/*{{{*/
#include<cstdio>
#include<cstdlib>
#include<cstring>
#include<cmath>
#include<algorithm>
#include<string>
#include<iostream>
#include<sstream>
#include<set>
#include<map>
#include<queue>
#include<bitset>
#include<vector>
#include<limits.h>
#include<assert.h>
#define SZ(X) ((int)(X).size())
#define ALL(X) (X).begin(), (X).end()
#define REP(I, N) for (int I = 0; I < (N); ++I)
#define REPP(I, A, B) for (int I = (A); I < (B); ++I)
#define FOR(I, A, B) for (int I = (A); I <= (B); ++I)
#define FORS(I, S) for (int I = 0; S[I]; ++I)
#define RS(X) scanf("%s", (X))
#define SORT_UNIQUE(c) (sort(c.begin(),c.end()), c.resize(distance(c.begin(),unique(c.begin(),c.end()))))
#define GET_POS(c,x) (lower_bound(c.begin(),c.end(),x)-c.begin())
#define CASET int ___T; scanf("%d", &___T); for(int cs=1;cs<=___T;cs++)
#define MP make_pair
#define PB emplace_back
#define MS0(X) memset((X), 0, sizeof((X)))
#define MS1(X) memset((X), -1, sizeof((X)))
#define LEN(X) strlen(X)
#define F first
#define S second
using namespace std;
typedef long long LL;
typedef unsigned long long ULL;
typedef long double LD;
typedef pair<int,int> PII;
typedef vector<int> VI;
typedef vector<LL> VL;
typedef vector<PII> VPII;
typedef pair<LL,LL> PLL;
typedef vector<PLL> VPLL;
template<class T> void _R(T &x) { cin >> x; }
void _R(int &x) { scanf("%d", &x); }
void _R(int64_t &x) { scanf("%lld", &x); }
void _R(double &x) { scanf("%lf", &x); }
void _R(char &x) { scanf(" %c", &x); }
void _R(char *x) { scanf("%s", x); }
void R() {}
template<class T, class... U> void R(T &head, U &... tail) { _R(head); R(tail...); }
template<class T> void _W(const T &x) { cout << x; }
void _W(const int &x) { printf("%d", x); }
void _W(const int64_t &x) { printf("%lld", x); }
void _W(const double &x) { printf("%.16f", x); }
void _W(const char &x) { putchar(x); }
void _W(const char *x) { printf("%s", x); }
template<class T,class U> void _W(const pair<T,U> &x) {_W(x.F); putchar(' '); _W(x.S);}
template<class T> void _W(const vector<T> &x) { for (auto i = x.begin(); i != x.end(); _W(*i++)) if (i != x.cbegin()) putchar(' '); }
void W() {}
template<class T, class... U> void W(const T &head, const U &... tail) { _W(head); putchar(sizeof...(tail) ? ' ' : '\n'); W(tail...); }
#ifdef HOME
 #define DEBUG(...) {printf("[DEBUG] ");W(__VA_ARGS__);}
#else
 #define DEBUG(...)
#endif
int MOD = 1e9+7;
void ADD(LL& x,LL v){x=(x+v)%MOD;if(x<0)x+=MOD;}
/*}}}*/
const int SIZE = 1<<10;
#define INF 1034567890
const int MAX_EDGE_NUM = 1000000;
const int MAX_NODE_NUM = 100000;
struct EDGE{
        int y,c,v;
        EDGE(int _y=0,int _c=0,int _v=0):y(_y),c(_c),v(_v){}
}es[MAX_EDGE_NUM];
vector<int>e[MAX_NODE_NUM];
int en;
int EE; // sink
void flow_clear(int _EE){
    EE=_EE;
    REP(i,EE+1)e[i].clear();
    en=0;
}
void add_edge(int x,int y,int c,int v){
        e[x].PB(en);
        es[en++]=EDGE(y,c,v);
        e[y].PB(en);
        es[en++]=EDGE(x,0,-v);
        
}
int mi[MAX_NODE_NUM],lt[MAX_NODE_NUM],bfs[10000000],used[MAX_NODE_NUM];
int flow(){
        REP(i,EE+1)mi[i]=INF,used[i]=0;
        mi[EE]=INF;
        bfs[0]=0;
        mi[0]=0;
        int rr=1;
        for(int i=0;i<rr;i++){
                int x=bfs[i];
                used[x]=0;
                REP(j,SZ(e[x])){
                        int r=e[x][j];
                        if(es[r].c>0&&mi[x]+es[r].v<mi[es[r].y]){
                                mi[es[r].y]=mi[x]+es[r].v;
                                lt[es[r].y]=r;
                                if(!used[es[r].y]){
                                        used[es[r].y]=1;
                                        bfs[rr++]=es[r].y;
                                }
                        }
                }
        }
        if(mi[EE]==INF)return -1;
        int now=EE;
        while(now){
                int r=lt[now];
                es[r].c--;
                es[r^1].c++;
                now=es[r^1].y;
        }
        return mi[EE];
}
int to[SIZE];
bitset<10>s[SIZE];
void add(vector<char>&an, bitset<10>v){
    REP(i,10){
        if(v[i]){
            an.PB('0'+i);
        }
    }
}
void solve(int nn){
    int v=0;
    REP(i,nn)v+=flow();
    VI st;
    for(int i=0;i<en;i+=2){
        if(es[i].y>nn&&es[i^1].y<=nn&&!es[i].c){
            if(!es[i^1].y){
                st.PB(es[i].y-nn);
            }else{
                to[es[i^1].y]=es[i].y-nn;
            }
        }
    }
    vector<char>an;
    for(int x:st){
        if(SZ(an)){
            an.PB('R');
        }
        add(an,s[x]);
        int now=x;
        while(to[now]){
            add(an,s[now]^s[to[now]]);
            now=to[now];
        }
    }
    W(SZ(an));
    W(an);
}
int n;
void solve() {
    flow_clear(2*n+1);
    FOR(i,1,n){
        add_edge(0,n+i,1,s[i].count()+1);
        add_edge(0,i,1,0);
        add_edge(n+i,2*n+1,1,0);
        FOR(j,1,n){
            if(i==j){continue;}
            if((s[i]&s[j])==s[j]){
                add_edge(j,i+n,1,s[i].count()-s[j].count());
            }
        }
    }
    solve(n);
}
void input() {
    int d;
    R(d,n);
    FOR(i,1,n){
        string _s;
        R(_s);
        REP(j,d){
            if(_s[j]=='1')s[i][j]=1;
        }
    }
}
int main(){
    input();
    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
/*{{{*/
#include<cstdio>
#include<cstdlib>
#include<cstring>
#include<cmath>
#include<algorithm>
#include<string>
#include<iostream>
#include<sstream>
#include<set>
#include<map>
#include<queue>
#include<bitset>
#include<vector>
#include<limits.h>
#include<assert.h>
#define SZ(X) ((int)(X).size())
#define ALL(X) (X).begin(), (X).end()
#define REP(I, N) for (int I = 0; I < (N); ++I)
#define REPP(I, A, B) for (int I = (A); I < (B); ++I)
#define FOR(I, A, B) for (int I = (A); I <= (B); ++I)
#define FORS(I, S) for (int I = 0; S[I]; ++I)
#define RS(X) scanf("%s", (X))
#define SORT_UNIQUE(c) (sort(c.begin(),c.end()), c.resize(distance(c.begin(),unique(c.begin(),c.end()))))
#define GET_POS(c,x) (lower_bound(c.begin(),c.end(),x)-c.begin())
#define CASET int ___T; scanf("%d", &___T); for(int cs=1;cs<=___T;cs++)
#define MP make_pair
#define PB emplace_back
#define MS0(X) memset((X), 0, sizeof((X)))
#define MS1(X) memset((X), -1, sizeof((X)))
#define LEN(X) strlen(X)
#define F first
#define S second
using namespace std;
typedef long long LL;
typedef unsigned long long ULL;
typedef long double LD;
typedef pair<int,int> PII;
typedef vector<int> VI;
typedef vector<LL> VL;
typedef vector<PII> VPII;
typedef pair<LL,LL> PLL;
typedef vector<PLL> VPLL;
template<class T> void _R(T &x) { cin >> x; }
void _R(int &x) { scanf("%d", &x); }
void _R(int64_t &x) { scanf("%lld", &x); }
void _R(double &x) { scanf("%lf", &x); }
void _R(char &x) { scanf(" %c", &x); }
void _R(char *x) { scanf("%s", x); }
void R() {}
template<class T, class... U> void R(T &head, U &... tail) { _R(head); R(tail...); }
template<class T> void _W(const T &x) { cout << x; }
void _W(const int &x) { printf("%d", x); }
void _W(const int64_t &x) { printf("%lld", x); }
void _W(const double &x) { printf("%.16f", x); }
void _W(const char &x) { putchar(x); }
void _W(const char *x) { printf("%s", x); }
template<class T,class U> void _W(const pair<T,U> &x) {_W(x.F); putchar(' '); _W(x.S);}
template<class T> void _W(const vector<T> &x) { for (auto i = x.begin(); i != x.end(); _W(*i++)) if (i != x.cbegin()) putchar(' '); }
void W() {}
template<class T, class... U> void W(const T &head, const U &... tail) { _W(head); putchar(sizeof...(tail) ? ' ' : '\n'); W(tail...); }
#ifdef HOME
 #define DEBUG(...) {printf("[DEBUG] ");W(__VA_ARGS__);}
#else
 #define DEBUG(...)
#endif
int MOD = 1e9+7;
void ADD(LL& x,LL v){x=(x+v)%MOD;if(x<0)x+=MOD;}
/*}}}*/
const int SIZE = 1<<10;
#define INF 1034567890
const int MAX_EDGE_NUM = 1000000;
const int MAX_NODE_NUM = 100000;
struct EDGE{
        int y,c,v;
        EDGE(int _y=0,int _c=0,int _v=0):y(_y),c(_c),v(_v){}
}es[MAX_EDGE_NUM];
vector<int>e[MAX_NODE_NUM];
int en;
int EE; // sink
void flow_clear(int _EE){
    EE=_EE;
    REP(i,EE+1)e[i].clear();
    en=0;
}
void add_edge(int x,int y,int c,int v){
        e[x].PB(en);
        es[en++]=EDGE(y,c,v);
        e[y].PB(en);
        es[en++]=EDGE(x,0,-v);
        
}
int mi[MAX_NODE_NUM],lt[MAX_NODE_NUM],bfs[10000000],used[MAX_NODE_NUM];
int flow(){
        REP(i,EE+1)mi[i]=INF,used[i]=0;
        mi[EE]=INF;
        bfs[0]=0;
        mi[0]=0;
        int rr=1;
        for(int i=0;i<rr;i++){
                int x=bfs[i];
                used[x]=0;
                REP(j,SZ(e[x])){
                        int r=e[x][j];
                        if(es[r].c>0&&mi[x]+es[r].v<mi[es[r].y]){
                                mi[es[r].y]=mi[x]+es[r].v;
                                lt[es[r].y]=r;
                                if(!used[es[r].y]){
                                        used[es[r].y]=1;
                                        bfs[rr++]=es[r].y;
                                }
                        }
                }
        }
        if(mi[EE]==INF)return -1;
        int now=EE;
        while(now){
                int r=lt[now];
                es[r].c--;
                es[r^1].c++;
                now=es[r^1].y;
        }
        return mi[EE];
}
int to[SIZE];
bitset<10>s[SIZE];
void add(vector<char>&an, bitset<10>v){
    REP(i,10){
        if(v[i]){
            an.PB('0'+i);
        }
    }
}
void solve(int nn){
    int v=0;
    REP(i,nn)v+=flow();
    VI st;
    for(int i=0;i<en;i+=2){
        if(es[i].y>nn&&es[i^1].y<=nn&&!es[i].c){
            if(!es[i^1].y){
                st.PB(es[i].y-nn);
            }else{
                to[es[i^1].y]=es[i].y-nn;
            }
        }
    }
    vector<char>an;
    for(int x:st){
        if(SZ(an)){
            an.PB('R');
        }
        add(an,s[x]);
        int now=x;
        while(to[now]){
            add(an,s[now]^s[to[now]]);
            now=to[now];
        }
    }
    W(SZ(an));
    W(an);
}
int n;
void solve() {
    flow_clear(2*n+1);
    FOR(i,1,n){
        add_edge(0,n+i,1,s[i].count()+1);
        add_edge(0,i,1,0);
        add_edge(n+i,2*n+1,1,0);
        FOR(j,1,n){
            if(i==j){continue;}
            if((s[i]&s[j])==s[j]){
                add_edge(j,i+n,1,s[i].count()-s[j].count());
            }
        }
    }
    solve(n);
}
void input() {
    int d;
    R(d,n);
    FOR(i,1,n){
        string _s;
        R(_s);
        REP(j,d){
            if(_s[j]=='1')s[i][j]=1;
        }
    }
}
int main(){
    input();
    solve();
    return 0;
}

```