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

#define fs first
#define sc second

const LL MOD = 1e9+7;
const double EPS = 1e-10;

template<class T>bool chmax(T &a, const T &b) {
    if (a < b) { a = b; return true; }
    return false;
}
template<class T>bool chmin(T &a, const T &b) {
    if (b < a) { a = b; return true; }
    return false;
}

// std::vector Declaration
template<typename T>
vector<T> make_v(size_t a) { return vector<T>(a); }
template<typename T,typename... Ts>
auto make_v(size_t a,Ts... ts) {
    return vector<decltype(make_v<T>(ts...))>(a,make_v<T>(ts...));
}

// std::vector Declaration and Initialization
template<typename T>
vector<T> make_vector(size_t a, T x) { return vector<T>(a, x); }
template<typename T, typename U, typename... Ts>
auto make_vector(size_t a, U b, Ts... ts) {
    return vector<decltype(make_vector<T>(b,ts...))>(a,make_vector<T>(b,ts...));
}

// std::vector Input
template<typename T>
istream& operator>>(istream& is, vector<T>& v) {
    for (auto &e : v) {
        is >> e;
    }
    return is;
}

// std::vector Debug
template<typename T>
ostream& operator<<(ostream& os, const vector<T>& v) {
    os << "[";
    bool a = 1;
    for (auto e : v) {
        os << (a ? "" : " ");
        os << e;
        a = 0;
    }
    os << "]";
    return os;
}

// std::array Debug
template<typename T, size_t n>
ostream& operator<<(ostream& os, const array<T, n>& v) {
    os << "[";
    bool a = 1;
    for (auto e : v) {
        os << (a ? "" : " ");
        os << e;
        a = 0;
    }
    os << "]";
    return os;
}

// std::deque Debug
template<typename T>
ostream& operator<<(ostream& os, const deque<T>& d) {
    os << "[";
    bool a = 1;
    for (auto e : d) {
        os << (a ? "" : " ");
        os << e;
        a = 0;
    }
    os << "]";
    return os;
}

// std::pair Debug
template<typename T, typename U>
ostream& operator<<(ostream& os, const pair<T, U>& p) {
    os << "(" << p.first << " " << p.second << ")";
    return os;
}

// std::set Debug
template<typename T>
ostream& operator<<(ostream& os, const set<T>& st) {
    os << "{";
    bool a = 1;
    for (auto e : st) {
        os << (a ? "" : " ");
        os << e;
        a = 0;
    }
    os << "}";
    return os;
}

// std::multiset Debug
template<typename T>
ostream& operator<<(ostream& os, const multiset<T>& st) {
    os << "{";
    bool a = 1;
    for (auto e : st) {
        os << (a ? "" : " ");
        os << e;
        a = 0;
    }
    os << "}";
    return os;
}

// std::map Debug
template<typename T, typename U>
ostream& operator<<(ostream& os, const map<T, U>& mp) {
    os << "{";
    bool a = 1;
    for (auto e : mp) {
        os << (a ? "" : " ");
        os << e.first << ":" << e.second;
        a = 0;
    }
    os << "}";
    return os;
}

// std::tuple Debug
template<int N, class Tuple>
void out(ostream& os, const Tuple& t){}
template<int N, class Tuple, class H, class ...Ts>
void out(ostream& os, const Tuple& t) {
    if (N) os << " ";
    os << get<N>(t);
    out<N+1,Tuple,Ts...>(os, t);
}
template<class ...Ts>
ostream& operator<<(ostream& os, const tuple<Ts...>& t) {
    os << "(";
    out<0,tuple<Ts...>,Ts...>(os, t);
    os << ")";
    return os;
}

// Debug
#define DUMP(x) cerr<<#x<<" = "<<(x)<<endl

// Weighted edge
template<typename T>
struct edge {
    int src, to;
    T cost;

    edge(int to, T cost) : src(-1), to(to), cost(cost) {}
    edge(int src, int to, T cost) : src(src), to(to), cost(cost) {}

    edge &operator=(const int &x) {
        to = x;
        return *this;
    }

    operator int() const { return to; }

    friend ostream& operator<<(ostream& os, const edge& e) {
        return os << "(" << e.src << "->" << e.to << ":" << e.cost << ")";
    }
};

template<typename T>
using Edges = vector<edge<T>>;
template<typename T>
using WeightedGraph = vector<Edges<T>>;
using UnWeightedGraph = vector<vector<int>>;
template<typename T>
using MatrixGraph = vector<vector<T>>;

int main()
{
    while (true) {
        int m, n; cin >> m >> n;
        if (m == 0 && n == 0) {
            break;
        }
        vector<string> a(n); cin >> a;

        vector<int> dp((1<<m)*(1<<m), m);
        for (int s = (1<<m)-1; s >= 0; --s) {
            for (int t = (1<<m)-1; t >= 0; --t) {
                t &= s;

                int cnt = 0;
                for (int i = 0; i < n; ++i) {
                    bool valid = true;
                    for (int j = 0; j < m; ++j) if (s & (1<<j)) {
                        if (a[i][j]-'0' != (t>>j&1)) {
                            valid = false;
                            break;
                        }
                    }
                    if (valid) {
                        ++cnt;
                    }
                }

                if (cnt <= 1) {
                    dp[s*(1<<m) + t] = 0;
                    continue;
                }

                for (int j = 0; j < m; ++j) if (!(s & (1<<j))) {
                    chmin(dp[s*(1<<m) + t], max(
                            dp[(s | (1<<j))*(1<<m) + (t | (1<<j))],
                            dp[(s | (1<<j))*(1<<m) + t]) + 1);
                }
            }
        }

        cout << dp[0] << endl;
    }

    return 0;
}



Measured memory_bytes: 19508