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 Java8 (OpenJDK 1.8.0) (judge verdict: Accepted)

import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.io.BufferedWriter;
import java.util.Set;
import java.util.InputMismatchException;
import java.io.IOException;
import java.util.ArrayList;
import java.util.HashSet;
import java.util.List;
import java.io.Writer;
import java.io.OutputStreamWriter;
import java.util.ArrayDeque;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author prakharjain
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        OutputWriter out = new OutputWriter(outputStream);
        arc099_c solver = new arc099_c();
        solver.solve(1, in, out);
        out.close();
    }

    static class arc099_c {
        int inf = 100000000;

        public void solve(int testNumber, InputReader in, OutputWriter out) {
            int n = in.nextInt();

            int m = in.nextInt();

            Set[] g = new Set[n];

            for (int i = 0; i < n; i++) {
                g[i] = new HashSet();
            }

            int[] u = new int[m];
            int[] v = new int[m];
            for (int i = 0; i < n; i++) {
                for (int j = i + 1; j < n; j++) {
                    g[i].add(j);
                    g[j].add(i);
                }
            }

            for (int i = 0; i < m; i++) {
                int a = in.nextInt() - 1;
                int b = in.nextInt() - 1;

                u[i] = a;
                v[i] = b;

                g[a].remove(b);
                g[b].remove(a);
            }

            IsBipartite isb = new IsBipartite(g);

            List<cp> cps = new ArrayList<>();
            for (int i = 0; i < n; i++) {
                if (!isb.vis[i]) {
                    boolean isBipar = isb.isBipartite(i);
                    if (!isBipar) {
                        out.println(-1);
                        return;
                    }
                    isb.oneColorNodes = 0;
                    isb.zeroColorNodes = 0;
                    isb.assign2Colors(i);
                    cps.add(new cp(isb.oneColorNodes, isb.zeroColorNodes));
                }
            }

            boolean[][] dp = new boolean[cps.size()][n + 1];

            dp[0][cps.get(0).o] = true;
            dp[0][cps.get(0).z] = true;

            for (int i = 1; i < cps.size(); i++) {
                cp ccp = cps.get(i);
                for (int j = 0; j <= n; j++) {
                    if (j >= ccp.o) {
                        dp[i][j] |= dp[i - 1][j - ccp.o];
                    }
                    if (j >= ccp.z) {
                        dp[i][j] |= dp[i - 1][j - ccp.z];
                    }
                }
            }

            int ans = inf;
            for (int i = 0; i <= n; i++) {
                if (dp[cps.size() - 1][i]) {
                    int s1 = i;
                    int s2 = n - i;

                    ans = Math.min(ans, cs(s1) + cs(s2));
                }
            }

            if (ans == inf) {
                out.println(-1);
                return;
            }

            out.println(ans);
        }

        int cs(int i) {
            return (i * (i - 1)) / 2;
        }

        class IsBipartite {
            Set[] g;
            int n;
            boolean[] vis;
            boolean[] colorVis;
            int[] level;
            int[] color;
            int zeroColorNodes = 0;
            int oneColorNodes = 0;

            public IsBipartite(Set[] g) {
                this.g = g;
                this.n = g.length;
                this.vis = new boolean[n];
                this.level = new int[n];
                this.color = new int[n];
                this.colorVis = new boolean[n];
            }

            boolean isBipartite(int u) {
                ArrayDeque<Integer> queue = new ArrayDeque<>();

                queue.addLast(u);
                vis[u] = true;
                level[u] = 0;

                while (queue.size() > 0) {
                    int front = queue.removeFirst();

                    for (int v : (Set<Integer>) g[front]) {
                        if (vis[v]) {
                            if (level[v] == level[front]) {
                                return false;
                            }
                        } else {
                            queue.addLast(v);
                            vis[v] = true;
                            level[v] = level[front] + 1;
                        }
                    }
                }

                return true;
            }

            void assign2Colors(int u) {
                dfs(u, -1);
            }

            void dfs(int u, int prevColor) {
                if (prevColor == -1) {
                    color[u] = 0;
                } else {
                    color[u] = 1 - prevColor;
                }

                if (color[u] == 0)
                    zeroColorNodes++;
                else
                    oneColorNodes++;

                colorVis[u] = true;

                for (int v : (Set<Integer>) g[u]) {
                    if (!colorVis[v])
                        dfs(v, color[u]);
                }
            }

        }

        class cp {
            int o;
            int z;

            public cp(int o, int z) {
                this.o = o;
                this.z = z;
            }

        }

    }

    static class InputReader {
        private InputStream stream;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;
        private InputReader.SpaceCharFilter filter;

        public InputReader(InputStream stream) {
            this.stream = stream;
        }

        public static boolean isWhitespace(int c) {
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

        public int read() {
            if (numChars == -1) {
                throw new InputMismatchException();
            }
            if (curChar >= numChars) {
                curChar = 0;
                try {
                    numChars = stream.read(buf);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }
                if (numChars <= 0) {
                    return -1;
                }
            }
            return buf[curChar++];
        }

        public int nextInt() {
            int c = read();
            while (isSpaceChar(c)) {
                c = read();
            }
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            int res = 0;
            do {
                if (c < '0' || c > '9') {
                    throw new InputMismatchException();
                }
                res *= 10;
                res += c - '0';
                c = read();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

        public boolean isSpaceChar(int c) {
            if (filter != null) {
                return filter.isSpaceChar(c);
            }
            return isWhitespace(c);
        }

        public interface SpaceCharFilter {
            public boolean isSpaceChar(int ch);

        }

    }

    static class OutputWriter {
        private final PrintWriter writer;

        public OutputWriter(OutputStream outputStream) {
            writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(outputStream)));
        }

        public OutputWriter(Writer writer) {
            this.writer = new PrintWriter(writer);
        }

        public void close() {
            writer.close();
        }

        public void println(int i) {
            writer.println(i);
        }

    }
}