#include <bits/stdc++.h>

using namespace std;

inline int toInt(string s) {int v; istringstream sin(s);sin>>v;return v;}
template<class T> inline string toString(T x) {ostringstream sout;sout<<x;return sout.str();}
template<class T> inline T sqr(T x) {return x*x;}

typedef vector<int> vi;
typedef vector<vi> vvi;
typedef vector<string> vs;
typedef pair<int, int> pii;
typedef long long ll;

#define all(a)  (a).begin(),(a).end()
#define rall(a) (a).rbegin(), (a).rend()
#define pb push_back
#define mp make_pair
#define each(i,c) for(typeof((c).begin()) i=(c).begin(); i!=(c).end(); ++i)
#define exist(s,e) ((s).find(e)!=(s).end())
#define range(i,a,b) for(int i=(a);i<(b);++i)
#define rep(i,n)  range(i,0,n)
#define clr(a,b) memset((a), (b) ,sizeof(a))
#define dump(x)  cerr << #x << " = " << (x) << endl;
#define debug(x) cerr << #x << " = " << (x) << " (L" << __LINE__ << ")" << " " << __FILE__ << endl;

const double eps = 1e-10;
const double pi  = acos(-1.0);
const ll INF =1LL << 62;
const int inf =1 << 29;

int m,n;

int a[128];
int memo[1<<11][1<<11];

int rec(int mask,int yes,int depth){
	int& ret=memo[mask][yes];
	if(ret>=0) return ret;

	ret=m;
	vi cur;
	rep(i,n){
		bool ok=true;
		rep(j,m) if(mask&(1<<j)) if( (yes&(1<<j))!=(a[i]&(1<<j)) ) ok=false;
		if(ok) cur.pb(a[i]);
	}

	if(cur.size()<=1) return ret=depth;

	rep(i,m){
		if(mask&(1<<i)) continue;
		int nmask=mask|(1<<i);
		int nyes=yes|(1<<i);
		int nno=yes;
		int cur=max(rec(nmask,nyes,depth+1),rec(nmask,nno,depth+1));
		ret=min(ret,cur);
	}
	return ret;
}

int main(void){
	while(cin >> m >> n,m){
		rep(i,n){
			string in;
			cin >> in;
			a[i]=0;
			rep(j,m) a[i]=(a[i]<<1)|(in[j]-'0');
		}
		clr(memo,-1);
		cout << rec(0,0,0) << endl;
	}
	return 0;
}