// template.cpp
// use inp.txt/out.txt for file IO
/*
Pragma:
If ever in doubt about whether your pragmas are correct,
turn on most compiler warnings with the command-line option -Wall(or the more specific -Wunknown-pragmas).
use assert(__builtin_cpu_supports("avx2")) to check if intruction set is available
*/
// #pragma GCC optimize ("O2,unroll-loops")
// #pragma GCC optimize("no-stack-protector,fast-math")
// #pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,avx,tune=native")
// #pragma GCC optimize("O3","unroll-loops")
// #pragma GCC optimize ("Ofast")
// #pragma GCC target("avx2,bmi,bmi2,popcnt,lzcnt")
// #pragma GCC target("sse4") // instead of avx2
// __attribute__((target("avx2"), optimize("O3", "unroll-loops")))
#include <bits/stdc++.h>
#define oo (1000'000'000'000'000'000LL)
#define cif(i, n) for(int i = 0; i < n; i++)
#define ccif(i, l, r) for(int i = l; i < r; i++)
#define rif(i, n) for(int i = n-1; i >= 0; i--)
#define rrif(i, l, r) for(int i = r-1; i >= l; i--)
#define scan(a, __n) {for(int __ = 0; __ < __n; __++)cin >> a[__];}
#define print(a, __n) {for(int __ = 0; __ < __n; __++)cout << a[__] << ' '; cout << '\n';}
#define sz(s) ((int)s.size())
#define dbg(x) cerr << #x << " : " << x << endl;
#define rep(i, l, r) for(int i = l; i < r; i++)
// #define mset(a, chr) memset(a, chr, sizeof a)
#define mset(a) memset(a, 0, sizeof a)
#define int ll
#define fastIO ios::sync_with_stdio(false), cin.tie(NULL), cout.tie(NULL);
#define ff first
#define ss second
#define all(v) v.begin(), v.end()
#define uni(v) sort(all(v)), v.resize(unique(all(v))-v.begin());
// #define c0 (v<<1)
// #define c1 (c0|1)
// #define md ((l+r)/2)
using namespace std;
typedef unsigned long long ull;
typedef long long ll;
typedef long double ld;
typedef pair<int, int> pii;
typedef pair<ll, ll> pll;
typedef vector<int> vi;
typedef vector<ll> vl;
typedef vector<pii> vii;
typedef vector<pll> vll;
typedef vector<ld> vd;
typedef pair<ld, ld> pt;
typedef vector<pt> vpt;
ostream& operator<<(ostream& os, pt p) {
return os << "(" << p.ff << "," << p.ss << ")";
}
const ld PI = 3.14159265359;
const int mod = 1e9+7;
// const int maxFac = 1e6+7;
// ll fac[maxFac], _fac[maxFac];
// ll po(ll b, ll p){
// b %= mod;
// p %= mod-1;
// ll r = 1;
// while(p){
// if(p&1)r = r*b%mod;
// p >>= 1;
// b = b*b%mod;
// }
// return r;
// }
// ll choose(ll k, ll n){
// return fac[n]*_fac[k]%mod*_fac[n-k]%mod;
// }
// ll factorial(ll n, ll k){
// ll ret = 1;
// for(ll i = n; i >= n-k+1; i--){
// ret = ret*i%mod;
// }
// return ret;
// }
// vii adj = {{1, 0}, {-1, 0}, {0, 1}, {0, -1}};
const int maxN = 1e6+7;
int mark[maxN];
vi cyc, g[maxN];
int findcyc(int nw, int pr){
mark[nw] = 1;
for(auto u : g[nw]){
if(u == pr)continue;
if(!mark[u]){
int rt = findcyc(u, nw);
if(rt >= 0){
cyc.push_back(nw);
return rt == nw ? -1 : rt;
}
}
else{
cyc.push_back(nw);
return u;
}
}
return -1;
}
vi merge(const vi& a, const vi& b){
vi c{0, 0, 0, 0};
c[0] = max({a[0], b[0]});
c[2] = max({a[2], b[2], a[0]+b[0]});
if(a[0] == c[0])c[1] += a[1];
if(b[0] == c[0])c[1] += b[1];
if(a[2] == c[2])c[3] += a[3];
if(b[2] == c[2])c[3] += b[3];
if(a[0]+b[0] == c[2])c[3] += a[1]*b[1];
return c;
}
vi diam(int nw){ // max depth, # max depth, diam, # diam
mark[nw] = 1;
vi ret = {0, 1, 0, 1};
for(auto u : g[nw]){
if(!mark[u]){
auto x = diam(u);
x[0]++;
ret = merge(ret, x);
}
}
return ret;
}
inline void slv(){
int n;
cin >> n;
cif(i, n){
int a, b;
cin >> a >> b;
a--; b--;
g[a].push_back(b);
g[b].push_back(a);
}
findcyc(0, 0);
int m = sz(cyc);
mset(mark);
for(auto u : cyc)mark[u] = 1;
vi tr[m];
int ans = 0, d = 0;
cif(i, m){
tr[i] = diam(cyc[i]);
if(d < tr[i][2])d = tr[i][2], ans = 0;
if(d == tr[i][2])ans += tr[i][3];
}
map<int, int> cnt;
set<int> st;
int lz = 0;
cif(i, m/2){
st.insert(tr[i][0] - lz);
cnt[tr[i][0] - lz] += tr[i][1];
lz++;
}
int nw = m/2;
int ls = 0;
while(ls < m){
if(d < tr[nw][0] + (*st.rbegin()) + lz)d = tr[nw][0] + (*st.rbegin()) + lz, ans = 0;
if(d == tr[nw][0] + (*st.rbegin()) + lz)ans += tr[nw][1] * cnt[*st.rbegin()];
st.insert(tr[nw][0] - lz);
cnt[tr[nw][0] - lz] += tr[nw][1];
cnt[tr[ls][0] + m/2 - lz] -= tr[ls][1];
if(cnt[tr[ls][0] + m/2 - lz] == 0){
st.erase(tr[ls][0] + m/2 - lz);
}
nw++;
if(nw == m)nw = 0;
ls++;
lz++;
}
cout << ans << '\n';
// cout << d << '\n';
}
/*
*/
inline void prep(){
// fac[0] = 1;
// for(int i = 1; i < maxFac; i++)fac[i] = fac[i-1]*i%mod;
// _fac[maxFac-1] = po(fac[maxFac-1], mod-2);
// for(int i = maxFac-2; i >= 0; i--)_fac[i] = _fac[i+1]*(i+1)%mod;
// w[0] = 1;
// for(int i = 1; i < maxN; i++)w[i] = w[i-1]*p%mod;
// _w[maxN-1] = po(w[maxN-1], mod-2);
// for(int i = maxN-2; i >= 0; i--)_w[i] = _w[i+1]*p%mod;
// for(int i = 2; i < maxN; i++){
// if(lp[i] == 0){
// lp[i] = i;
// pr.push_back(i);
// }
// for (int j = 0; i * pr[j] < maxN; ++j) {
// lp[i * pr[j]] = pr[j];
// if (pr[j] == lp[i]) {
// break;
// }
// }
// }
}
signed main(){
// freopen("inp.txt", "r", stdin);
// freopen("out.txt", "w", stdout);
fastIO;
// cout << fixed << setprecision (15);
prep();
int t = 1;
// cin >> t;
while(t--){
// cout << slv() << '\n';
slv();
// string s;
// cin >> s;
// bool x = slv();
// cout << (x?"YES":"NO") << '\n';
}
cout.flush();
}
/*
*/
