#pragma GCC optimize("Ofast")
#pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,avx,avx2,fma")
#pragma GCC optimize("unroll-loops")
// #include <atcoder/all>
// #include <bits/stdc++.h>
#include <cassert>
#include <complex>
#include <queue>
#include <set>
#include <unordered_set>
#include <list>

#include <chrono>
#include <random>
#include <iostream>
#include <algorithm>
#include <cmath>
#include <string>
#include <vector>
#include <map>
#include <unordered_map>
#include <stack>
#include <iomanip>
#include <fstream>
#include <functional>
#include <iostream>
#include <vector>
#include <numeric>
using namespace std;
// using namespace atcoder;

typedef long long ll;
typedef long double ld;
typedef pair<ll, ll> p32;
typedef pair<ll, ll> p64;
typedef pair<p64, p64> pp64;
typedef pair<double, double> pdd;
typedef vector<ll> v64;
typedef vector<ll> v32;
typedef vector<vector<ll>> vv32;
typedef vector<vector<ll>> vv64;
typedef vector<vector<p64>> vvp64;
typedef vector<p64> vp64;
typedef vector<p32> vp32;
ll MOD = 998244353;
double eps = 1e-12;
#define forn(i, e) for (ll i = 0; i < e; i++)
#define forsn(i, s, e) for (ll i = s; i < e; i++)
#define rforn(i, s) for (ll i = s; i >= 0; i--)
#define rforsn(i, s, e) for (ll i = s; i >= e; i--)
#define ln '\n'
#define dbg(x) cout << #x << " = " << x << ln
#define mp make_pair
#define pb push_back
#define fi first
#define se second
// #define INF 2e18
#define fast_cin()                    \
    ios_base::sync_with_stdio(false); \
    cin.tie(NULL);                    \
    cout.tie(NULL)
#define all(x) (x).begin(), (x).end()
#define sz(x) ((ll)(x).size())
// #define zero ll(0)
#define set_bits(x) __builtin_popcountll(x)
// #define mll modll998244353

ll mpow(ll a, ll b)
{
    if (a == 0)
        return 0;
    if (b == 0)
        return 1;
    ll t1 = mpow(a, b / 2);
    t1 *= t1;
    t1 %= MOD;
    if (b % 2)
        t1 *= a;
    t1 %= MOD;
    return t1;
}

ll mpow(ll a, ll b, ll p)
{
    if (a == 0)
        return 0;
    if (b == 0)
        return 1;
    ll t1 = mpow(a, b / 2, p);
    t1 *= t1;
    t1 %= p;
    if (b % 2)
        t1 *= a;
    t1 %= p;
    return t1;
}

ll modinverse(ll a, ll m)
{
    ll m0 = m;
    ll y = 0, x = 1;
    if (m == 1)
        return 0;
    while (a > 1)
    {
        ll q = a / m;
        ll t = m;
        m = a % m, a = t;
        t = y;
        y = x - q * y;
        x = t;
    }
    if (x < 0)
        x += m0;
    return x;
}

mt19937_64 mt(chrono::steady_clock::now().time_since_epoch().count());

ll range(ll l, ll r)
{
    return l + mt() % (r - l + 1);
}

ll rev(ll v)
{
    return mpow(v, MOD - 2);
}

ll ceil(ll p, ll q)
{
    return (p + q - 1) / q;
}

#define F first
#define S second
const int INF = 2e9 + 5;
// vertices are 0-indexed
struct graph
{
    typedef int flow_type; // **** flow type ****
    typedef int cost_type; // **** cost type ****
    struct edge
    {
        int src, dst;
        flow_type capacity, flow;
        cost_type cost;
        size_t rev;
    };
    vector<edge> edges;
    void add_edge(int src, int dst, flow_type cap, cost_type cost)
    {
        adj[src].push_back({src, dst, cap, 0, cost, adj[dst].size()});
        adj[dst].push_back({dst, src, 0, 0, -cost, adj[src].size() - 1});
    }
    int n;
    vector<vector<edge>> adj;
    graph(int n) : n(n), adj(n) {}

    pair<flow_type, cost_type> min_cost_max_flow(int s, int t)
    {
        flow_type flow = 0;
        cost_type cost = 0;

        for (int u = 0; u < n; ++u) // initialize
            for (auto &e : adj[u])
                e.flow = 0;

        vector<cost_type> p(n, 0);

        auto rcost = [&](edge e) { return e.cost + p[e.src] - p[e.dst]; };
        for (int iter = 0;; ++iter)
        {
            vector<int> prev(n, -1);
            prev[s] = 0;
            vector<cost_type> dist(n, INF);
            dist[s] = 0;
            if (iter == 0)
            { // use Bellman-Ford to remove negative cost edges
                vector<int> count(n);
                count[s] = 1;
                queue<int> que;
                for (que.push(s); !que.empty();)
                {
                    int u = que.front();
                    que.pop();
                    count[u] = -count[u];
                    for (auto &e : adj[u])
                    {
                        if (e.capacity > e.flow && dist[e.dst] > dist[e.src] + rcost(e))
                        {
                            dist[e.dst] = dist[e.src] + rcost(e);
                            prev[e.dst] = e.rev;
                            if (count[e.dst] <= 0)
                            {
                                count[e.dst] = -count[e.dst] + 1;
                                que.push(e.dst);
                            }
                        }
                    }
                }
                for (int i = 0; i < n; i++)
                    p[i] = dist[i]; // added it
                continue;
            }
            else
            { // use Dijkstra
                typedef pair<cost_type, int> node;
                priority_queue<node, vector<node>, greater<node>> que;
                que.push({0, s});
                while (!que.empty())
                {
                    node a = que.top();
                    que.pop();
                    if (a.S == t)
                        break;
                    if (dist[a.S] > a.F)
                        continue;
                    for (auto e : adj[a.S])
                    {
                        if (e.capacity > e.flow && dist[e.dst] > a.F + rcost(e))
                        {
                            dist[e.dst] = dist[e.src] + rcost(e);
                            prev[e.dst] = e.rev;
                            que.push({dist[e.dst], e.dst});
                        }
                    }
                }
            }
            if (prev[t] == -1)
                break;

            for (int u = 0; u < n; ++u)
                if (dist[u] < dist[t])
                    p[u] += dist[u] - dist[t];

            function<flow_type(int, flow_type)> augment = [&](int u, flow_type cur) {
                if (u == s)
                    return cur;
                edge &r = adj[u][prev[u]], &e = adj[r.dst][r.rev];
                flow_type f = augment(e.src, min(e.capacity - e.flow, cur));
                e.flow += f;
                r.flow -= f;
                return f;
            };
            flow_type f = augment(t, INF);
            flow += f;
            cost += f * (p[t] - p[s]);
        }
        return {flow, cost};
    }
};

int d, n;
void out(int s, int t)
{
    for (int i = 0; i < d; i++)
    {
        if (((t & 1 << i) != 0) && ((s & 1 << i) == 0))
            cout << i << " ";
    }
}

void solve()
{
    cin >> d >> n;
    v64 nodes(1, 0);
    int maxi = (1 << d);
    for (int i = 1; i <= n; i++)
    {
        string s;
        cin >> s;
        int num = 0;
        for (int j = 0; j < d; j++)
        {
            if (s[j] == '1')
                num += (1 << j);
        }
        nodes.push_back(num);
    }
    // cout << sz(nodes) << endl;
    graph g(2 * maxi + 2);
    for (int i = 0; i < sz(nodes); i++)
    {
        for (int j = 0; j < sz(nodes); j++)
        {
            if (nodes[j] != nodes[i])
            {
                if ((nodes[i] & nodes[j]) == nodes[j])
                {
                    int cap = 1;
                    int cost = set_bits(nodes[i]) - set_bits(nodes[j]);
                    if (nodes[j] == 0)
                        cost++;
                    // cout << nodes[i] << " " << nodes[j] << endl;
                    g.add_edge(nodes[i] + 1, nodes[j] + maxi + 1, cap, cost);
                }
            }
        }
    }
    for (int i = 0; i < maxi; i++)
    {
        g.add_edge(0, i + 1, 1, 0);
        int cap = 1;
        if (i == 0)
            cap = n;
        g.add_edge(maxi + i + 1, 2 * maxi + 1, cap, 0);
    }
    p32 ans = g.min_cost_max_flow(0, 2 * maxi + 1);
    // cout << "a" << ans.fi << " " << g.n << endl;
    v64 starts;
    v64 next(maxi + 10, -1);
    for (int i = 1; i < maxi; i++)
    {
        for (int j = 0; j < sz(g.adj[i + 1]); j++)
        {
            if (g.adj[i + 1][j].flow > 0)
            {
                if (g.adj[i + 1][j].dst == maxi + 1)
                {
                    starts.push_back(i);
                }
                else
                {
                    // cout << i << "c" << g.adj[i + 1][j].dst - maxi - 1 << endl;
                    next[g.adj[i + 1][j].dst - maxi - 1] = i;
                }
            }
        }
    }
    // cout << next[1] << "b" << endl;
    cout << ans.se - 1 << endl;
    for (int i = 0; i < sz(starts); i++)
    {
        if (i > 0)
            cout << "R ";
        out(0, starts[i]);
        int cur = starts[i];
        while (next[cur] != -1)
        {
            out(cur, next[cur]);
            cur = next[cur];
        }
    }
}

int main()
{
    fast_cin();
    ll t = 1;
    // cin >> t;
    forn(i, t)
    {
        // cout << "Case #" << i+1 << ": ";
        solve();
    }
    return 0;
}
### Prompt

In CPP, your task is to solve 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
#pragma GCC optimize("Ofast")
#pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,avx,avx2,fma")
#pragma GCC optimize("unroll-loops")
// #include <atcoder/all>
// #include <bits/stdc++.h>
#include <cassert>
#include <complex>
#include <queue>
#include <set>
#include <unordered_set>
#include <list>

#include <chrono>
#include <random>
#include <iostream>
#include <algorithm>
#include <cmath>
#include <string>
#include <vector>
#include <map>
#include <unordered_map>
#include <stack>
#include <iomanip>
#include <fstream>
#include <functional>
#include <iostream>
#include <vector>
#include <numeric>
using namespace std;
// using namespace atcoder;

typedef long long ll;
typedef long double ld;
typedef pair<ll, ll> p32;
typedef pair<ll, ll> p64;
typedef pair<p64, p64> pp64;
typedef pair<double, double> pdd;
typedef vector<ll> v64;
typedef vector<ll> v32;
typedef vector<vector<ll>> vv32;
typedef vector<vector<ll>> vv64;
typedef vector<vector<p64>> vvp64;
typedef vector<p64> vp64;
typedef vector<p32> vp32;
ll MOD = 998244353;
double eps = 1e-12;
#define forn(i, e) for (ll i = 0; i < e; i++)
#define forsn(i, s, e) for (ll i = s; i < e; i++)
#define rforn(i, s) for (ll i = s; i >= 0; i--)
#define rforsn(i, s, e) for (ll i = s; i >= e; i--)
#define ln '\n'
#define dbg(x) cout << #x << " = " << x << ln
#define mp make_pair
#define pb push_back
#define fi first
#define se second
// #define INF 2e18
#define fast_cin()                    \
    ios_base::sync_with_stdio(false); \
    cin.tie(NULL);                    \
    cout.tie(NULL)
#define all(x) (x).begin(), (x).end()
#define sz(x) ((ll)(x).size())
// #define zero ll(0)
#define set_bits(x) __builtin_popcountll(x)
// #define mll modll998244353

ll mpow(ll a, ll b)
{
    if (a == 0)
        return 0;
    if (b == 0)
        return 1;
    ll t1 = mpow(a, b / 2);
    t1 *= t1;
    t1 %= MOD;
    if (b % 2)
        t1 *= a;
    t1 %= MOD;
    return t1;
}

ll mpow(ll a, ll b, ll p)
{
    if (a == 0)
        return 0;
    if (b == 0)
        return 1;
    ll t1 = mpow(a, b / 2, p);
    t1 *= t1;
    t1 %= p;
    if (b % 2)
        t1 *= a;
    t1 %= p;
    return t1;
}

ll modinverse(ll a, ll m)
{
    ll m0 = m;
    ll y = 0, x = 1;
    if (m == 1)
        return 0;
    while (a > 1)
    {
        ll q = a / m;
        ll t = m;
        m = a % m, a = t;
        t = y;
        y = x - q * y;
        x = t;
    }
    if (x < 0)
        x += m0;
    return x;
}

mt19937_64 mt(chrono::steady_clock::now().time_since_epoch().count());

ll range(ll l, ll r)
{
    return l + mt() % (r - l + 1);
}

ll rev(ll v)
{
    return mpow(v, MOD - 2);
}

ll ceil(ll p, ll q)
{
    return (p + q - 1) / q;
}

#define F first
#define S second
const int INF = 2e9 + 5;
// vertices are 0-indexed
struct graph
{
    typedef int flow_type; // **** flow type ****
    typedef int cost_type; // **** cost type ****
    struct edge
    {
        int src, dst;
        flow_type capacity, flow;
        cost_type cost;
        size_t rev;
    };
    vector<edge> edges;
    void add_edge(int src, int dst, flow_type cap, cost_type cost)
    {
        adj[src].push_back({src, dst, cap, 0, cost, adj[dst].size()});
        adj[dst].push_back({dst, src, 0, 0, -cost, adj[src].size() - 1});
    }
    int n;
    vector<vector<edge>> adj;
    graph(int n) : n(n), adj(n) {}

    pair<flow_type, cost_type> min_cost_max_flow(int s, int t)
    {
        flow_type flow = 0;
        cost_type cost = 0;

        for (int u = 0; u < n; ++u) // initialize
            for (auto &e : adj[u])
                e.flow = 0;

        vector<cost_type> p(n, 0);

        auto rcost = [&](edge e) { return e.cost + p[e.src] - p[e.dst]; };
        for (int iter = 0;; ++iter)
        {
            vector<int> prev(n, -1);
            prev[s] = 0;
            vector<cost_type> dist(n, INF);
            dist[s] = 0;
            if (iter == 0)
            { // use Bellman-Ford to remove negative cost edges
                vector<int> count(n);
                count[s] = 1;
                queue<int> que;
                for (que.push(s); !que.empty();)
                {
                    int u = que.front();
                    que.pop();
                    count[u] = -count[u];
                    for (auto &e : adj[u])
                    {
                        if (e.capacity > e.flow && dist[e.dst] > dist[e.src] + rcost(e))
                        {
                            dist[e.dst] = dist[e.src] + rcost(e);
                            prev[e.dst] = e.rev;
                            if (count[e.dst] <= 0)
                            {
                                count[e.dst] = -count[e.dst] + 1;
                                que.push(e.dst);
                            }
                        }
                    }
                }
                for (int i = 0; i < n; i++)
                    p[i] = dist[i]; // added it
                continue;
            }
            else
            { // use Dijkstra
                typedef pair<cost_type, int> node;
                priority_queue<node, vector<node>, greater<node>> que;
                que.push({0, s});
                while (!que.empty())
                {
                    node a = que.top();
                    que.pop();
                    if (a.S == t)
                        break;
                    if (dist[a.S] > a.F)
                        continue;
                    for (auto e : adj[a.S])
                    {
                        if (e.capacity > e.flow && dist[e.dst] > a.F + rcost(e))
                        {
                            dist[e.dst] = dist[e.src] + rcost(e);
                            prev[e.dst] = e.rev;
                            que.push({dist[e.dst], e.dst});
                        }
                    }
                }
            }
            if (prev[t] == -1)
                break;

            for (int u = 0; u < n; ++u)
                if (dist[u] < dist[t])
                    p[u] += dist[u] - dist[t];

            function<flow_type(int, flow_type)> augment = [&](int u, flow_type cur) {
                if (u == s)
                    return cur;
                edge &r = adj[u][prev[u]], &e = adj[r.dst][r.rev];
                flow_type f = augment(e.src, min(e.capacity - e.flow, cur));
                e.flow += f;
                r.flow -= f;
                return f;
            };
            flow_type f = augment(t, INF);
            flow += f;
            cost += f * (p[t] - p[s]);
        }
        return {flow, cost};
    }
};

int d, n;
void out(int s, int t)
{
    for (int i = 0; i < d; i++)
    {
        if (((t & 1 << i) != 0) && ((s & 1 << i) == 0))
            cout << i << " ";
    }
}

void solve()
{
    cin >> d >> n;
    v64 nodes(1, 0);
    int maxi = (1 << d);
    for (int i = 1; i <= n; i++)
    {
        string s;
        cin >> s;
        int num = 0;
        for (int j = 0; j < d; j++)
        {
            if (s[j] == '1')
                num += (1 << j);
        }
        nodes.push_back(num);
    }
    // cout << sz(nodes) << endl;
    graph g(2 * maxi + 2);
    for (int i = 0; i < sz(nodes); i++)
    {
        for (int j = 0; j < sz(nodes); j++)
        {
            if (nodes[j] != nodes[i])
            {
                if ((nodes[i] & nodes[j]) == nodes[j])
                {
                    int cap = 1;
                    int cost = set_bits(nodes[i]) - set_bits(nodes[j]);
                    if (nodes[j] == 0)
                        cost++;
                    // cout << nodes[i] << " " << nodes[j] << endl;
                    g.add_edge(nodes[i] + 1, nodes[j] + maxi + 1, cap, cost);
                }
            }
        }
    }
    for (int i = 0; i < maxi; i++)
    {
        g.add_edge(0, i + 1, 1, 0);
        int cap = 1;
        if (i == 0)
            cap = n;
        g.add_edge(maxi + i + 1, 2 * maxi + 1, cap, 0);
    }
    p32 ans = g.min_cost_max_flow(0, 2 * maxi + 1);
    // cout << "a" << ans.fi << " " << g.n << endl;
    v64 starts;
    v64 next(maxi + 10, -1);
    for (int i = 1; i < maxi; i++)
    {
        for (int j = 0; j < sz(g.adj[i + 1]); j++)
        {
            if (g.adj[i + 1][j].flow > 0)
            {
                if (g.adj[i + 1][j].dst == maxi + 1)
                {
                    starts.push_back(i);
                }
                else
                {
                    // cout << i << "c" << g.adj[i + 1][j].dst - maxi - 1 << endl;
                    next[g.adj[i + 1][j].dst - maxi - 1] = i;
                }
            }
        }
    }
    // cout << next[1] << "b" << endl;
    cout << ans.se - 1 << endl;
    for (int i = 0; i < sz(starts); i++)
    {
        if (i > 0)
            cout << "R ";
        out(0, starts[i]);
        int cur = starts[i];
        while (next[cur] != -1)
        {
            out(cur, next[cur]);
            cur = next[cur];
        }
    }
}

int main()
{
    fast_cin();
    ll t = 1;
    // cin >> t;
    forn(i, t)
    {
        // cout << "Case #" << i+1 << ": ";
        solve();
    }
    return 0;
}
```