// Blackpink in your area
// corner cases // int vs ll // clear structures // statement // doublesz // line order // 0-1-indexed
#include <bits/stdc++.h>
#define endl '\n'
#define fst first
#define snd second
#define pb push_back
#define sz(x) int(x.size())
#define REP(i,n) for(int i = 0; i < int(n); ++i)
#define trace(x) cerr << #x << " = " << x << endl
#define fastio ios_base::sync_with_stdio(0);cin.tie(0);cout.tie(0)
using namespace std;
typedef long long ll;
typedef pair<int,int> ii;

typedef ll tf;
typedef ll tc;
const tf INFFLOW = 1e9;
const tc INFCOST = 1e9;
const int MAXN = 1024 * 2 + 20;

int to_mask(string s){
	int ans = 0;
	for(int i = 0; i < sz(s); ++i){
		if(s[i] == '1'){
			ans |= (1 << i);
		}
	}
	return ans;
}

const int inf = 1e9;
int d, n;
int mark[MAXN];
int get_mask[MAXN];
int in_node[MAXN], out_node[MAXN];

struct MCF{
	int n;
	vector<tc> prio, pot;
	vector<tf> curflow;
	vector<int> prevedge, prevnode;
	priority_queue<pair<tc,int>, vector<pair<tc,int>>, greater<pair<tc,int>>> q;
	struct edge{ int to, rev; tf f, cap; tc cost; };
	vector< vector<edge> > g;
	MCF(int n) : n(n), prio(n), curflow(n), prevedge(n), prevnode(n), pot(n), g(n){}
	void add_edge(int s, int t, tf cap, tc cost){
		// cout << "Adding edge from " << s << " to " << t << " cap = " << cap << " cost = " << cost << endl;
		g[s].pb((edge){t, sz(g[t]), 0, cap, cost});
		g[t].pb((edge){s, sz(g[s])-1, 0, 0, -cost});
	}
	pair<tf,tc> get_flow(int s, int t){
		tf flow = 0;
		tc flowcost = 0;
		while(1){
			q.push({0,s});
			fill(prio.begin(), prio.end(), INFCOST);
			prio[s] = 0; curflow[s] = INFFLOW;
			while(!q.empty()){
				auto cur = q.top();
				tc d = cur.first;
				int u = cur.second;
				q.pop();
				if(d != prio[u]) continue;
				for(int i = 0; i < sz(g[u]); ++i){
					edge &e = g[u][i];
					int v = e.to;
					if(e.cap <= e.f) continue;
					tc nprio = prio[u] + e.cost + pot[u] - pot[v];
					if(prio[v] > nprio){
						prio[v] = nprio;
						q.push({nprio, v});
						prevnode[v] = u; prevedge[v] = i;
						curflow[v] = min(curflow[u], e.cap - e.f);
					}
				}
			}
			if(prio[t] == INFCOST) break;
			REP(i,n) pot[i] += prio[i];
			tf df = min(curflow[t], INFFLOW - flow);
			flow += df;
			for(int v = t; v != s; v = prevnode[v]){
				edge &e = g[prevnode[v]][prevedge[v]];
				e.f += df; g[v][e.rev].f -= df;
				flowcost += df * e.cost;
			}
		}
		return {flow, flowcost};
	}

	vector<int> solve(int s, int t, int flow){
		vector<int> ans;
		t--; // ssink -> sink
		while(flow--){
			int now = s;
			while(1){
				// cross self
				int v = -1;
				int cur_msk = get_mask[now];
				for(auto &e : g[now]){
					if(e.f > 0){
						e.f--;
						v = e.to;
						break;
					}
				}
				assert(v >= 0);
				now = v;
				v = -1;
				// cross to another mask
				for(auto &e : g[now]){
					if(e.f > 0){
						e.f--;
						v = e.to;
						break;
					}
				}
				assert(v >= 0);
				if(v == t) break;
				now = v;
				int bit = -1;
				int new_msk = get_mask[now];
				for(int i = 0; i < d; ++i){
					if( (cur_msk & (1 << i)) == 0 && (new_msk & (1 << i)) > 0 ){
						bit = i;
						break;
					}
				}
				assert(bit >= 0);
				ans.pb(bit);
			}
			ans.pb(-1);
		}
		ans.pop_back();
		return ans;
	}

};

int src = 0, sink = MAXN - 5;
int ssink = sink + 1;
vector<int> ans;
vector< array<int,4> > edges;

int network_cost(int lim, int last = 0){
	MCF network(MAXN);
	for(auto ar : edges){
		network.add_edge(ar[0], ar[1], ar[2], ar[3]);
	}
	network.add_edge(sink, ssink, lim, 0);
	auto f = network.get_flow(src, ssink);
	if(last){
		ans = network.solve(src, ssink, f.fst);
	}
	return f.snd;
}

int main(){

	fastio;
	cin >> d >> n;
	
	MCF network(MAXN);
	int gid = 0;
	for(int m = 0; m < (1 << d); ++m){
		in_node[m] = gid++;
		out_node[m] = gid++;
		get_mask[in_node[m]] = m;
		get_mask[out_node[m]] = m;
		edges.pb({in_node[m], out_node[m], inf, 0});
		if(m > 0){
			edges.pb({out_node[m], sink, inf, 0});
		}
	}

	for(int m = 0; m < (1 << d); ++m){
		for(int j = 0; j < d; ++j){
			if(m & (1 << j)) continue;
			int nm = m | (1 << j);
			edges.pb({out_node[m], in_node[nm], inf, 1});
		}
	}

	for(int i = 0; i < n; ++i){
		string s;
		cin >> s;
		int msk = to_mask(s);
		edges.pb({in_node[msk], out_node[msk], 1, int(-1e5)});
	}

	int lo = 0, hi = 254;
	while(hi - lo > 1){
		int mid = (lo + hi) / 2;
		if(network_cost(mid) >= network_cost(mid+1)) lo = mid;
		else hi = mid;
	}

	network_cost(lo+1, 1);

	cout << sz(ans) << endl;
	for(int x : ans){
		if(x == -1) cout << "R ";
		else cout << x << " ";
	}
	cout << endl;

	return 0;
}

### Prompt

Your task is to create a CPP solution to the following problem:

You are standing in front of the room with great treasures. The only thing stopping you is the door with a push-button combination lock. This lock has d buttons with digits from 0 to d - 1. Whenever you press a button, it stays pushed down. You can not pop back up just one button, but there is a "RESET" button — pressing it pops up all other buttons. Initially, no buttons are pushed down.

The door instantly opens when some specific set of digits is pushed down. Sadly, you don't know the password for it. Having read the documentation for this specific lock, you found out that there are n possible passwords for this particular lock. 

Find the shortest sequence of button presses, such that all possible passwords appear at least once during its execution. Any shortest correct sequence of button presses will be accepted.

Input

The first line contains two integers d and n (1 ≤ d ≤ 10; 1 ≤ n ≤ 2^d - 1). Next n lines describe possible passwords. Each line contains a string s_i of d zeros and ones: for all j from 1 to d the j-th character is 1 iff the button with the digit j - 1 must be pushed down.

All strings s_i are different, and each string contains at least one 1.

Output

On the first line, print the number k — the minimum number of button presses. On the second line, print k tokens, describing the sequence. Whenever you press a button with a digit, print that digit. Whenever you press "RESET", print "R".

Examples

Input


2 2
10
11


Output


2
0 1 


Input


3 4
001
111
101
011


Output


6
2 0 R 1 2 0 

Note

In the second example, the sequence 1 2 R 2 0 1 is also possible.

### Response

```cpp
// Blackpink in your area
// corner cases // int vs ll // clear structures // statement // doublesz // line order // 0-1-indexed
#include <bits/stdc++.h>
#define endl '\n'
#define fst first
#define snd second
#define pb push_back
#define sz(x) int(x.size())
#define REP(i,n) for(int i = 0; i < int(n); ++i)
#define trace(x) cerr << #x << " = " << x << endl
#define fastio ios_base::sync_with_stdio(0);cin.tie(0);cout.tie(0)
using namespace std;
typedef long long ll;
typedef pair<int,int> ii;

typedef ll tf;
typedef ll tc;
const tf INFFLOW = 1e9;
const tc INFCOST = 1e9;
const int MAXN = 1024 * 2 + 20;

int to_mask(string s){
	int ans = 0;
	for(int i = 0; i < sz(s); ++i){
		if(s[i] == '1'){
			ans |= (1 << i);
		}
	}
	return ans;
}

const int inf = 1e9;
int d, n;
int mark[MAXN];
int get_mask[MAXN];
int in_node[MAXN], out_node[MAXN];

struct MCF{
	int n;
	vector<tc> prio, pot;
	vector<tf> curflow;
	vector<int> prevedge, prevnode;
	priority_queue<pair<tc,int>, vector<pair<tc,int>>, greater<pair<tc,int>>> q;
	struct edge{ int to, rev; tf f, cap; tc cost; };
	vector< vector<edge> > g;
	MCF(int n) : n(n), prio(n), curflow(n), prevedge(n), prevnode(n), pot(n), g(n){}
	void add_edge(int s, int t, tf cap, tc cost){
		// cout << "Adding edge from " << s << " to " << t << " cap = " << cap << " cost = " << cost << endl;
		g[s].pb((edge){t, sz(g[t]), 0, cap, cost});
		g[t].pb((edge){s, sz(g[s])-1, 0, 0, -cost});
	}
	pair<tf,tc> get_flow(int s, int t){
		tf flow = 0;
		tc flowcost = 0;
		while(1){
			q.push({0,s});
			fill(prio.begin(), prio.end(), INFCOST);
			prio[s] = 0; curflow[s] = INFFLOW;
			while(!q.empty()){
				auto cur = q.top();
				tc d = cur.first;
				int u = cur.second;
				q.pop();
				if(d != prio[u]) continue;
				for(int i = 0; i < sz(g[u]); ++i){
					edge &e = g[u][i];
					int v = e.to;
					if(e.cap <= e.f) continue;
					tc nprio = prio[u] + e.cost + pot[u] - pot[v];
					if(prio[v] > nprio){
						prio[v] = nprio;
						q.push({nprio, v});
						prevnode[v] = u; prevedge[v] = i;
						curflow[v] = min(curflow[u], e.cap - e.f);
					}
				}
			}
			if(prio[t] == INFCOST) break;
			REP(i,n) pot[i] += prio[i];
			tf df = min(curflow[t], INFFLOW - flow);
			flow += df;
			for(int v = t; v != s; v = prevnode[v]){
				edge &e = g[prevnode[v]][prevedge[v]];
				e.f += df; g[v][e.rev].f -= df;
				flowcost += df * e.cost;
			}
		}
		return {flow, flowcost};
	}

	vector<int> solve(int s, int t, int flow){
		vector<int> ans;
		t--; // ssink -> sink
		while(flow--){
			int now = s;
			while(1){
				// cross self
				int v = -1;
				int cur_msk = get_mask[now];
				for(auto &e : g[now]){
					if(e.f > 0){
						e.f--;
						v = e.to;
						break;
					}
				}
				assert(v >= 0);
				now = v;
				v = -1;
				// cross to another mask
				for(auto &e : g[now]){
					if(e.f > 0){
						e.f--;
						v = e.to;
						break;
					}
				}
				assert(v >= 0);
				if(v == t) break;
				now = v;
				int bit = -1;
				int new_msk = get_mask[now];
				for(int i = 0; i < d; ++i){
					if( (cur_msk & (1 << i)) == 0 && (new_msk & (1 << i)) > 0 ){
						bit = i;
						break;
					}
				}
				assert(bit >= 0);
				ans.pb(bit);
			}
			ans.pb(-1);
		}
		ans.pop_back();
		return ans;
	}

};

int src = 0, sink = MAXN - 5;
int ssink = sink + 1;
vector<int> ans;
vector< array<int,4> > edges;

int network_cost(int lim, int last = 0){
	MCF network(MAXN);
	for(auto ar : edges){
		network.add_edge(ar[0], ar[1], ar[2], ar[3]);
	}
	network.add_edge(sink, ssink, lim, 0);
	auto f = network.get_flow(src, ssink);
	if(last){
		ans = network.solve(src, ssink, f.fst);
	}
	return f.snd;
}

int main(){

	fastio;
	cin >> d >> n;
	
	MCF network(MAXN);
	int gid = 0;
	for(int m = 0; m < (1 << d); ++m){
		in_node[m] = gid++;
		out_node[m] = gid++;
		get_mask[in_node[m]] = m;
		get_mask[out_node[m]] = m;
		edges.pb({in_node[m], out_node[m], inf, 0});
		if(m > 0){
			edges.pb({out_node[m], sink, inf, 0});
		}
	}

	for(int m = 0; m < (1 << d); ++m){
		for(int j = 0; j < d; ++j){
			if(m & (1 << j)) continue;
			int nm = m | (1 << j);
			edges.pb({out_node[m], in_node[nm], inf, 1});
		}
	}

	for(int i = 0; i < n; ++i){
		string s;
		cin >> s;
		int msk = to_mask(s);
		edges.pb({in_node[msk], out_node[msk], 1, int(-1e5)});
	}

	int lo = 0, hi = 254;
	while(hi - lo > 1){
		int mid = (lo + hi) / 2;
		if(network_cost(mid) >= network_cost(mid+1)) lo = mid;
		else hi = mid;
	}

	network_cost(lo+1, 1);

	cout << sz(ans) << endl;
	for(int x : ans){
		if(x == -1) cout << "R ";
		else cout << x << " ";
	}
	cout << endl;

	return 0;
}

```