#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
#include <bits/stdc++.h>
#define fi first
#define se second
#define pb push_back
#define sz(a) (int)a.size()
#define all(a) a.begin(), a.end()
#define rall(a) a.rbegin(), a.rend()
#define ff(i,a,b) for(int i=a;i<=b;i++)
#define fb(i,b,a) for(int i=b;i>=a;i--)
using namespace std;
using namespace __gnu_pbds;
typedef long long ll;
typedef pair<int,ll> pii;
const int maxn = 200005;
const int inf = 1e9 + 5;
template<typename T>
using ordered_set = tree<T, null_type, less<T>, rb_tree_tag, tree_order_statistics_node_update>;
// os.order_of_key(k) the number of elements in the os less than k
// *os.find_by_order(k) print the k-th smallest number in os(0-based)
int n;
vector<int> g[maxn];
vector<int> krug;
int par[maxn];
int visited[maxn];
void dfs1(int v, int p) {
visited[v] = 1;
par[v] = p;
for(auto u : g[v]) {
if(u == p)continue;
if(!visited[u])dfs1(u, v);
else {
if(visited[u] == 1) {
int A = v;
while(A != u) {
krug.pb(A);
A = par[A];
}
krug.pb(u);
}
}
}
visited[v] = 2;
}
pii dia = {0, 0};
pii ja[maxn];
pii cmb(pii X, pii Y) {
if(X.fi == Y.fi)return {X.fi, X.se + Y.se};
return (X.fi > Y.fi ? X : Y);
}
bool bio[maxn];
pii dfs2(int v, int p, int duz) {
bio[v] = 1;
pii best = {duz, 1};
for(auto u : g[v]) {
if(u == p || bio[u])continue;
pii dist = dfs2(u, v, duz + 1);
dia = cmb(dia, {best.fi + dist.fi - 2 * duz, 1ll * dist.se * best.se});
best = cmb(best, dist);
}
return best;
}
pii bor[4 * maxn];
void build(int v, int tl, int tr) {
if(tl == tr) {
bor[v] = {ja[tl].fi - tl, ja[tl].se};
return;
}
int mid = (tl + tr) / 2;
build(v * 2, tl, mid);
build(v * 2 + 1, mid + 1, tr);
bor[v] = cmb(bor[v * 2], bor[v * 2 + 1]);
}
pii kveri(int v, int tl, int tr, int l, int r) {
if(tl > r || l > tr)return {-inf, 0};
if(tl >= l && tr <= r)return bor[v];
int mid = (tl + tr) / 2;
return cmb(kveri(v * 2, tl, mid, l, r), kveri(v * 2 + 1, mid + 1, tr, l, r));
}
int main()
{
ios::sync_with_stdio(false);
cout.tie(nullptr);
cin.tie(nullptr);
cin >> n;
ff(i,1,n) {
int u, v;
cin >> u >> v;
g[u].pb(v);
g[v].pb(u);
}
dfs1(1, -1);
for(auto c : krug)bio[c] = 1;
int M = sz(krug);
ff(i,0,M - 1)ja[i] = dfs2(krug[i], -1, 0);
int pola = M / 2;
build(1,0,M - 1);
ff(i,0,M - 1) {
pii L = kveri(1,0,M - 1, max(0,i - pola), i - 1);
pii R = kveri(1,0,M - 1, min(M - 1, i + pola - !(M&1)) + 1, M - 1);
R.fi += M + i, L.fi += i;
pii X = cmb(L, R);
dia = cmb(dia, {X.fi + ja[i].fi, 1ll * X.se * ja[i].se});
}
cout << dia.se << endl;
return 0;
}
/**
6
1 2
1 3
2 4
4 3
4 5
4 6
// probati bojenje sahovski ili slicno
**/
