Problem: You are given a tournament — complete directed graph.

In one operation you can pick any vertex v and change the direction of all edges with v on one of the ends (i.e all edges u → v change their orientation to v → u and vice versa).

You want to make the tournament strongly connected with the smallest possible number of such operations if it is possible. 

Also, if it is possible, you need to find the number of ways to make this number of operations to make graph strongly connected (two ways are different if for some i vertex that we chose on i-th operation in one way is different from vertex that we chose on i-th operation in another way). You only need to find this value modulo 998 244 353.

Input

The first line of input contains one integer n (3 ≤ n ≤ 2000): the number of vertices in the tournament.

Following n lines contain a description of the given tournament, each of them contains a binary string of length n. If j-th character of i-th string is equal to '1', then the graph has an edge i → j.

It is guaranteed that there are no edges i → i and the graph has exactly one edge among i → j and j → i for different i and j.

Output

If it is not possible to convert tournament to strongly connected with the given operations, output "-1".

Otherwise, output two integers: the smallest number of operations that you need to make the given graph strongly connected and the number of ways to do this number of operations to make graph strongly connected, modulo 998 244 353.

Examples

Input


3
010
001
100


Output


0 1


Input


4
0010
1000
0100
1110


Output


-1


Input


6
010000
001000
100000
111001
111100
111010


Output


2 18

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using vi = vector<int>;
using vvi = vector<vi>;
using vll = vector<ll>;
using vvll = vector<vll>;
using vb = vector<bool>;
using vd = vector<double>;
using vs = vector<string>;
using pii = pair<int, int>;
using pll = pair<ll, ll>;
using pdd = pair<double, double>;
using vpii = vector<pii>;
using vvpii = vector<vpii>;
using vpll = vector<pll>;
using vvpll = vector<vpll>;
using vpdd = vector<pdd>;
using vvpdd = vector<vpdd>;
template <typename T>
void ckmin(T& a, const T& b) {
  a = min(a, b);
}
template <typename T>
void ckmax(T& a, const T& b) {
  a = max(a, b);
}
mt19937_64 rng(chrono::steady_clock::now().time_since_epoch().count());
namespace __input {
template <class T1, class T2>
void re(pair<T1, T2>& p);
template <class T>
void re(vector<T>& a);
template <class T, size_t SZ>
void re(array<T, SZ>& a);
template <class T>
void re(T& x) {
  cin >> x;
}
void re(double& x) {
  string t;
  re(t);
  x = stod(t);
}
template <class Arg, class... Args>
void re(Arg& first, Args&... rest) {
  re(first);
  re(rest...);
}
template <class T1, class T2>
void re(pair<T1, T2>& p) {
  re(p.first, p.second);
}
template <class T>
void re(vector<T>& a) {
  for (int i = 0; i < (int((a).size())); i++) re(a[i]);
}
template <class T, size_t SZ>
void re(array<T, SZ>& a) {
  for (int i = 0; i < (SZ); i++) re(a[i]);
}
}  // namespace __input
using namespace __input;
namespace __output {
template <class T1, class T2>
void pr(const pair<T1, T2>& x);
template <class T, size_t SZ>
void pr(const array<T, SZ>& x);
template <class T>
void pr(const vector<T>& x);
template <class T>
void pr(const deque<T>& x);
template <class T>
void pr(const set<T>& x);
template <class T1, class T2>
void pr(const map<T1, T2>& x);
template <class T>
void pr(const T& x) {
  cout << x;
}
template <class Arg, class... Args>
void pr(const Arg& first, const Args&... rest) {
  pr(first);
  pr(rest...);
}
template <class T1, class T2>
void pr(const pair<T1, T2>& x) {
  pr("{", x.first, ", ", x.second, "}");
}
template <class T, bool pretty = true>
void prContain(const T& x) {
  if (pretty) pr("{");
  bool fst = 1;
  for (const auto& a : x) pr(!fst ? pretty ? ", " : " " : "", a), fst = 0;
  if (pretty) pr("}");
}
template <class T>
void pc(const T& x) {
  prContain<T, false>(x);
  pr("\n");
}
template <class T, size_t SZ>
void pr(const array<T, SZ>& x) {
  prContain(x);
}
template <class T>
void pr(const vector<T>& x) {
  prContain(x);
}
template <class T>
void pr(const deque<T>& x) {
  prContain(x);
}
template <class T>
void pr(const set<T>& x) {
  prContain(x);
}
template <class T1, class T2>
void pr(const map<T1, T2>& x) {
  prContain(x);
}
void ps() { pr("\n"); }
template <class Arg>
void ps(const Arg& first) {
  pr(first);
  ps();
}
template <class Arg, class... Args>
void ps(const Arg& first, const Args&... rest) {
  pr(first, " ");
  ps(rest...);
}
}  // namespace __output
using namespace __output;
namespace __algorithm {
template <typename T>
void dedup(vector<T>& v) {
  sort((v).begin(), (v).end());
  v.erase(unique((v).begin(), (v).end()), v.end());
}
template <typename T>
typename vector<T>::iterator find(vector<T>& v, const T& x) {
  auto it = lower_bound((v).begin(), (v).end(), x);
  return it != v.end() && *it == x ? it : v.end();
}
template <typename T>
size_t index(vector<T>& v, const T& x) {
  auto it = find(v, x);
  assert(it != v.end() && *it == x);
  return it - v.begin();
}
template <typename C, typename T, typename OP>
vector<T> prefixes(const C& v, T id, OP op) {
  vector<T> r(int((v).size()) + 1, id);
  for (int i = 0; i < (int((v).size())); i++) r[i + 1] = op(r[i], v[i]);
  return r;
}
template <typename C, typename T, typename OP>
vector<T> suffixes(const C& v, T id, OP op) {
  vector<T> r(int((v).size()) + 1, id);
  for (int i = (int((v).size())) - 1; i >= 0; i--) r[i] = op(v[i], r[i + 1]);
  return r;
}
}  // namespace __algorithm
using namespace __algorithm;
#pragma GCC diagnostic push
#pragma GCC diagnostic ignored "-Wunused-parameter"
struct monostate {
  friend istream& operator>>(istream& is, const monostate& ms) { return is; }
  friend ostream& operator<<(ostream& os, const monostate& ms) { return os; }
  friend monostate operator+(const monostate& a, const monostate& b) {
    return a;
  }
} ms;
#pragma GCC diagnostic pop
namespace __io {
void setIn(string second) { freopen(second.c_str(), "r", stdin); }
void setOut(string second) { freopen(second.c_str(), "w", stdout); }
void setIO(string second = "") {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cout << fixed << setprecision(15);
  if (int((second).size())) {
    setIn(second + ".in"), setOut(second + ".out");
  }
}
}  // namespace __io
using namespace __io;
int main() {
  setIO();
  int N;
  re(N);
  vs g(N);
  re(g);
  if (N <= 6) {
    int ans = INT_MAX, ways = 0;
    for (int m = 0; m < (1 << N); m++) {
      vi reach(N);
      for (int i = 0; i < (N); i++) {
        reach[i] |= 1 << i;
        for (int j = (i + 1); j < (N); j++) {
          bool ij = (g[i][j] == '1') ^ ((m >> i) & 1) ^ ((m >> j) & 1);
          if (ij)
            reach[i] |= 1 << j;
          else
            reach[j] |= 1 << i;
        }
      }
      for (int k = 0; k < (N); k++)
        for (int i = 0; i < (N); i++)
          if (reach[i] & (1 << k)) reach[i] |= reach[k];
      bool strong = 1;
      for (int i = 0; i < (N); i++) strong &= __builtin_popcount(reach[i]) == N;
      if (strong) {
        int flip = __builtin_popcount(m);
        if (flip < ans) {
          ans = flip;
          ways = 0;
        }
        if (flip == ans) ways++;
      }
    }
    if (ans == INT_MAX)
      ps(-1);
    else {
      for (int v = (1); v < (ans + 1); v++) ways *= v;
      ps(ans, ways);
    }
    return 0;
  }
  vi out_deg(N);
  vi with_out(N);
  auto count_sccs = [&]() {
    fill((with_out).begin(), (with_out).end(), 0);
    for (auto& e : out_deg) with_out[e]++;
    int nodes = 0;
    int tot_out = 0;
    int ans = 0;
    for (int out = (N)-1; out >= 0; out--) {
      for (int _ = 0; _ < (with_out[out]); _++) {
        nodes++;
        tot_out += out;
        if (tot_out == nodes * (N - nodes) + nodes * (nodes - 1) / 2) ans++;
      }
    }
    return ans;
  };
  for (int i = 0; i < (N); i++)
    for (int j = 0; j < (N); j++) {
      out_deg[i] += g[i][j] == '1';
    }
  if (count_sccs() == 1) {
    ps(0, 1);
    return 0;
  }
  int ways = 0;
  vi tmp(int((out_deg).size()));
  for (int i = 0; i < (N); i++) {
    copy((out_deg).begin(), (out_deg).end(), tmp.begin());
    for (int j = 0; j < (N); j++)
      if (j != i) {
        if (g[i][j] == '1') {
          tmp[i]--;
          tmp[j]++;
        } else {
          tmp[i]++;
          tmp[j]--;
        }
      }
    swap(tmp, out_deg);
    if (count_sccs() == 1) ways++;
    swap(tmp, out_deg);
  }
  assert(ways);
  ps(1, ways);
  return 0;
}