx %= r;
      cury %= c;
      x.first--;
    }
  }
  cout << r << " " << c << endl;
  printmatrix(g, r, c, 2);
  return;
}
vector<pair<int, int>> countFreq(vector<int> arr, int n) {
  unordered_map<int, int> mp;
  for (int i = 0; i < n; i++) mp[arr[i]]++;
  for (auto x : mp) {
    c.push_back({x.second, x.first});
  }
  sort(c.begin(), c.end(), greater<pair<int, int>>());
  return c;
}
void solvecase() {
  int n;
  vector<int> a;
  cin >> n;
  readvec(a, n);
  vector<pair<int, int>> p = countFreq(a, n);
  vector<int> f;
  for (pair<int, int> ip : p) f.push_back(ip.first);
  int m = p.size();
  int ans = 0;
  int r, c;
  for (int i = 1; i * i <= n; i++) {
    int dim = best(i, f, m);
    int cur = i * dim;
    if (ans < cur) {
      ans = cur;
      r = i;
      c = dim;
    }
  }
  cout << ans << endl;
  printboard(r, c, p);
}
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  int cases = 1;
  while (cases--) {
    solvecase();
  }
  return 0;
}