#include <bits/stdc++.h>

using namespace std;

const int SHIFT = 10000;
const int INF = 1 << 29;

int N, A, B, C, M;
int color[10000], small[10005];
vector< int > g[10005];
pair< int, int > v[3][10005];

void solve(int start, int id)
{
  queue< int > que;
  v[id][start] = {0, small[start]};
  que.emplace(start);
  while(!que.empty()) {
    int p = que.front();
    que.pop();
    for(auto &to : g[p]) {
      if(v[id][p].first + 1 == v[id][to].first) {
        v[id][to].second = min(v[id][to].second, v[id][p].second);
      } else if(v[id][p].first + 1 < v[id][to].first) {
        v[id][to] = {v[id][p].first + 1, min(small[to], v[id][p].second)};
        que.emplace(to);
      }
    }
  }
}

int main()
{
  memset(color, -1, sizeof(color));
  fill_n(small, 10005, INF);

  scanf("%d %d %d %d", &N, &A, &B, &C);
  for(int i = 0; i < N; i++) small[i] = i;
  for(int i = 0; i < A + B + C; i++) {
    int K;
    scanf("%d", &K);
    --K;
    if(i < A) color[K] = 0;
    else if(i < A + B) color[K] = 1;
    else color[K] = 2;
    small[color[K] + SHIFT] = min(small[color[K] + SHIFT], K);
  }

  scanf("%d", &M);
  while(M--) {
    int a, b;
    scanf("%d %d", &a, &b);
    --a, --b;
    if(~color[a]) a = color[a] + SHIFT;
    if(~color[b]) b = color[b] + SHIFT;
    g[a].emplace_back(b);
    g[b].emplace_back(a);
  }
  fill_n(*v, 3 * 10005, make_pair(INF, INF));
  solve(SHIFT, 0);
  solve(SHIFT + 1, 1);
  solve(SHIFT + 2, 2);

  vector< int > vertex;
  vertex.push_back(SHIFT);
  vertex.push_back(SHIFT + 1);
  vertex.push_back(SHIFT + 2);
  for(int i = 0; i < N; i++) {
    if(~color[i]) continue;
    vertex.push_back(i);
  }
  int ret = 114514, beet;
  for(auto &i : vertex) {
    int cost = v[0][i].first + v[1][i].first + v[2][i].first;
    int latte = min({v[0][i].second, v[1][i].second, v[2][i].second});
    if(cost < ret) ret = cost, beet = latte;
    else if(cost == ret) beet = min(beet, latte);
  }
  printf("%d %d\n", ret, beet + 1);
}
### 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>

using namespace std;

const int SHIFT = 10000;
const int INF = 1 << 29;

int N, A, B, C, M;
int color[10000], small[10005];
vector< int > g[10005];
pair< int, int > v[3][10005];

void solve(int start, int id)
{
  queue< int > que;
  v[id][start] = {0, small[start]};
  que.emplace(start);
  while(!que.empty()) {
    int p = que.front();
    que.pop();
    for(auto &to : g[p]) {
      if(v[id][p].first + 1 == v[id][to].first) {
        v[id][to].second = min(v[id][to].second, v[id][p].second);
      } else if(v[id][p].first + 1 < v[id][to].first) {
        v[id][to] = {v[id][p].first + 1, min(small[to], v[id][p].second)};
        que.emplace(to);
      }
    }
  }
}

int main()
{
  memset(color, -1, sizeof(color));
  fill_n(small, 10005, INF);

  scanf("%d %d %d %d", &N, &A, &B, &C);
  for(int i = 0; i < N; i++) small[i] = i;
  for(int i = 0; i < A + B + C; i++) {
    int K;
    scanf("%d", &K);
    --K;
    if(i < A) color[K] = 0;
    else if(i < A + B) color[K] = 1;
    else color[K] = 2;
    small[color[K] + SHIFT] = min(small[color[K] + SHIFT], K);
  }

  scanf("%d", &M);
  while(M--) {
    int a, b;
    scanf("%d %d", &a, &b);
    --a, --b;
    if(~color[a]) a = color[a] + SHIFT;
    if(~color[b]) b = color[b] + SHIFT;
    g[a].emplace_back(b);
    g[b].emplace_back(a);
  }
  fill_n(*v, 3 * 10005, make_pair(INF, INF));
  solve(SHIFT, 0);
  solve(SHIFT + 1, 1);
  solve(SHIFT + 2, 2);

  vector< int > vertex;
  vertex.push_back(SHIFT);
  vertex.push_back(SHIFT + 1);
  vertex.push_back(SHIFT + 2);
  for(int i = 0; i < N; i++) {
    if(~color[i]) continue;
    vertex.push_back(i);
  }
  int ret = 114514, beet;
  for(auto &i : vertex) {
    int cost = v[0][i].first + v[1][i].first + v[2][i].first;
    int latte = min({v[0][i].second, v[1][i].second, v[2][i].second});
    if(cost < ret) ret = cost, beet = latte;
    else if(cost == ret) beet = min(beet, latte);
  }
  printf("%d %d\n", ret, beet + 1);
}
```