parent={}
no_of_friends={}

def findparent(x):
    if parent[x] == x:
        return x
    parent[x] = findparent(parent[x])
    return parent[x]

def value (n):
    t1=n*(n+1)*(2*n+1)
    t1/=6
    t2=n*(n+1)
    t2/=2
    return t1-t2

    
def valueOfFriendsship(n,m, friendships):
    # Write your code here
    total, current, ans =0,0,0
    for i in range(1,n+1):
        parent[i] = i
        no_of_friends[i] = 1
    for i in range(m):
        u,v=friendships[i][0],friendships[i][1]
        pu,pv = findparent(u),findparent(v)
        if pu != pv:
                parent[pv] = pu
                no_of_friends[pu] += no_of_friends[pv]              
    p=[]
    for i in range(1,n+1):
        if(parent[i] == i):
            p.append(no_of_friends[i])
    p.sort(reverse=True)
    for i in range(len(p)):
        current+=(p[i]-1)
        ans +=value(p[i])+total*(p[i]-1)
        total+=(p[i] * (p[i]-1))
    ans+=((m-current)*total)
    return int(ans)