Imagine a city with n junctions and m streets. Junctions are numbered from 1 to n.

In order to increase the traffic flow, mayor of the city has decided to make each street one-way. This means in the street between junctions u and v, the traffic moves only from u to v or only from v to u. 

The problem is to direct the traffic flow of streets in a way that maximizes the number of pairs (u, v) where 1 ≤ u, v ≤ n and it is possible to reach junction v from u by passing the streets in their specified direction. Your task is to find out maximal possible number of such pairs.

Input

The first line of input contains integers n and m, (<image>), denoting the number of junctions and streets of the city.

Each of the following m lines contains two integers u and v, (u ≠ v), denoting endpoints of a street in the city.

Between every two junctions there will be at most one street. It is guaranteed that before mayor decision (when all streets were two-way) it was possible to reach each junction from any other junction.

Output

Print the maximal number of pairs (u, v) such that that it is possible to reach junction v from u after directing the streets.

Examples

Input

5 4
1 2
1 3
1 4
1 5


Output

13


Input

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


Output

16


Input

2 1
1 2


Output

3


Input

6 7
1 2
2 3
1 3
1 4
4 5
5 6
6 4


Output

27

Note

In the first sample, if the mayor makes first and second streets one-way towards the junction 1 and third and fourth streets in opposite direction, there would be 13 pairs of reachable junctions: {(1, 1), (2, 2), (3, 3), (4, 4), (5, 5), (2, 1), (3, 1), (1, 4), (1, 5), (2, 4), (2, 5), (3, 4), (3, 5)}
#include <bits/stdc++.h>
using namespace std;
const long long MAXN = 2e3 + 10;
const long long MAXM = 1e6 + 10;
vector<long long> tree[MAXN];
vector<pair<long long, long long> > vertex[MAXN];
vector<long long> comp;
long long z[MAXN];
long long c[MAXN];
long long w[MAXN];
long long dp[MAXN];
long long height[MAXN];
long long subtree[MAXN];
bool knapsack[MAXN][MAXN];
bool check[MAXN];
bool edge_check[MAXM];
long long ans = 0;
void set_check(bool t) {
  for (long long j = 0; j < comp.size(); j++) {
    check[comp[j]] = t;
  }
}
void cut_edge(long long v, long long h) {
  check[v] = true;
  height[v] = h;
  dp[v] = v;
  comp.push_back(v);
  for (long long i = 0; i < vertex[v].size(); i++) {
    if (check[vertex[v][i].first] &&
        height[vertex[v][i].first] + 1 != height[v] &&
        height[vertex[v][i].first] < height[dp[v]]) {
      dp[v] = vertex[v][i].first;
    }
  }
  for (long long i = 0; i < vertex[v].size(); i++) {
    if (!check[vertex[v][i].first]) {
      cut_edge(vertex[v][i].first, h + 1);
      if (height[dp[vertex[v][i].first]] < height[dp[v]]) {
        dp[v] = dp[vertex[v][i].first];
      }
      if (dp[vertex[v][i].first] == vertex[v][i].first) {
        edge_check[vertex[v][i].second] = true;
      }
    }
  }
}
void tree_generator(long long v, long long t) {
  check[v] = true;
  c[v] = t;
  w[c[v]]++;
  for (long long i = 0; i < vertex[v].size(); i++) {
    if (!check[vertex[v][i].first]) {
      if (!edge_check[vertex[v][i].second]) {
        tree_generator(vertex[v][i].first, t);
      } else {
        tree_generator(vertex[v][i].first, vertex[v][i].first);
        tree[c[v]].push_back(c[vertex[v][i].first]);
        tree[c[vertex[v][i].first]].push_back(c[v]);
      }
    }
  }
}
void dfs_down(long long v) {
  check[v] = true;
  subtree[v] = w[v];
  knapsack[v][0] = true;
  ans += w[v] * w[v];
  for (long long i = 0; i < tree[v].size(); i++) {
    if (!check[tree[v][i]]) {
      dfs_down(tree[v][i]);
      subtree[v] += subtree[tree[v][i]];
      z[v] += z[tree[v][i]];
      for (long long j = (long long)(comp.size()); j >= subtree[tree[v][i]];
           j--) {
        knapsack[v][j] |= knapsack[v][j - subtree[tree[v][i]]];
      }
    }
  }
  z[v] += (subtree[v] - w[v]) * w[v];
  for (long long i = (long long)(comp.size());
       i >= (long long)(comp.size()) - subtree[v]; i--) {
    knapsack[v][i] |= knapsack[v][i - (long long)(comp.size()) + subtree[v]];
  }
}
long long dfs_up(long long v) {
  check[v] = true;
  long long res = 0;
  for (long long i = 0; i < tree[v].size(); i++) {
    if (!check[tree[v][i]]) {
      z[tree[v][i]] =
          z[v] - w[v] * subtree[tree[v][i]] +
          w[tree[v][i]] * ((long long)(comp.size()) - subtree[tree[v][i]]);
      res = max(res, dfs_up(tree[v][i]));
    }
  }
  for (long long i = 0; i <= (long long)(comp.size()) - w[v]; i++) {
    if (knapsack[v][i]) {
      res = max(res, i * ((long long)(comp.size()) - w[v] - i) + z[v]);
    }
  }
  return res;
}
int main() {
  ios_base ::sync_with_stdio(false);
  cin.tie(0);
  long long n, m;
  cin >> n >> m;
  for (long long i = 0; i < m; i++) {
    long long v, u;
    cin >> v >> u;
    vertex[v].push_back(make_pair(u, i));
    vertex[u].push_back(make_pair(v, i));
  }
  for (long long i = 1; i <= n; i++) {
    if (!check[i]) {
      comp.clear();
      cut_edge(i, 1);
      set_check(false);
      tree_generator(i, i);
      set_check(false);
      dfs_down(i);
      set_check(false);
      ans += dfs_up(i);
      set_check(true);
    }
  }
  cout << ans;
}
