//#pragma GCC optimize("O3")
//#pragma GCC optimize("Ofast")
//#pragma GCC optimize("unroll-loops")
//#pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,avx,tune=native")
#include <bits/stdc++.h>
using namespace std;
namespace debug {
template <class c> struct rge { c b, e; };
template <class c> rge<c> range(c i, c j) { return rge<c>{i, j}; }
template <class c> char spk(...);
template <class c> auto spk(c *a) -> decltype(cerr << *a, 0);
struct stream {
~stream() { cerr << endl; }
template <class c>
typename enable_if<sizeof spk<c>(0) != 1, stream &>::type operator<<(c i) {
cerr << boolalpha << i;
return *this;
}
template <class c>
typename enable_if<sizeof spk<c>(0) == 1, stream &>::type operator<<(c i) {
return *this << range(begin(i), end(i));
}
template <class a, class b> stream &operator<<(pair<a, b> p) {
return *this << "(" << p.first << ", " << p.second << ")";
}
template <class c> stream &operator<<(rge<c> d) {
*this << "[";
for (auto it = d.b; it != d.e; it++)
*this << ", " + 2 * (it == d.b) << *it;
return *this << "]";
}
stream &_dbg(const string &s, int i, int b) { return *this; }
template <class c, class... cs>
stream &_dbg(const string &s, int i, int b, c arg, cs... args) {
if (i == (int)(s.size()))
return (*this << ": " << arg);
b += (s[i] == '(') + (s[i] == '[') + (s[i] == '{') - (s[i] == ')') -
(s[i] == ']') - (s[i] == '}');
return (s[i] == ',' && b == 0)
? (*this << ": " << arg << " ")._dbg(s, i + 1, b, args...)
: (s[i] == ' ' ? *this : *this << s[i])
._dbg(s, i + 1, b, arg, args...);
}
};
} // namespace debug
#ifdef DEBUG
#define dout debug::stream()
#define dbg(...) \
((dout << "line:" << __LINE__ << " >> ") \
._dbg(#__VA_ARGS__, 0, 0, __VA_ARGS__))
#else
#define dout
#define dbg(...)
#endif
// ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
void PrintAnswer(bool exists, const vector<int> &A, const vector<int> &B) {
if (!exists) {
cout << -1 << '\n';
exit(0);
}
cout << A.size() << '\n';
for (int x : A) {
cout << x << " ";
}
cout << '\n';
cout << B.size() << '\n';
for (int x : B) {
cout << x << " ";
}
cout << '\n';
exit(0);
}
pair<vector<int>, vector<int>>
SplitWithArithmeticSequence(const vector<int> &v, int start, int diff) {
vector<int> A, B;
for (int i = 0; i < (int)v.size(); i++) {
if (v[i] == start) {
A.push_back(v[i]);
start += diff;
} else {
B.push_back(v[i]);
}
}
return {A, B};
}
void AlignSequences(const vector<int> &A, vector<int> B) {
multiset<int> elements(A.begin(), A.end()), diffs;
for (int i = 1; i < (int)A.size(); i++) {
diffs.insert(A[i] - A[i - 1]);
}
while (!B.empty() && *diffs.begin() != *diffs.rbegin()) {
int b = B.back();
B.pop_back();
auto it = elements.insert(b);
if (it != elements.begin() && next(it) != elements.end()) {
diffs.erase(diffs.find(*next(it) - *prev(it)));
}
if (it != elements.begin()) {
diffs.insert(*it - *prev(it));
}
if (next(it) != elements.end()) {
diffs.insert(*next(it) - *it);
}
}
if (!B.empty()) {
PrintAnswer(true, vector<int>(elements.begin(), elements.end()), B);
}
}
int main() {
cin.tie(nullptr);
ios_base::sync_with_stdio(false);
int n;
cin >> n;
vector<int> h(n);
for (auto &x : h)
cin >> x;
sort(h.begin(), h.end());
if (n == 2) {
PrintAnswer(true, {h[0]}, {h[1]});
}
for (const auto &p :
{make_pair(h[0], h[1] - h[0]), make_pair(h[0], h[2] - h[0]),
make_pair(h[1], h[2] - h[1])}) {
auto [A, B] = SplitWithArithmeticSequence(h, p.first, p.second);
if (B.empty()) {
PrintAnswer(true, vector<int>(A.begin(), prev(A.end())), {A.back()});
}
AlignSequences(B, A);
}
PrintAnswer(false, {}, {});
return 0;
}
