#include <bits/stdc++.h>
using namespace std;
#define pil pair<int, long long>
#define f first
#define s second
const int mx = 2e5 + 5;
int n, cycA, cycB, par[mx]; bool vis[mx], inCyc[mx]; pil ans; vector<int> adj[mx];
pil comb(pil A, pil B){
if (A.f > B.f) B = A;
else if (A.f == B.f) B.s += A.s;
return B;
}
void getcyc(int u){
vis[u] = 1;
for (int v : adj[u]) if (v != par[u]){
if (vis[v]) tie(cycA, cycB) = {u, v};
else par[v] = u, getcyc(v);
}
}
pil dfs(int u, int p){
pil bst = {0, 1};
for (int v : adj[u]) if (v != p and !inCyc[v]){
pil tmp = dfs(v, u); tmp.f++;
pil pth = {tmp.f + bst.f, bst.s * tmp.s};
ans = comb(pth, ans);
bst = comb(tmp, bst);
}
return bst;
}
int main(){
cin >> n;
for (int i = 0; i < n; i++){
int a, b; cin >> a >> b;
adj[a].push_back(b); adj[b].push_back(a);
}
getcyc(1); vector<int> cyc;
while (cycB != par[cycA]){
inCyc[cycB] = 1; cyc.push_back(cycB);
cycB = par[cycB];
}
vector<pil> store; map<int, long long> window; pil bstL = {0, 0};
for (int i = 0, l = -(cyc.size() / 2); i < cyc.size(); i++, l++){
if (l >= 0){
window[store[l].f - l] -= store[l].s;
if (!window[store[l].f - l]) window.erase(store[l].f - l);
}
pil mxD = dfs(cyc[i], 0); store.push_back(mxD);
if (window.size()){
pil bstW = *prev(window.end());
ans = comb({bstW.f + mxD.f + i, bstW.s * mxD.s}, ans);
}
ans = comb({bstL.f + mxD.f - i, bstL.s * mxD.s}, ans);
if (l >= 0){
pil mid = store[l];
if (cyc.size() % 2 == 0) mid.s *= 2; //2 paths
ans = comb({mid.f + mxD.f + (i - l), mid.s * mxD.s}, ans);
}
window[mxD.f - i] += mxD.s;
if (l >= 0) bstL = comb({store[l].f + cyc.size() + l, store[l].s}, bstL);
}
cout<<ans.s<<endl;
}
