#include <bits/stdc++.h>
#define ll long long
#define INF 1000000005
#define MOD 1000000007
#define EPS 1e-10
#define rep(i,n) for(int i=0;i<(int)(n);++i)
#define rrep(i,n) for(int i=(int)(n)-1;i>=0;--i)
#define srep(i,s,t) for(int i=(int)(s);i<(int)(t);++i)
#define each(a,b) for(auto& (a): (b))
#define all(v) (v).begin(),(v).end()
#define len(v) (int)(v).size()
#define zip(v) sort(all(v)),v.erase(unique(all(v)),v.end())
#define cmx(x,y) x=max(x,y)
#define cmn(x,y) x=min(x,y)
#define fi first
#define se second
#define pb push_back
#define show(x) cout<<#x<<" = "<<(x)<<endl
#define spair(p) cout<<#p<<": "<<p.fi<" "<<p.se<<endl
#define sar(a,n) cout<<#a<<":";rep(pachico,n)cout<<" "<<a[pachico];cout<<endl
#define svec(v) cout<<#v<<":";rep(pachico,v.size())cout<<" "<<v[pachico];cout<<endl
#define svecp(v) cout<<#v<<":";each(pachico,v)cout<<" {"<<pachico.first<<":"<<pachico.second<<"}";cout<<endl
#define sset(s) cout<<#s<<":";each(pachico,s)cout<<" "<<pachico;cout<<endl
#define smap(m) cout<<#m<<":";each(pachico,m)cout<<" {"<<pachico.first<<":"<<pachico.second<<"}";cout<<endl
 
using namespace std;
 
typedef pair<int,int> P;
typedef pair<ll,ll> pll;
typedef vector<int> vi;
typedef vector<vi> vvi;
typedef vector<ll> vl;
typedef vector<vl> vvl;
typedef vector<double> vd;
typedef vector<P> vp;
typedef vector<string> vs;
 
const int MAX_N = 10005;
 
vector<int> G[MAX_N];
int kind[MAX_N];
bool used[MAX_N][MAX_N];
 
int main()
{
    cin.tie(0);
    ios::sync_with_stdio(false);
    int n;
    int t[3];
    cin >> n >> t[0] >> t[1] >> t[2];
    int mn[3];
    vi vec[3];
    rep(i,3){
        vec[i].resize(t[i]);
    }
    rep(i,n){
        kind[i] = -1;
    }
    rep(i,3){
        mn[i] = INF;
        rep(j,t[i]){
            cin >> vec[i][j];
            vec[i][j]--;
            kind[vec[i][j]] = i;
            cmn(mn[i],vec[i][j]);
        }
    }
    int m;
    cin >> m;
    rep(i,m){
        int a,b;
        cin >> a >> b;
        --a,--b;
        if(kind[a] >= 0){
            a = mn[kind[a]];
        }
        if(kind[b] >= 0){
            b = mn[kind[b]];
        }
        if(a == b){
            continue;
        }else if(a > b){
            swap(a, b);
        }
        if(!used[a][b]){
            G[a].pb(b),G[b].pb(a);
            used[a][b] = true;
        }
    }
    vp d[3];
    rep(i,3){
        queue<int> que;
        d[i].resize(n,P(INF/10,INF/10));
        d[i][mn[i]] = P(0,mn[i]);
        que.push(mn[i]);
        while(!que.empty()){
            int p = que.front();
            que.pop();
            each(v,G[p]){
                if(d[i][p].fi+1 < d[i][v].fi){
                    d[i][v] = P(d[i][p].fi+1,min(d[i][p].se,v));
                    que.push(v);
                }else if(d[i][p].fi+1 == d[i][v].fi && d[i][v].se > d[i][p].se){
                    d[i][v].se = d[i][p].se;
                    que.push(v);
                }
            }
        }
    }
    P ans = P(INF,INF);
    rep(i,n){
        cmn(ans,P(d[0][i].fi+d[1][i].fi+d[2][i].fi,min({d[0][i].se,d[1][i].se,d[2][i].se})));
    }
    cout << ans.fi << " " << ans.se+1 << "\n";
    return 0;
}

### Prompt

Please provide a cpp coded solution to the problem described below:

Example

Input

4 2 1 1
1 2
3
4
3
1 2
2 4
3 4


Output

2 1

### Response

```cpp
#include <bits/stdc++.h>
#define ll long long
#define INF 1000000005
#define MOD 1000000007
#define EPS 1e-10
#define rep(i,n) for(int i=0;i<(int)(n);++i)
#define rrep(i,n) for(int i=(int)(n)-1;i>=0;--i)
#define srep(i,s,t) for(int i=(int)(s);i<(int)(t);++i)
#define each(a,b) for(auto& (a): (b))
#define all(v) (v).begin(),(v).end()
#define len(v) (int)(v).size()
#define zip(v) sort(all(v)),v.erase(unique(all(v)),v.end())
#define cmx(x,y) x=max(x,y)
#define cmn(x,y) x=min(x,y)
#define fi first
#define se second
#define pb push_back
#define show(x) cout<<#x<<" = "<<(x)<<endl
#define spair(p) cout<<#p<<": "<<p.fi<" "<<p.se<<endl
#define sar(a,n) cout<<#a<<":";rep(pachico,n)cout<<" "<<a[pachico];cout<<endl
#define svec(v) cout<<#v<<":";rep(pachico,v.size())cout<<" "<<v[pachico];cout<<endl
#define svecp(v) cout<<#v<<":";each(pachico,v)cout<<" {"<<pachico.first<<":"<<pachico.second<<"}";cout<<endl
#define sset(s) cout<<#s<<":";each(pachico,s)cout<<" "<<pachico;cout<<endl
#define smap(m) cout<<#m<<":";each(pachico,m)cout<<" {"<<pachico.first<<":"<<pachico.second<<"}";cout<<endl
 
using namespace std;
 
typedef pair<int,int> P;
typedef pair<ll,ll> pll;
typedef vector<int> vi;
typedef vector<vi> vvi;
typedef vector<ll> vl;
typedef vector<vl> vvl;
typedef vector<double> vd;
typedef vector<P> vp;
typedef vector<string> vs;
 
const int MAX_N = 10005;
 
vector<int> G[MAX_N];
int kind[MAX_N];
bool used[MAX_N][MAX_N];
 
int main()
{
    cin.tie(0);
    ios::sync_with_stdio(false);
    int n;
    int t[3];
    cin >> n >> t[0] >> t[1] >> t[2];
    int mn[3];
    vi vec[3];
    rep(i,3){
        vec[i].resize(t[i]);
    }
    rep(i,n){
        kind[i] = -1;
    }
    rep(i,3){
        mn[i] = INF;
        rep(j,t[i]){
            cin >> vec[i][j];
            vec[i][j]--;
            kind[vec[i][j]] = i;
            cmn(mn[i],vec[i][j]);
        }
    }
    int m;
    cin >> m;
    rep(i,m){
        int a,b;
        cin >> a >> b;
        --a,--b;
        if(kind[a] >= 0){
            a = mn[kind[a]];
        }
        if(kind[b] >= 0){
            b = mn[kind[b]];
        }
        if(a == b){
            continue;
        }else if(a > b){
            swap(a, b);
        }
        if(!used[a][b]){
            G[a].pb(b),G[b].pb(a);
            used[a][b] = true;
        }
    }
    vp d[3];
    rep(i,3){
        queue<int> que;
        d[i].resize(n,P(INF/10,INF/10));
        d[i][mn[i]] = P(0,mn[i]);
        que.push(mn[i]);
        while(!que.empty()){
            int p = que.front();
            que.pop();
            each(v,G[p]){
                if(d[i][p].fi+1 < d[i][v].fi){
                    d[i][v] = P(d[i][p].fi+1,min(d[i][p].se,v));
                    que.push(v);
                }else if(d[i][p].fi+1 == d[i][v].fi && d[i][v].se > d[i][p].se){
                    d[i][v].se = d[i][p].se;
                    que.push(v);
                }
            }
        }
    }
    P ans = P(INF,INF);
    rep(i,n){
        cmn(ans,P(d[0][i].fi+d[1][i].fi+d[2][i].fi,min({d[0][i].se,d[1][i].se,d[2][i].se})));
    }
    cout << ans.fi << " " << ans.se+1 << "\n";
    return 0;
}

```