Problem:
Score : 700 points

Problem Statement

In the State of Takahashi in AtCoderian Federation, there are N cities, numbered 1, 2, ..., N.
M bidirectional roads connect these cities.
The i-th road connects City A_i and City B_i.
Every road connects two distinct cities.
Also, for any two cities, there is at most one road that directly connects them.

One day, it was decided that the State of Takahashi would be divided into two states, Taka and Hashi.
After the division, each city in Takahashi would belong to either Taka or Hashi.
It is acceptable for all the cities to belong Taka, or for all the cities to belong Hashi.
Here, the following condition should be satisfied:

Any two cities in the same state, Taka or Hashi, are directly connected by a road.

Find the minimum possible number of roads whose endpoint cities belong to the same state.
If it is impossible to divide the cities into Taka and Hashi so that the condition is satisfied, print -1.

Constraints

2 \leq N \leq 700

0 \leq M \leq N(N-1)/2

1 \leq A_i \leq N

1 \leq B_i \leq N

A_i \neq B_i

If i \neq j, at least one of the following holds: A_i \neq A_j and B_i \neq B_j.

If i \neq j, at least one of the following holds: A_i \neq B_j and B_i \neq A_j.

Input

Input is given from Standard Input in the following format:

N M
A_1 B_1
A_2 B_2
:
A_M B_M

Output

Print the answer.

Sample Input 1

5 5
1 2
1 3
3 4
3 5
4 5

Sample Output 1

4

For example, if the cities 1, 2 belong to Taka and the cities 3, 4, 5 belong to Hashi, the condition is satisfied.
Here, the number of roads whose endpoint cities belong to the same state, is 4.

Sample Input 2

5 1
1 2

Sample Output 2

-1

In this sample, the condition cannot be satisfied regardless of which cities belong to each state.

Sample Input 3

4 3
1 2
1 3
2 3

Sample Output 3

3

Sample Input 4

10 39
7 2
7 1
5 6
5 8
9 10
2 8
8 7
3 10
10 1
8 10
2 3
7 4
3 9
4 10
3 4
6 1
6 7
9 5
9 7
6 9
9 4
4 6
7 5
8 3
2 5
9 2
10 7
8 6
8 9
7 3
5 3
4 5
6 3
2 10
5 10
4 2
6 2
8 4
10 6

Sample Output 4

21

Solution in C++14 (GCC 5.4.1) (judge verdict: Accepted)

#define _USE_MATH_DEFINES
#define _CRT_SECURE_NO_WARNINGS
#include "bits/stdc++.h"
#define rep(i, n) for (int i = 0; i < (n); ++i)
#define FOR(i, m, n) for (int i = (m); i < (n); ++i)
#define rrep(i, n) for (int i = (n) - 1; i >= 0; --i)
#define rfor(i, m, n) for (int i = (m); i >= (n); --i)
#define sz(x) ((int)(x).size())
#define all(x) (x).begin(),(x).end()
#define rall(x) (x).rbegin(),(x).rend()
#define range_it(a, l, r) (a).begin() + (l), (a).begin() + (r)

using namespace std;
using ll = long long;		using ld = long double;
using VB = vector<bool>;	using VVB = vector<VB>;
using VI = vector<int>;		using VVI = vector<VI>;
using VL = vector<ll>;		using VVL = vector<VL>;
using VS = vector<string>;	using VD = vector<ld>;
using PII = pair<int, int>;	using VP = vector<PII>;
using PLL = pair<ll, ll>;	using VPL = vector<PLL>;
template<class T>using PQ = priority_queue<T>;
template<class T>using PQS = priority_queue<T, vector<T>, greater<T>>;
constexpr int inf = (int)1e9;
constexpr ll inf_ll = (ll)1e18, MOD = 1000000007;
constexpr ld PI = M_PI, EPS = 1e-12;

// --- input --- //
#ifdef _WIN32
#define getchar_unlocked _getchar_nolock
#define putchar_unlocked _putchar_nolock
#define fwrite_unlocked fwrite
#define fflush_unlocked _fflush_nolock
#endif
inline int gc() { return getchar_unlocked(); }
template<class T>inline void InputF(T& v) { cin >> v; }
inline void InputF(char& v) { while (isspace(v = gc())); }
inline void InputF(bool& v) { char c; InputF(c); v = c != '0'; }
inline void InputF(string& v) {
	v.clear(); char c; for (InputF(c); !isspace(c); c = gc())v += c;
}
inline void InputF(int& v) {
	bool neg = false; v = 0; char c; InputF(c);
	if (c == '-') { neg = true; c = gc(); }
	for (; isdigit(c); c = gc())v = v * 10 + (c - '0');
	if (neg)v = -v;
}
inline void InputF(long long& v) {
	bool neg = false; v = 0; char c; InputF(c);
	if (c == '-') { neg = true; c = gc(); }
	for (; isdigit(c); c = gc())v = v * 10 + (c - '0');
	if (neg)v = -v;
}
inline void InputF(double& v) {
	double dp = 1; bool neg = false, adp = false; v = 0; char c; InputF(c);
	if (c == '-') { neg = true; c = gc(); }
	for (; isdigit(c) || c == '.'; c = gc()) {
		if (c == '.')adp = true;
		else if (adp)v += (c - '0') * (dp *= 0.1);
		else v = v * 10 + (c - '0');
	}
	if (neg)v = -v;
}
template<class T, class U>inline void InputF(pair<T, U>& v) {
	InputF(v.first); InputF(v.second);
}
template<class T>inline void InputF(vector<T>& v) {
	for (auto& e : v)InputF(e);
}
template<class T>inline T InputF() { T v; InputF(v); return v; }
inline string GetLine() {
	string v; char c; for (InputF(c); c != '\n' && c != '\0'; c = gc())v += c; return v;
}
struct InputV {
	int n, m;
	InputV(int N) :n(N), m(0) {}
	InputV(pair<int, int> N) :n(N.first), m(N.second) {}
	template<class T>operator vector<T>() {
		vector<T> v(n); InputF(v); return v;
	}
	template<class T>operator vector<vector<T>>() {
		vector<vector<T>> v(n, vector<T>(m)); InputF(v); return v;
	}
};
struct Input {
	template<class T>operator T() { return InputF<T>(); }
	int operator--(int) { int v; InputF(v); v--; return v; }
	InputV operator[](int n) { return InputV(n); }
	InputV operator[](pair<int, int> n) { return InputV(n); }
	void operator()() {}
	template<class H, class...T>void operator()(H&& h, T&& ...t) {
		InputF(h); operator()(forward<T>(t)...);
	}
}in;
#define input(T) InputF<T>()
#define INT input(int)
#define LL input(ll)
#define STR input(string)
#define inputs(T, ...) T __VA_ARGS__; in(__VA_ARGS__)
#define ini(...) inputs(int, __VA_ARGS__)
#define inl(...) inputs(ll, __VA_ARGS__)
#define ins(...) inputs(string, __VA_ARGS__)

// --- output --- //
struct BoolStr {
	const char* t, * f; BoolStr(const char* _t, const char* _f) :t(_t), f(_f) {}
}Yes("Yes", "No"), yes("yes", "no"), YES("YES", "NO"), Int("1", "0");
struct DivStr {
	const char* d, * l; DivStr(const char* _d, const char* _l) :d(_d), l(_l) {}
}spc(" ", "\n"), no_spc("", "\n"), end_line("\n", "\n"), comma(",", "\n"), no_endl(" ", "");
class Output {
	BoolStr B{ Yes }; DivStr D{ spc };
	void p(int v) {
		if (v < 0)putchar_unlocked('-'), v = -v;
		char b[10]; int i = 0;
		while (v)b[i++] = '0' + v % 10, v /= 10;
		if (!i)b[i++] = '0';
		while (i--)putchar_unlocked(b[i]);
	}
	void p(ll v) {
		if (v < 0)putchar_unlocked('-'), v = -v;
		char b[20]; int i = 0;
		while (v)b[i++] = '0' + v % 10, v /= 10;
		if (!i)b[i++] = '0';
		while (i--)putchar_unlocked(b[i]);
	}
	void p(bool v) { p(v ? B.t : B.f); }
	void p(char v) { putchar_unlocked(v); }
	void p(const char* v) { fwrite_unlocked(v, 1, strlen(v), stdout); }
	void p(double v) { printf("%.20f", v); }
	void p(ld v) { printf("%.20Lf", v); }
	template<class T> void p(const T& v) { cout << v; }
	template<class T, class U>void p(const pair<T, U>& v) { p(v.first); p(D.d); p(v.second); }
	template<class T>void p(const vector<T>& v) { rep(i, sz(v)) { if (i)p(D.d); p(v[i]); } }
	template<class T>void p(const vector<vector<T>>& v) { rep(i, sz(v)) { if (i)p(D.l); p(v[i]); } }
public:
	Output& operator()() { p(D.l); return *this; }
	template<class H>Output& operator()(H&& h) { p(h); p(D.l); return *this; }
	template<class H, class...T>Output& operator()(H&& h, T&& ...t) {
		p(h); p(D.d); return operator()(forward<T>(t)...);
	}
	template<class...T>void exit(T&& ...t) { operator()(forward<T>(t)...); std::exit(EXIT_SUCCESS); }
	Output& flush() { fflush_unlocked(stdout); return *this; }
	Output& set(const BoolStr& b) { B = b; return *this; }
	Output& set(const DivStr& d) { D = d; return *this; }
	Output& set(const char* t, const char* f) { B = BoolStr(t, f); return *this; }
}out;

// --- step --- //
template<class T>struct Step {
	class It {
		T a, b, c;
	public:
		constexpr It() : a(T()), b(T()), c(T()) {}
		constexpr It(T _b, T _c, T _s) : a(_b), b(_c), c(_s) {}
		constexpr It& operator++() { --b; a += c; return *this; }
		constexpr It operator++(int) { It tmp = *this; --b; a += c; return tmp; }
		constexpr const T& operator*()const { return a; }
		constexpr const T* operator->()const { return &a; }
		constexpr bool operator==(const It& i)const { return b == i.b; }
		constexpr bool operator!=(const It& i)const { return !(b == i.b); }
		constexpr T start()const { return a; }
		constexpr T count()const { return b; }
		constexpr T step()const { return c; }
	};
	constexpr Step(T b, T c, T s) : be(b, c, s) {}
	constexpr It begin()const { return be; }
	constexpr It end()const { return en; }
	constexpr T start()const { return be.start(); }
	constexpr T count()const { return be.count(); }
	constexpr T step()const { return be.step(); }
	constexpr T sum()const { return start() * count() + step() * (count() * (count() - 1) / 2); }
	operator vector<T>()const { return as_vector(); }
	template<class F>void each(const F& f)const { for (T i : *this)f(i); }
	vector<T> as_vector()const {
		vector<T> res; res.reserve(count()); each([&](T i) {res.push_back(i); }); return res;
	}
	template<class F, class U = decay_t<result_of_t<F(T)>>>auto map(const F& f)const {
		vector<U> res; res.reserve(count()); each([&](T i) {res.push_back(f(i)); }); return res;
	}
	template<class F>vector<T> select(const F& f)const {
		vector<T> res; each([&](T i) {if (f(i))res.push_back(i); }); return res;
	}
	template<class F>int count_if(const F& f)const { int res = 0; each([&](T i) {if (f(i))++res; }); return res; }
	template<class F>T find_if(const F& f)const { for (T i : *this)if (f(i))return i; return 0; }
	template<class F>auto max_by(const F& f)const { auto v = map(f); return *max_element(v.begin(), v.end()); }
	template<class F>auto min_by(const F& f)const { auto v = map(f); return *min_element(v.begin(), v.end()); }
	template<class F, class U = decay_t<result_of_t<F(T)>>>auto sum(const F& f)const {
		U res = 0; each([&](T i) {res += static_cast<U>(f(i)); }); return res;
	}
	using value_type = T;
	using iterator = It;
private:
	It be, en;
};
template<class T>inline constexpr auto step(T a) { return Step<T>(0, a, 1); }
template<class T>inline constexpr auto step(T a, T b) { return Step<T>(a, b - a, 1); }
template<class T>inline constexpr auto step(T a, T b, T c) { return Step<T>(a, a < b ? (b - a - 1) / c + 1 : 0, c); }

// --- functions --- //
inline namespace {
	template<class T>inline void Sort(T& a) { sort(all(a)); }
	template<class T>inline void RSort(T& a) { sort(rall(a)); }
	template<class T>inline T Sorted(T a) { Sort(a); return a; }
	template<class T>inline T RSorted(T a) { RSort(a); return a; }
	template<class T, class F>inline void Sort(T& a, const F& f) {
		sort(all(a), [&](const auto& x, const auto& y) {return f(x) < f(y); });
	}
	template<class T, class F>inline void RSort(T& a, const F& f) {
		sort(rall(a), [&](const auto& x, const auto& y) {return f(x) < f(y); });
	}
	template<class T>inline void Reverse(T& a) { reverse(all(a)); }
	template<class T>inline void Unique(T& a) { a.erase(unique(all(a)), a.end()); }
	template<class T>inline void Uniq(T& a) { Sort(a); Unique(a); }
	template<class T>inline void Rotate(T& a, int left) { rotate(a.begin(), a.begin() + left, a.end()); }
	template<class T>inline T Reversed(T a) { Reverse(a); return a; }
	template<class T>inline T Uniqued(T a) { Unique(a); return a; }
	template<class T>inline T Uniqed(T a) { Uniq(a); return a; }
	template<class T>inline T Rotated(T a, int left) { Rotate(a, left); return a; }
	template<class T>inline auto Max(const T& a) { return *max_element(all(a)); }
	template<class T>inline auto Min(const T& a) { return *min_element(all(a)); }
	template<class T>inline int MaxPos(const T& a) { return max_element(all(a)) - a.begin(); }
	template<class T>inline int MinPos(const T& a) { return min_element(all(a)) - a.begin(); }
	template<class T, class F>inline auto Max(const T& a, const F& f) {
		return *max_element(all(a), [&](const auto& x, const auto& y) {return f(x) < f(y); });
	}
	template<class T, class F>inline auto Min(const T& a, const F& f) {
		return *min_element(all(a), [&](const auto& x, const auto& y) {return f(x) < f(y); });
	}
	template<class T, class U>inline int Count(const T& a, const U& v) { return count(all(a), v); }
	template<class T, class F>inline int CountIf(const T& a, const F& f) { return count_if(all(a), f); }
	template<class T, class U>inline int Find(const T& a, const U& v) { return find(all(a), v) - a.begin(); }
	template<class T, class F>inline int FindIf(const T& a, const F& f) { return find_if(all(a), f) - a.begin(); }
	template<class T, class U = typename T::value_type>inline U Sum(const T& a) { return accumulate(all(a), U()); }
	template<class T, class F>inline auto Sum(const T& v, const F& f) {
		return accumulate(next(v.begin()), v.end(), f(v.front()), [&](auto a, auto b) {return a + f(b); });
	}
	template<class T, class U>inline int Lower(const T& a, const U& v) { return lower_bound(all(a), v) - a.begin(); }
	template<class T, class U>inline int Upper(const T& a, const U& v) { return upper_bound(all(a), v) - a.begin(); }
	template<class T, class F>inline void RemoveIf(T& a, const F& f) { a.erase(remove_if(all(a), f), a.end()); }
	template<class F>inline auto Vector(size_t size, const F& f) {
		vector<decay_t<result_of_t<F(size_t)>>> res(size); for (size_t i = 0; i < size; ++i)res[i] = f(i); return res;
	}
	template<class T>inline auto Grid(size_t h, size_t w, const T& v = T()) { return vector<vector<T>>(h, vector<T>(w, v)); }
	template<class T>inline auto Slice(const T& v, size_t i, size_t len) {
		return i < v.size() ? T(v.begin() + i, v.begin() + min(i + len, v.size())) : T();
	}
	template<class T, class F>inline auto Each(const T& v, const F& f) { for (auto& i : v)f(i); }
	template<class T, class F>inline auto Select(const T& v, const F& f) {
		T res; for (const auto& e : v)if (f(e))res.push_back(e); return res;
	}
	template<class T, class F>inline auto Map(const T& v, const F& f) {
		vector<decay_t<result_of_t<F(typename T::value_type)>>> res(v.size());
		size_t i = 0; for (const auto& e : v)res[i++] = f(e); return res;
	}
	template<class T, class F>inline auto MapIndex(const T& v, const F& f) {
		vector<decay_t<result_of_t<F(size_t, typename T::value_type)>>> res(v.size());
		size_t i = 0; for (auto it = v.begin(); it != v.end(); ++it, ++i)res[i] = f(i, *it); return res;
	}
	template<class T, class F>inline auto TrueIndex(const T& v, const F& f) {
		vector<size_t> res; for (size_t i = 0; i < v.size(); ++i)if (f(v[i]))res.push_back(i); return res;
	}
	inline string operator*(string s, size_t n) { string ret; for (size_t i = 0; i < n; ++i)ret += s; return ret; }
	template<class T>inline T Ceil(T n, T m) { return (n + m - 1) / m; }
	template<class T>inline T Ceil2(T n, T m) { return Ceil(n, m) * m; }
	template<class T>inline T Tri(T n) { return (n & 1) ? (n + 1) / 2 * n : n / 2 * (n + 1); }
	template<class T>inline T nC2(T n) { return (n & 1) ? (n - 1) / 2 * n : n / 2 * (n - 1); }
	template<class T>inline T Mid(const T& l, const T& r) { return l + (r - l) / 2; }
	inline int pop_count(int n) { return bitset<32>(n).count(); }
	inline int pop_count(ll n) { return bitset<64>(n).count(); }
	template<class T>inline bool chmax(T& a, const T& b) { if (a < b) { a = b; return true; } return false; }
	template<class T>inline bool chmin(T& a, const T& b) { if (a > b) { a = b; return true; } return false; }
	template<class T>inline bool inRange(const T& v, const T& min, const T& max) { return min <= v && v < max; }
	template<class T = ll>inline T BIT(int b) { return T(1) << b; }
	template<class T>inline T Gcd(T n, T m) { return m ? Gcd(m, n % m) : n; }
	template<class T>inline T Lcm(T n, T m) { return n / Gcd(n, m) * m; }
	template<class T, class U = typename T::value_type>inline U Gcdv(const T& v) {
		return accumulate(next(v.begin()), v.end(), U(*v.begin()), Gcd<U>);
	}
	template<class T, class U = typename T::value_type>inline U Lcmv(const T& v) {
		return accumulate(next(v.begin()), v.end(), U(*v.begin()), Lcm<U>);
	}
	template<class T>inline T Pow(T a, T n) { T r = 1; while (n > 0) { if (n & 1)r *= a; a *= a; n /= 2; } return r; }
	template<class T>inline T Powmod(T a, T n, T m = MOD) {
		T r = 1; while (n > 0) { if (n & 1)r = r * a % m, n--; else a = a * a % m, n /= 2; }return r;
	}
}

// --- dump --- //
#if __has_include("dump.hpp")
#include "dump.hpp"
#else
#define dump(...) ((void)0)
#endif

// ---------------------------------------------------------------- //

vector<pair<int, int>> BipartiteGraph(const VVI& graph) {
	int V = graph.size(), cnt1 = 0, cnt2 = 0;
	vector<int> flag(V);
	function<bool(int, int)> dfs = [&](int v, int c) {
		flag[v] = c;
		cnt1 += c == 1;
		cnt2 += c == -1;
		for (auto e : graph[v]) {
			if (flag[e] == c)return false;
			if (flag[e] == 0 && !dfs(e, -c))return false;
		}
		return true;
	};
	vector<pair<int, int>> x;
	for (int i = 0; i < V; i++) {
		if (flag[i] == 0) {
			if (!dfs(i, 1))return {};
			x.emplace_back(cnt1, cnt2);
			cnt1 = 0; cnt2 = 0;
		}
	}
	return x;
}

int main() {
	ini(n, m);
	VVB flag = Grid<bool>(n, n, true);
	rep(i, m) {
		int a = in--, b = in--;
		flag[a][b] = false;
		flag[b][a] = false;
	}

	VVI g(n);
	rep(i, n)rep(j, n)if (i != j && flag[i][j]) {
		g[i].push_back(j);
	}

	auto res = BipartiteGraph(g);
	if (res.empty()) {
		out.exit(-1);
	}

	VB dp(n + 1);
	dp[0] = true;
	for (const auto& p : res) {
		VB dp2(n + 1);
		rep(i, n + 1)if (dp[i]) {
			dp2[i + p.first] = true;
			dp2[i + p.second] = true;
		}
		dp = dp2;
	}

	int ans = inf;
	rep(i, n + 1)if (dp[i]) {
		chmin(ans, nC2(i) + nC2(n - i));
	}
	out(ans);
}