#include <bits/stdc++.h>
using namespace std;

const int MXN = 1000005;
int N, M, hei[MXN], stk[MXN], top(-1), lb[MXN], rb[MXN], ans;
int lg2[MXN];
char str[MXN];

inline int func(int ls, int rs, int len) {
  int fil(lg2[(ls + len + len - 1) / len]);
  int nle((len << fil) - ((ls + len - 1) / len * len - ls));
  return fil + lg2[(ls + len + rs + nle - 1) / nle];
}
inline int calc(int ls, int rs, int len) {
  return min(func(ls, rs, len), func(rs, ls, len));
}

int main() {
  cin >> N >> M, ans = N * M;
  lg2[0] = -1;
  for (int i(2); i <= max(N, M); ++i) lg2[i] = lg2[i >> 1] + 1;
  for (int i(0); i != N; ++i) {
    cin >> str;
    for (int j(0); j != M; ++j) {
      hei[j] = (str[j] == '1' ? hei[j] + 1 : 0);
      while (~top && hei[stk[top]] > hei[j]) rb[stk[top--]] = j;
      lb[j] = (~top ? stk[top] : -1);
      stk[++top] = j;
    }
    while (~top) rb[stk[top--]] = M;
    for (int j(0); j != M; ++j)
      if (hei[j]) {
        int l1(rb[j] - lb[j] - 1), l2(hei[j]);
        int ls1(lb[j] + 1), rs1(M - rb[j]);
        int ls2(i + 1 - hei[j]), rs2(N - 1 - i);
        ans = min(ans, calc(ls1, rs1, l1) + calc(ls2, rs2, l2));
      }
  }
  cout << ans << endl;
  return 0;
}