Gargari is jealous that his friend Caisa won the game from the previous problem. He wants to prove that he is a genius.

He has a n × n chessboard. Each cell of the chessboard has a number written on it. Gargari wants to place two bishops on the chessboard in such a way that there is no cell that is attacked by both of them. Consider a cell with number x written on it, if this cell is attacked by one of the bishops Gargari will get x dollars for it. Tell Gargari, how to place bishops on the chessboard to get maximum amount of money.

We assume a cell is attacked by a bishop, if the cell is located on the same diagonal with the bishop (the cell, where the bishop is, also considered attacked by it).

Input

The first line contains a single integer n (2 ≤ n ≤ 2000). Each of the next n lines contains n integers aij (0 ≤ aij ≤ 109) — description of the chessboard.

Output

On the first line print the maximal number of dollars Gargari will get. On the next line print four integers: x1, y1, x2, y2 (1 ≤ x1, y1, x2, y2 ≤ n), where xi is the number of the row where the i-th bishop should be placed, yi is the number of the column where the i-th bishop should be placed. Consider rows are numbered from 1 to n from top to bottom, and columns are numbered from 1 to n from left to right.

If there are several optimal solutions, you can print any of them.

Examples

Input

4
1 1 1 1
2 1 1 0
1 1 1 0
1 0 0 1


Output

12
2 2 3 2
#include <bits/stdc++.h>
using namespace std;
string to_string(string s) { return '"' + s + '"'; }
string to_string(char s) { return string(1, s); }
string to_string(const char* s) { return to_string((string)s); }
string to_string(bool b) { return (b ? "true" : "false"); }
template <typename A>
string to_string(A);
template <typename A, typename B>
string to_string(pair<A, B> p) {
  return "(" + to_string(p.first) + ", " + to_string(p.second) + ")";
}
template <typename A>
string to_string(A v) {
  bool f = 1;
  string r = "{";
  for (const auto& x : v) {
    if (!f) r += ", ";
    f = 0;
    r += to_string(x);
  }
  return r + "}";
}
void debug_out() { cout << '\n'; }
template <typename Head, typename... Tail>
void debug_out(Head H, Tail... T) {
  cout << " " << to_string(H);
  debug_out(T...);
}
const long double eps = 1e-7;
const long long mod = 1000000007;
const long long N = 998244353;
long long binpow(long long b, long long p) {
  long long ans = 1;
  while (p > 0) {
    if (p & 1) ans = (ans * b) % mod;
    b = (b * b) % mod;
    p >>= 1;
  }
  return ans;
}
long long modinv(long long x) { return binpow(x, mod - 2); }
const long long mxn = 2050;
long long d1[2 * mxn], d2[2 * mxn], a[mxn][mxn];
signed main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  long long n, i, j, c;
  cin >> n;
  for (i = 1; i <= n; i++) {
    for (j = 1; j <= n; j++) {
      cin >> a[i][j];
      d1[i + j] += a[i][j];
      d2[i - j + n] += a[i][j];
    }
  }
  long long ans[2];
  pair<long long, long long> p[2];
  ans[0] = ans[1] = -1;
  for (i = 1; i <= n; i++) {
    for (j = 1; j <= n; j++) {
      c = (i + j) % 2;
      if (d1[i + j] + d2[i - j + n] - a[i][j] > ans[c]) {
        ans[c] = d1[i + j] + d2[i - j + n] - a[i][j];
        p[c].first = i;
        p[c].second = j;
      }
    }
  }
  cout << ans[0] + ans[1] << '\n';
  cout << p[0].first << " " << p[0].second << " " << p[1].first << " "
       << p[1].second;
}
