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

-----Sample Output-----
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.

```python

USER_FILENAME = "<user_code>"
import sys, json, builtins
import math, heapq, bisect, itertools, functools, collections, statistics, fractions, decimal, operator, array, random, re, string, os, pathlib
try:
    import resource as _res
except Exception:
    _res = None
from collections import Counter, defaultdict, deque, OrderedDict
from functools import lru_cache, reduce
from itertools import accumulate, permutations, combinations, product
from math import gcd, ceil, floor, sqrt
from decimal import Decimal
try:
    from typing import *
except Exception:
    pass
try:
    sys.setrecursionlimit(1_000_000)
except Exception:
    pass
try:
    import site as _site
    try:
        _sys_sites = _site.getsitepackages() if hasattr(_site, "getsitepackages") else []
        for _p in _sys_sites:
            if _p and _p not in sys.path:
                sys.path.append(_p)
    except Exception:
        pass
    try:
        _usp = _site.getusersitepackages()
        if isinstance(_usp, str):
            _usp = [_usp]
        for _p in _usp:
            if _p and _p not in sys.path:
                sys.path.append(_p)
    except Exception:
        pass
except Exception:
    pass

ns = {"__name__": "__main__"}
for _k, _v in list(globals().items()):
    if not _k.startswith("_"):
        ns[_k] = _v
_CODE = '# 問題の趣旨：できるだけ辺が少なくなるように2つの完全グラフに分けたい\n# まず、2つの完全グラフに分けられるのかを調べる必要がある。\n# これが不可能であれば-1を出力して即座に終了。\n# 分けられる場合は、できるだけ街の数を均等にしたい。\n\n# 以下のアルゴリズムを考える。\n# まずお互い繋がっていない都市の組A,Bを選ぶ。\n# すると、Aにしか繋がっていない街、Bにしか繋がっていない街、\n# 両方に繋がっている街の3グループに分かれる。\n# 最初の2グループについてはグループのサイズを保存しておく。\n# 最後のグループが空でない場合は、このグループに対してまた同様の処理を行う。\n# 街がなくなるか、両方に繋がっている街のグループが\n# 完全グラフになった時点で終了。\n\n# 上記のアルゴリズムにより、グループのサイズの列と最後に残った街の数が求められる。\n# これをもとに、動的計画法で考えられる街の振り分け方を全て洗い出す。\n# 最も均等に近く振り分けた場合について、完全グラフの辺数を計算して\n# 出力すれば問題が解ける。\n\ndef main():\n    from sys import stdin\n    input = stdin.readline\n    n, m = map(int, input().split())\n    ab = [list(map(int, input().split())) for _ in [0]*m]\n\n    rest = n  # 残りの辺\n    g = [set() for _ in [0]*n]\n    [g[a-1].add(b-1) for a, b in ab]\n    [g[b-1].add(a-1) for a, b in ab]\n    s = set([i for i in range(n)])\n\n    a_list, b_list = [], []\n    while True:\n        if m == rest*(rest-1)//2:\n            break\n        a = [-1, 10**10]\n        for i in s:\n            length = len(g[i])\n            if length < a[1]:\n                a = [i, length]\n        a = a[0]\n        b = [-1, 10**10]\n        for i in s-g[a]-{a}:\n            length = len(g[i])\n            if length < b[1]:\n                b = [i, length]\n        b = b[0]\n        a_set, b_set = {a}, {b}\n        s.remove(a)\n        s.remove(b)\n        rest -= 2\n        remain = set()  # 最後のグループ\n        for i in s:\n            flag_a = True\n            for j in a_set:\n                if j not in g[i]:\n                    flag_a = False\n                else:\n                    g[i].remove(j)\n                    g[j].remove(i)\n                    m -= 1\n            flag_b = True\n            for j in b_set:\n                if j not in g[i]:\n                    flag_b = False\n                else:\n                    g[i].remove(j)\n                    g[j].remove(i)\n                    m -= 1\n            if flag_a+flag_b == 0:\n                print(-1)\n                return\n            elif flag_a*flag_b == 0:\n                q = {i}\n                flag = flag_a  # True→A、False→B\n                while q:\n                    qq = set()\n                    while q:\n                        i = q.pop()\n                        if flag:\n                            a_set.add(i)\n                        else:\n                            b_set.add(i)\n                        for j in remain:\n                            if j not in g[i]:\n                                qq.add(j)\n                            else:\n                                g[i].remove(j)\n                                g[j].remove(i)\n                                m -= 1\n                        for j in q:\n                            g[i].remove(j)\n                            g[j].remove(i)\n                            m -= 1\n                    for i in qq:\n                        remain.remove(i)\n                    flag ^= True\n                    q = qq\n            else:\n                remain.add(i)\n        for i in (a_set | b_set)-{a}-{b}:\n            s.remove(i)\n            rest -= 1\n\n        a_list.append(len(a_set))\n        b_list.append(len(b_set))\n\n    k = len(a_list)\n    dp = [False]*(n+1)\n    dp[0] = True\n\n    for i in range(k):\n        a, b = a_list[i], b_list[i]\n        dp2 = [False]*(n+1)\n        for j in range(n-max(a, b)+1):\n            dp2[j+a] |= dp[j]\n            dp2[j+b] |= dp[j]\n        dp = dp2\n\n    ans = 10**10\n    for j in range(rest+1):\n        for i in range(n-j+1):\n            if dp[i]:\n                p = i+j\n                q = n-p\n                ans = min(ans, p*(p-1)//2+q*(q-1)//2)\n    print(ans)\n\n\nmain()'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 16019