#pragma GCC optimize ("O3")
#include <iostream>
#include <iomanip>
#include <istream>
#include <ostream>
#include <sstream>
#include <iterator>
#include <vector>
#include <algorithm>
#include <queue>
#include <deque>
#include <list>
#include <stack>
#include <map>
#include <unordered_map>
#include <set>
#include <bitset>
#include <utility>
#include <cmath>
#include <cstdio>
#include <cstring>
#include <string>
#include <ctime>
#include <cctype>
#include <cstdlib>
#include <numeric>
#define IINF 1000000000
#define INF 9223372036854775807
#define MOD 998244353
#define mod 998244353
#define INT_MAX_ 2147483647
#define EPS (1e-10)
#define REP(i, a, n) for (ll i = a; i < (ll)(n); i++)
#define REPE(i, a, n) for (ll i = a; i <= (ll)(n); i++)
#define rep(i,n)for (ll i = 0; i < (ll)(n); i++)
#define rep1(i,n) for(int i=1;i<=(int)(n);i++)
#define Endl endl
#define fi first
#define se second
#define pb push_back
#define mp make_pair
#define mt make_tuple
#define eb emplace_back
#define mmax(x,y)(x>y?x:y)
#define mmin(x,y)(x<y?x:y)
#define chmax(x,y) x=mmax(x,y)
#define chmin(x,y) x=mmin(x,y)
#define all(x) (x).begin(),(x).end()
#define siz(x) (ll)(x).size()
#define PI acos(-1.0)
#define me memset
#define bit(n,k) ((n>>k)&1)
using namespace std;
typedef long long int ll;
typedef unsigned long long int ull;
typedef long double ld;
typedef pair<int,int>Pin;
typedef pair<ll,ll>Pll;
template<class T> using V=vector<T>;
template<typename T> using min_priority_queue = priority_queue<T, vector<T>, greater<T> >;
long long GCD(long long a, long long b) {return b?GCD(b,a%b):a;}
long long LCM(long long a, long long b) {return a/GCD(a,b)*b;}
int dx[4]={-1,0,1,0};
int dy[4]={0,-1,0,1};
int ddx[8]={-1,0,1,0,1,1,-1,-1};
int ddy[8]={0,-1,0,1,1,-1,1,-1};
ll cmp1(pair<ll,ll> a,pair<ll,ll> b){
        if(a.se!=b.se)
        return a.se<b.se;
        else
        return a.fi>b.fi;
}
//----------------------------------------------------------------------
int M, N;
int character[150][15];
map<V<int>, int> m;

int dfs(V<int> S) {
    if (S.size() <= 1) return 0;
    int ret = m[S];
    if (ret > 0) return ret;
    ret = M;
    for (int i = 0; i < M; i++) {
        V<int> left, right;
        for (int v : S) {
            if (character[v][i]) left.push_back(v);
            else right.push_back(v);
        }
        if (left.empty() || right.empty()) continue;
        ret = min(ret, 1+max(dfs(left), dfs(right)));
    }
    m[S]=ret;
    return ret;
}
//----------------------------------------------------------------------
int main(){
    cin.tie(0);
    ios::sync_with_stdio(false);
    //-------------------------------  
    //ll begin_t=clock();
    //freopen("input.txt", "r", stdin);
    //freopen("output.txt", "w", stdout);
    //-------------------------------
    while (cin >> M >> N) {
        if (M == 0 && N == 0) break;

        for (int i = 0; i < N; i++) {
            string s;
            cin >> s;
            for (int j = 0; j < M; j++) {
                character[i][j] = s[j] - '0';
            }
        }

        m.clear();
        vector<int> S(N);


        for (int i = 0; i < N; i++)
            S[i] = i;
        cout << dfs(S) << endl;
    }
    //-------------------------------  
    //fclose(stdin);
    //fclose(stdout);
    //ll end_t=clock();cout<<"time="<<end_t-begin_t<<"ms"<<endl;
    //-------------------------------
    return 0;
}
//----------------------------------------------------------------------











































Measured memory_bytes: 5292