//#pragma GCC optimize("Ofast,no-stack-protector")
//#pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,avx")
//#pragma GCC optimize("Ofast,fast-math")
//#pragma GCC target("avx,avx2")
//#pragma GCC optimize(2)
//#pragma GCC optimize(3)
//#pragma GCC optimize("Ofast")
#include <bits/stdc++.h>
using namespace std;
//#define int long long
typedef pair<int, int> pii;
typedef vector<int> vi;
typedef double db;
#define F(i, a, b) for(int i = a; i <= (b); ++i)
#define F2(i, a, b) for(int i = a; i < (b); ++i)
#define dF(i, a, b) for(int i = a; i >= (b); --i)
template<typename T> void debug(string s, T x) {
	cerr << "[" << s << "] = [" << x << "]\n";
}
template<typename T, typename... Args> void debug(string s, T x, Args... args) {
	for (int i = 0, b = 0; i < (int)s.size(); i++) if (s[i] == '(' || s[i] == '{') b++;
	else if (s[i] == ')' || s[i] == '}') b--;
	else if (s[i] == ',' && b == 0) {
		cerr << "[" << s.substr(0, i) << "] = [" << x << "] | ";
		debug(s.substr(s.find_first_not_of(' ', i + 1)), args...);
		break;
	}
}
#ifdef ONLINE_JUDGE
#define Debug(...)
#else
#define Debug(...) debug(#__VA_ARGS__, __VA_ARGS__)
#endif
#define pb push_back
#define fi first
#define se second
#define Mry fprintf(stderr, "%.3lf MB\n", (&Med - &Mbe) / 1048576.0)
#define Try cerr << 1e3 * clock() / CLOCKS_PER_SEC << " ms\n";
typedef long long ll;
// namespace Fread {const int SIZE = 1 << 17; char buf[SIZE], *S, *T; inline char getchar() {if (S == T) {T = (S = buf) + fread(buf, 1, SIZE, stdin); if (S == T) return '\n';} return *S++;}}
// namespace Fwrite {const int SIZE = 1 << 17; char buf[SIZE], *S = buf, *T = buf + SIZE; inline void flush() {fwrite(buf, 1, S - buf, stdout), S = buf;} inline void putchar(char c) {*S++ = c;if (S == T) flush();} struct NTR {~NTR() {flush();}} ztr;}
// #ifdef ONLINE_JUDGE
// #define getchar Fread::getchar
// #define putchar Fwrite::putchar
// #endif
inline int ri() {
	int x = 0;
	bool t = 0;
	char c = getchar();
	while (c < '0' || c > '9') t |= c == '-', c = getchar();
	while (c >= '0' && c <= '9') x = (x << 3) + (x << 1) + (c ^ 48), c = getchar();
	return t ? -x : x;
}
inline void wi(int x) {
	if (x < 0) {
		putchar('-'), x = -x;
	}
	if (x > 9) wi(x / 10);
	putchar(x % 10 + 48);
}
inline void wi(int x, char s) {
	wi(x), putchar(s);
}
bool Mbe;
// mt19937 rnd(chrono::steady_clock::now().time_since_epoch().count());
const int mod = 998244353;
const int inf = 0x3f3f3f3f;
const ll infll = 0x3f3f3f3f3f3f3f3f;
const int _ = 1e6 + 5;

int solve(int l, int m, int r) {
	// 左右要扩展的，长度，
	if (l == 0 && r == 0) return 0;
	if (l > r) swap(l, r);
	int pp = (l + m - 1) / m; // ceil(l/m)
	if (pp & 1) {
		return solve(max(0, l - m), m + min(l, m), r) + 1;
	} else {
		return solve(l, m + min(r, m), max(0, r - m)) + 1; 
	}
}

int R, C, h[_], tp, st[_], pre[_], nxt[_];

char str[_];

bool Med;
signed main() {
	// Mry;
	R = ri(), C = ri();
	int ans = inf;
	F(i, 0, R - 1) {
		scanf("%s", str);
		F(j, 0, C - 1) if(str[j] == '0') h[j] = 0;
		else h[j]++;
		// h : 往上最长1
		tp = 0;
		F(j, 0, C - 1) {
			nxt[j] = C;
			while(tp > 0 && h[st[tp]] > h[j]) {
				nxt[st[tp]] = j;
				tp--;
			}
			st[++tp] = j;
		}
		tp = 0;
		dF(j, C - 1, 0) {
			pre[j] = -1;
			while(tp && h[st[tp]] > h[j]) {
				pre[st[tp]] = j;
				tp--;
			}
			st[++tp] = j;
		}
		// 每一列左右第一个比他小的
		F(j, 0, C - 1) if(h[j]) {
			ans = min(ans, solve(pre[j] + 1, nxt[j] - pre[j] - 1, C - nxt[j]) + solve(i - h[j] + 1, h[j], R - i - 1));
		}
	}
	cout << ans << '\n';
	// Try;
	return 0;
}