3 3
1 2
3 1
2 3
 2 0
 10 17
1 2
1 3
1 4
1 5
1 6
1 7
1 8
1 9
1 10
2 3
3 4
4 5
5 6
6 7
7 8
8 9
9 10
 2 1
1 2
 8 13
1 2
2 3
3 4
4 1
2 4
1 3
5 6
6 7
7 8
8 5
6 8
5 7
1 8
 3 2
1 2
2 3
 10 9
1 2
1 3
1 4
1 5
1 6
1 7
1 8
1 9
1 10
 10 40
1 3
2 6
9 10
4 6
1 2
1 8
6 10
3 6
1 4
5 7
3 8
3 9
4 5
3 7
8 9
5 9
5 6
2 3
3 4
1 6
4 8
3 10
5 10
2 8
2 10
4 7
1 10
1 7
4 10
5 8
8 10
7 9
6 8
2 7
4 9
6 9
7 8
6 7
1 5
2 9
 10 9
1 2
2 3
3 1
4 5
5 6
6 7
7 4
4 6
5 7
 1000000 0
 8 11
1 2
1 3
1 4
2 3
2 7
7 4
4 2
7 5
8 1
1 7
7 8
 9 9
1 2
2 3
3 1
4 5
5 6
6 4
7 8
8 9
9 7
 15 14
1 2
1 3
1 4
1 5
2 6
2 7
7 8
7 9
3 10
10 11
4 12
12 13
13 14
13 15
 10 17
1 2
1 3
1 4
1 5
1 6
1 7
1 8
1 9
1 10
2 3
2 4
2 5
2 6
2 7
2 8
2 9
2 10
 9 12
1 2
2 3
3 1
1 4
4 5
5 1
1 6
6 7
7 1
1 8
8 9
9 1
 3 1
1 2
 10 5
5 7
4 8
9 10
7 10
6 10
 15 15
1 2
1 3
1 4
1 5
2 6
2 7
7 8
7 9
3 10
10 11
4 12
12 13
13 14
13 15
15 1
 4 3
1 2
2 3
3 1
 10 30
4 9
4 6
1 2
8 10
7 8
4 7
1 8
6 7
5 6
1 5
7 9
1 7
8 9
7 10
9 10
3 9
2 7
5 7
5 9
2 8
2 9
5 8
3 10
1 6
3 6
2 10
6 8
3 4
2 5
4 5
 4 3
1 2
1 3
1 4
 4 6
1 2
2 3
3 4
4 1
1 3
2 4
 10 9
1 2
1 3
1 4
2 5
5 6
2 7
3 8
3 9
9 10
 10 10
1 2
2 3
3 4
4 5
5 6
6 7
7 8
8 9
9 10
10 1
 3 0
 6 6
1 2
2 3
3 1
4 5
5 6
6 4
 10 0
 9 15
1 2
2 3
3 1
1 4
4 5
5 1
1 6
6 7
7 1
1 8
8 9
9 1
2 9
7 4
2 8
 4 0
 1 0

1
 0
 43
 0
 8
 0
 84
 82
 63
 166666166667000000
 21
 30
 292
 64
 36
 0
 84
 284
 1
 37
 1
 4
 59
 50
 1
 2
 120
 28
 4
 0

#include <bits/stdc++.h>
using namespace std;
const int maxn = 1e6 + 10;
vector<int> graph[maxn];
long long tin[maxn], tot[maxn], edges[maxn], f[maxn], len[maxn];
int find(int n) { return f[n] = f[n] == n ? n : find(f[n]); }
void merge(int a, int b) {
  a = find(a), b = find(b);
  if (a == b) {
    edges[a]++;
    return;
  }
  if (len[a] < len[b]) swap(a, b);
  len[a] += len[b];
  edges[a] += edges[b] + 1;
  f[b] = a;
}
long long dfs(int u) {
  long long ans = 0;
  for (int v : graph[u]) {
    if (tin[v] == -1) {
      tin[v] = tin[u] + 1;
      ans += dfs(v);
    } else {
      if (tin[u] - tin[v] + 1 == 3) ans++;
    }
  }
  return ans;
}
int main() {
  ios_base::sync_with_stdio(0), cin.tie(0), cout.tie(0);
  int n, m;
  cin >> n >> m;
  for (int i = 1; i <= n; ++i) {
    f[i] = i;
    len[i] = 1;
    tot[i] = i * (i + 1) / 2;
    tin[i] = -1;
  }
  for (int i = 1; i <= n; ++i) {
    tot[i] += tot[i - 1];
  }
  for (int i = 0; i < m; ++i) {
    int u, v;
    cin >> u >> v;
    graph[u].push_back(v);
    graph[v].push_back(u);
    merge(u, v);
  }
  long long out = 0, ans = 0;
  for (int i = 1; i <= n; ++i) {
    if (tin[i] != -1 || len[find(i)] < 3) continue;
    tin[i] = 0;
    long long ni = len[find(i)], ki = dfs(i), mi = edges[find(i)];
    out += mi * (n - 2ll) - 2ll * ki - (tot[ni - 2] - ki);
    long long left = tot[ni - 2] - (mi * (ni - 2ll) - ki) / 2;
    out += left;
    ans += ki;
  }
  cout << tot[n - 2] - out + ans << endl;
  return 0;
}
