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

#ifdef _WIN32
#define scanfll(x) scanf("%I64d", x)
#define printfll(x) printf("%I64d", x)
#else
#define scanfll(x) scanf("%lld", x)
#define printfll(x) printf("%lld", x)
#endif
#define rep(i,n) for(long long i = 0; i < (long long)(n); i++)
#define repi(i,a,b) for(long long i = (long long)(a); i < (long long)(b); i++)
#define pb push_back
#define all(x) (x).begin(), (x).end()
#define fi first
#define se second
#define mt make_tuple
#define mp make_pair
template<class T1, class T2> bool chmin(T1 &a, T2 b) { return b < a && (a = b, true); }
template<class T1, class T2> bool chmax(T1 &a, T2 b) { return a < b && (a = b, true); }

using ll = long long; using ld = long double; using vll = vector<ll>; using vvll = vector<vll>; using vld = vector<ld>; 
using vi = vector<int>; using vvi = vector<vi>;
vll conv(vi& v) { vll r(v.size()); rep(i, v.size()) r[i] = v[i]; return r; }
using P = pair<ll, ll>;

template <typename T, typename U> ostream &operator<<(ostream &o, const pair<T, U> &v) {  o << "(" << v.first << ", " << v.second << ")"; return o; }
template<size_t...> struct seq{}; template<size_t N, size_t... Is> struct gen_seq : gen_seq<N-1, N-1, Is...>{}; template<size_t... Is> struct gen_seq<0, Is...> : seq<Is...>{};
template<class Ch, class Tr, class Tuple, size_t... Is>
void print_tuple(basic_ostream<Ch,Tr>& os, Tuple const& t, seq<Is...>){ using s = int[]; (void)s{0, (void(os << (Is == 0? "" : ", ") << get<Is>(t)), 0)...}; }
template<class Ch, class Tr, class... Args> 
auto operator<<(basic_ostream<Ch, Tr>& os, tuple<Args...> const& t) -> basic_ostream<Ch, Tr>& { os << "("; print_tuple(os, t, gen_seq<sizeof...(Args)>()); return os << ")"; }
ostream &operator<<(ostream &o, const vvll &v) { rep(i, v.size()) { rep(j, v[i].size()) o << v[i][j] << " "; cout << endl; } return o; }
template <typename T> ostream &operator<<(ostream &o, const vector<T> &v) { o << '['; rep(i, v.size()) o << v[i] << (i != v.size()-1 ? ", " : ""); o << "]";  return o; }
template <typename T>  ostream &operator<<(ostream &o, const set<T> &m) { o << '['; for (auto it = m.begin(); it != m.end(); it++) o << *it << (next(it) != m.end() ? ", " : ""); o << "]";  return o; }
template <typename T, typename U>  ostream &operator<<(ostream &o, const map<T, U> &m) { o << '['; for (auto it = m.begin(); it != m.end(); it++) o << *it << (next(it) != m.end() ? ", " : ""); o << "]";  return o; }
template <typename T, typename U>  ostream &operator<<(ostream &o, const unordered_map<T, U> &m) { o << '['; for (auto it = m.begin(); it != m.end(); it++) o << *it; o << "]";  return o; }
void printbits(ll mask, ll n) { rep(i, n) { cout << !!(mask & (1ll << i)); } cout << endl; }
#define ldout fixed << setprecision(40) 

static const double EPS = 1e-14;
static const long long INF = 1e18;
static const long long mo = 1e9+7;

using lll = __int128_t; using ull = __uint128_t;

// int128_t?????????
std::ostream&
operator<<( std::ostream& dest, __int128_t value )
{
    std::ostream::sentry s( dest );
    if ( s ) {
        __uint128_t tmp = value < 0 ? -value : value;
        char buffer[ 128 ];
        char* d = std::end( buffer );
        do
        {
            -- d;
            *d = "0123456789"[ tmp % 10 ];
            tmp /= 10;
        } while ( tmp != 0 );
        if ( value < 0 ) {
            -- d;
            *d = '-';
        }
        int len = std::end( buffer ) - d;
        if ( dest.rdbuf()->sputn( d, len ) != len ) {
            dest.setstate( std::ios_base::badbit );
        }
    }
    return dest;
}
void printbits(__int128_t n) {
    rep(i, 128) {
        if (n & ((__int128_t)1 << (127 - i))) 
            cout << 1;
        else 
            cout << 0;
    }
    cout << endl;
}

ll popcount(lll x) {
    ll c = 0;
    rep(i, 128) {
        c += !!(x & ((lll)1 << i));
    }
    return c;
}

int main(void) {
    cin.tie(0); ios::sync_with_stdio(false);
    ll n, qnum; 
    while (cin >> n >> qnum && n && qnum) {
        vector<ll> a(qnum); 
        rep(i, qnum) rep(j, n) { 
            char c; cin >> c; if (c - '0') a[i] |= 1ll << (n-1-j); 
        }

        map<lll, ll> memo; // 1 if impossible
        function<ll(lll, ll)> f = [&](lll x, ll counter) -> ll {
//            if (counter > 3) return 0;
//            if (popcount(x) == qnum) return ;
            if (popcount(x) == qnum - 1) return 0;
            if (popcount(x) == qnum) return INF;
            if (memo.count(x)) return memo[x];

            ll ret = INF;
            rep(j, n) {
                lll yes, no; yes = no = x; 
                rep(i, qnum) {
                    ((a[i] & ((ll)1 << (n-1-j))) ? yes : no) |= ((lll)1 << i);
                }
                ll tmp = -1;
                ll yes_ret = INF, no_ret = INF; 
                if (yes != x)
                    yes_ret = f(yes, counter+1);
                if (no != x)
                    no_ret = f(no, counter+1);
                if (yes_ret != INF)
                    chmax(tmp, yes_ret);
                if (no_ret != INF)
                    chmax(tmp, no_ret);
                if (tmp != -1)
                    chmin(ret, tmp + 1);

                /*
                cout << "----" << endl;
                cout << j << endl;
                printbits(x); 
                printbits(yes); 
                printbits(no); 
                cout << yes_ret << endl;
                cout << popcount(yes) << endl;
                cout << no_ret << endl;
                cout << popcount(no) << endl;
                cout << qnum << endl;
                cout << tmp << endl;
                cout << ret << endl;
                */
            }
            return memo[x] = ret;
        };
        cout << f(0, 0) << endl;
        //        cout << __builtin_popcount((lll)(3)) << endl;
    }
    return 0;
}

Measured memory_bytes: 4592