#include <bits/stdc++.h>
#include <unordered_map>
using namespace std;

using ll = long long;
using ull = unsigned long long;
using pii = pair<int, int>;
using pll = pair<ll, ll>;
using vi = vector<int>;
using vl = vector<ll>;
#define rep3(i, a, b, c) for (ll i = (a); i < (b); i += (c))
#define rep2(i, a, b) rep3(i, a, b, 1)
#define rep1(i, n) rep2(i, 0, n)
#define rep0(n) rep1(aaaaa, n)
#define ov4(a, b, c, d, name, ...) name
#define rep(...) ov4(__VA_ARGS__, rep3, rep2, rep1, rep0)(__VA_ARGS__)
#define per(i, a, b) for (ll i = (a) - 1; i >= (b); i--)
#define fore(e, v) for (auto &&e : v)
#define all(a) begin(a), end(a)
#define sz(a) (int)(size(a))
#define lb(v, x) (lower_bound(all(v), x) - begin(v))
#define eb emplace_back

template <typename T, typename S> bool chmin(T &a, const S &b) {
  return a > b ? a = b, 1 : 0;
}
template <typename T, typename S> bool chmax(T &a, const S &b) {
  return a < b ? a = b, 1 : 0;
}
const int INF = 1e9 + 100;
const ll INFL = 3e18 + 100;
#define i128 __int128_t
struct _ {
  _() { cin.tie(0)->sync_with_stdio(0), cout.tie(0); }
} __;

int main() {
  int N;
  cin >> N;
  vector<vi> G(N);
  rep(N - 1) {
    int U, V;
    cin >> U >> V;
    --U, --V;
    G[U].push_back(V);
    G[V].push_back(U);
  }
  vi subtree(N, 1);
  auto dfs_subtree = [&](auto f, int v, int p) -> int {
    for (int u : G[v]) {
      if (u != p)
        subtree[v] += f(f, u, v);
    }
    return subtree[v];
  };
  dfs_subtree(dfs_subtree, 0, -1);

  auto dfs_centroid = [&](auto f, int v, int p) -> int {
    for (int u : G[v])
      if (u != p && subtree[u] * 2 > N)
        return f(f, u, v);
    return v;
  };
  int cent1 = dfs_centroid(dfs_centroid, 0, -1);

  int addv = 0, cent2 = -1;
  for (int u : G[cent1]) {
    if (subtree[u] * 2 == N) {
      addv = 1;
      cent2 = u;
    }
  }

  // 辺が重心なので頂点を追加
  if (addv) {
    rep(i, sz(G[cent1])) {
      if (G[cent1][i] == cent2) {
        swap(G[cent1][i], G[cent1].back());
        G[cent1].pop_back();
      }
    }
    rep(i, sz(G[cent2])) {
      if (G[cent2][i] == cent1) {
        swap(G[cent2][i], G[cent2].back());
        G[cent2].pop_back();
      }
    }
    G[cent1].push_back(N);
    G[cent2].push_back(N);
    G.push_back(vi{cent1, cent2});
    cent1 = N;
  }

  unordered_map<ll, pair<ull, ll>> ehash;
  auto e2id = [&](int from, int to) -> ll { return (((ll)from) << 20) + to; };

  auto dfs_hash = [&](auto f, int v, int p) -> pair<ull, ll> {
    vector<pair<ull, ll>> hs;
    for (int u : G[v]) {
      if (u != p)
        hs.push_back(f(f, u, v));
    }
    sort(all(hs));
    ll cnt = 1;
    ull nh = 0, lh = -1;
    for (auto [h, c] : hs) {
      if (h != lh) {
        lh = h;
        cnt += c;
      }
      nh = ((nh << 1) | (nh >> 63)) ^ h;
    }
    nh = ((nh << 1) | (nh >> 63));
    nh += 5889917383409443406ull;
    // cerr << p << ' ' << v << ' ' << cnt << endl;
    return ehash[e2id(p, v)] = make_pair(nh, cnt);
  };

  dfs_hash(dfs_hash, cent1, -1);

  ll ans = 0;
  auto dfs_calc = [&](auto f, int v, int p, ll rcnt) -> void {
    vector<pair<pair<ull, ll>, int>> hs;
    for (int u : G[v])
      if (u != p)
        hs.push_back(make_pair(ehash[e2id(v, u)], u));
    sort(all(hs));
    vi ch;
    ll bcnt = rcnt + 1 - (v == N);
    ull lh = -1;
    unordered_map<ull, ll> hcnt;
    for (auto [h, u] : hs) {
      hcnt[h.first]++;
      if (h.first != lh) {
        lh = h.first;
        bcnt += h.second;
        ch.push_back(u);
      }
    }
    // cerr << p << ' ' << v << ' ' << bcnt << endl;
    if (v != N)
      ans += bcnt;
    for (int u : ch) {
      // cerr << v << "->" << u << endl;
      auto [h, c] = ehash[e2id(v, u)];
      if (hcnt[h] > 1)
        f(f, u, v, bcnt);
      else
        f(f, u, v, bcnt - c);
    }
  };
  // cerr << "CALC" << endl;
  dfs_calc(dfs_calc, cent1, -1, 0);
  cout << ans << '\n';
}