file

#include <bits/stdc++.h>
#include <fstream>

using namespace std;

ifstream in("input.txt");
ofstream out("output.txt");

int ans = 7;

vector<int> res;

void rec(set<int> a, vector<int> dist){
    /*for (int t : dist) {
        cout << t << " ";
    }
    cout << endl;
    for (int v : a) {
        cout << v << " ";
    }
    cout << endl<< ":" << endl;*/
    if(a.size() == 0){
        if(dist.size() < ans){
            res = dist;
            ans = dist.size();
        }
        return;
    }
    if(dist.size() >= ans){
        return;
    }
    for(int i = 2; i <= 20; ++i){
        set<int> temp;
        bool flag = false;
        for(int j : a){
            if (j >= i)
                flag = true;
            if(j / i + j % i > 1) temp.insert(j / i + j % i);
        }
        if (flag) {
            dist.push_back(i);
            rec(temp, dist);
            dist.pop_back();
        }
    }
}


int main() {
    string s;
    vector<int> dist;
    int counter = 0;
    set<int> a;
    while(getline(in, s)){
        for(char i : s){
            if(i == ' '){
                ++counter;
            }
            else{
                if(counter > 1){
                    a.insert(counter);
                }
                counter = 0;
            }
        }
        if(counter > 1){
            a.insert(counter);
        }
        counter = 0;
    }
    for (int v : a) {
        cout << v << " ";
    }
    cout << endl;
    rec(a, dist);
    out << res.size() << endl;
    for(int i = 0; i < res.size(); ++i){
        out << res[i] << " ";
    }
}