# Reference: https://github.com/shakayami/ACL-for-python
class dsu():
    n=1
    parent_or_size=[-1 for i in range(n)]
    def __init__(self,N):
        self.n=N
        self.parent_or_size=[-1 for i in range(N)]
    def merge(self,a,b):
        assert 0<=a<self.n, "0<=a<n,a={0},n={1}".format(a,self.n)
        assert 0<=b<self.n, "0<=b<n,b={0},n={1}".format(b,self.n)
        x=self.leader(a)
        y=self.leader(b)
        if x==y:
            return x
        if (-self.parent_or_size[x]<-self.parent_or_size[y]):
            x,y=y,x
        self.parent_or_size[x]+=self.parent_or_size[y]
        self.parent_or_size[y]=x
        return x
    def same(self,a,b):
        assert 0<=a<self.n, "0<=a<n,a={0},n={1}".format(a,self.n)
        assert 0<=b<self.n, "0<=b<n,b={0},n={1}".format(b,self.n)
        return self.leader(a)==self.leader(b)
    def leader(self,a):
        assert 0<=a<self.n, "0<=a<n,a={0},n={1}".format(a,self.n)
        if (self.parent_or_size[a]<0):
            return a
        self.parent_or_size[a]=self.leader(self.parent_or_size[a])
        return self.parent_or_size[a]
    def size(self,a):
        assert 0<=a<self.n, "0<=a<n,a={0},n={1}".format(a,self.n)
        return -self.parent_or_size[self.leader(a)]
    def groups(self):
        leader_buf=[0 for i in range(self.n)]
        group_size=[0 for i in range(self.n)]
        for i in range(self.n):
            leader_buf[i]=self.leader(i)
            group_size[leader_buf[i]]+=1
        result=[[] for i in range(self.n)]
        for i in range(self.n):
            result[leader_buf[i]].append(i)
        result2=[]
        for i in range(self.n):
            if len(result[i])>0:
                result2.append(result[i])
        return result2

N, M = map(int, input().split())
tree = dsu(N)
mem = [[]for i in range(N)]
for i in range(M):
    r, c = map(int, input().split())
    mem[r-1].append(c-1)
for i in range(N):
    for j in range(1,len(mem[i])):
        tree.merge(mem[i][j], mem[i][j-1])
cnt = [0]*N
x = []
y = []
for i in range(N):
    if len(mem[i]) == 0:
        x.append(1)
        y.append(0)
    else:
        cnt[tree.leader(mem[i][0])] += 1
for i in range(N):
    if tree.leader(i) == i:
        x.append(cnt[i])
        y.append(tree.size(i))
inf = int(1e18)
ans = inf
K = len(x)
dp = [inf]*(N+1)
dp[0] = 0
for i in range(K):
    for j in reversed(range(N+1)):
        if j < x[i]:
            break
        dp[j] = min(dp[j], dp[j-x[i]]+y[i])
for i in range(N+1):
    if dp[i] == inf:
        continue
    ans = min(ans, N*N+2*i*dp[i]-dp[i]*N-i*N-M)
for i in range(K):
    x[i], y[i] = y[i], x[i]
dp = [inf]*(N+1)
dp[0] = 0
for i in range(K):
    for j in reversed(range(N+1)):
        if j < x[i]:
            break
        dp[j] = min(dp[j], dp[j-x[i]]+y[i])
for i in range(N+1):
    if dp[i] == inf:
        continue
    ans = min(ans, N*N+2*i*dp[i]-dp[i]*N-i*N-M)
print(ans)