Problem: It is Bubble Cup finals season and farmer Johnny Bubbles must harvest his bubbles. The bubbles are in a rectangular bubblefield formed of N x M square parcels divided into N rows and M columns. The parcel in i^{th} row and j^{th} column yields A_{i,j} bubbles.

Johnny Bubbles has available a very special self-driving bubble harvester that, once manually positioned at the beginning of a row or column, automatically harvests all the bubbles in that row or column. Once the harvester reaches the end of the row or column it stops and must be repositioned. The harvester can pass through any parcel any number of times, but it can collect bubbles from the parcel only once.

Johnny is very busy farmer, so he is available to manually position the harvester at most four times per day. Johnny is also impatient, so he wants to harvest as many bubbles as possible on the first day.

Please help Johnny to calculate what is the maximum number of bubbles he can collect on the first day.

Input

The first line contains two integers N and M (1 ≤ N, M ≤ N * M ≤ 10^{5}) - the bubblefield size.

Each of the next N lines contains M integers. The j^{th} element in the i^{th} line is A_{i,j} (0 ≤ a_{i,j} ≤ 10^{9}) — the yield of the parcel located in the i^{th} row and the j^{th} column.

Output

Output contains one integer number - maximum number of the bubbles Johnny can harvest on the first day.

Examples

Input


2 2
1 2
3 4


Output


10


Input


5 5
0 9 2 7 0
9 0 3 0 5
0 8 0 3 1
6 7 4 3 9
3 6 4 1 0


Output


80

Note

In the first example, farmer Johnny can harvest all the bubbles by positioning the harvester on the first and the second row.

In the second example, one way Johnny can harvest maximum number of bubbles is to position the harvester in the second row, the fourth row, the second column and the fourth column.

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
long long solve(int n, int m, vector<vector<long long>> a) {
  long long sum = 0;
  vector<long long> w(n), h(m);
  map<long long, int> s;
  for (long long i = 0; i < n; i++) {
    long long mn = a[i][0];
    for (long long j = 1; j < m; j++) mn += (a[i][j]);
    w[i] = mn;
    s[mn]++;
  }
  int cnt = 4;
  while (cnt && s.size()) {
    auto it = s.rbegin();
    int cot = min(cnt, it->second);
    cnt -= cot;
    sum += it->first * cot;
    s.erase(it->first);
  }
  long long sum2 = 0;
  s.clear();
  for (long long i = 0; i < m; i++) {
    long long mn = a[0][i];
    for (long long j = 1; j < n; j++) mn += (a[j][i]);
    h[i] = mn;
    s[mn]++;
  }
  cnt = 4;
  while (cnt && s.size()) {
    auto it = s.rbegin();
    int cot = min(cnt, it->second);
    cnt -= cot;
    sum2 += it->first * cot;
    s.erase(it->first);
  }
  sum2 = max(sum, sum2);
  sum = 0;
  for (long long k = 0; k < 4; k++) {
    vector<long long> w(n), h(m);
    for (long long i = 0; i < n; i++) {
      long long mn = a[i][0];
      for (long long j = 1; j < m; j++) mn += (a[i][j]);
      w[i] = mn;
    }
    for (long long i = 0; i < m; i++) {
      long long mn = a[0][i];
      for (long long j = 1; j < n; j++) mn += (a[j][i]);
      h[i] = mn;
    }
    long long mx = 0, mx_id = 0;
    for (long long i = 0; i < n; i++)
      if (w[i] > w[mx_id]) mx_id = i;
    mx = w[mx_id];
    long long mx2 = 0, mx_id2 = 0;
    for (long long i = 0; i < m; i++)
      if (h[i] > h[mx_id2]) mx_id2 = i;
    mx2 = h[mx_id2];
    if (mx > mx2) {
      for (long long j = 0; j < m; j++) a[mx_id][j] = 0;
    } else {
      for (long long j = 0; j < n; j++) a[j][mx_id2] = 0;
    }
    sum += max(mx2, mx);
  }
  return max(sum, sum2);
}
pair<long long, vector<int>> solve_bad(int n, int m,
                                       vector<vector<long long>> a,
                                       int step = 0) {
  if (step == 4) return {0, {}};
  auto copy = a;
  vector<int> rs;
  long long res = 0;
  for (int i = 0; i < n; i++) {
    long long sum = 0;
    for (int j = 0; j < m; j++) sum += a[i][j], copy[i][j] = 0;
    auto ee = solve_bad(n, m, copy, step + 1);
    long long sum2 = sum + ee.first;
    for (int j = 0; j < m; j++) copy[i][j] = a[i][j];
    if (sum2 > res) rs = ee.second, rs.push_back(i);
    res = max(res, sum2);
  }
  for (int i = 0; i < m; i++) {
    if (step == 0 && i == 1) {
      step = step;
    }
    if (step == 1 && i == 4) {
      step = step;
    }
    if (step == 2 && i == 2) {
      step = step;
    }
    if (step == 3 && i == 0) {
      step = step;
    }
    long long sum = 0;
    for (int j = 0; j < n; j++) sum += a[j][i], copy[j][i] = 0;
    auto ee = solve_bad(n, m, copy, step + 1);
    long long sum2 = sum + ee.first;
    for (int j = 0; j < n; j++) copy[j][i] = a[j][i];
    if (sum2 > res) rs = ee.second, rs.push_back(-i);
    res = max(res, sum2);
  }
  return {res, rs};
}
int main3() {
  long long n = 5, m = 5;
  vector<vector<long long>> a(n, vector<long long>(m));
  srand(1e3 + 1);
  for (int i = 0; i < n; i++)
    for (int j = 0; j < m; j++) a[i][j] = abs(rand() % 10);
  for (int i = 0; i < n; i++)
    for (int j = 0; j < m; j++) a[i][j] = abs(rand() % 10);
  for (int i = 0; i < n; i++)
    for (int j = 0; j < m; j++) a[i][j] = abs(rand() % 10);
  while (true) {
    for (int i = 0; i < n; i++)
      for (int j = 0; j < m; j++) a[i][j] = abs(rand() % 100);
    long long w = solve(n, m, a);
    auto z = solve_bad(n, m, a);
    for (auto e : z.second) cout << e << " ";
    cout << w << " " << z.first << endl;
    if (w != z.first) {
      for (int i = 0; i < n; i++) {
        for (int j = 0; j < m; j++) cout << a[i][j] << " ";
        cout << endl;
      }
    }
  }
  return -1;
}
int mai2n() {
  long long n = 5, m = 5;
  cin >> n >> m;
  vector<vector<long long>> a(n, vector<long long>(m));
  for (int i = 0; i < n; i++)
    for (int j = 0; j < m; j++) cin >> a[i][j];
  auto e = solve_bad(n, m, a);
  for (auto z : e.second) cout << z << " ";
  cout << e.first;
  cin >> a[0][0];
  return -2;
}
int main() {
  long long n = 5, m = 5;
  cin >> n >> m;
  vector<vector<long long>> a(n, vector<long long>(m));
  for (int i = 0; i < n; i++)
    for (int j = 0; j < m; j++) cin >> a[i][j];
  cout << solve(n, m, a);
  cin >> a[0][0];
}