#include <bits/stdc++.h>
using namespace std;
using ll = long long;
template <class t, class u>
void chmax(t& first, u second) {
  if (first < second) first = second;
}
template <class t, class u>
void chmin(t& first, u second) {
  if (second < first) first = second;
}
template <class t>
using vc = vector<t>;
template <class t>
using vvc = vc<vc<t>>;
using pi = pair<ll, ll>;
using vi = vc<ll>;
template <class t, class u>
ostream& operator<<(ostream& os, const pair<t, u>& p) {
  return os << "{" << p.first << "," << p.second << "}";
}
template <class t>
ostream& operator<<(ostream& os, const vc<t>& v) {
  os << "{";
  for (auto e : v) os << e << ",";
  return os << "}";
}
using uint = unsigned;
using ull = unsigned long long;
template <class t, size_t n>
ostream& operator<<(ostream& os, const array<t, n>& first) {
  return os << vc<t>(first.begin(), first.end());
}
template <ll i, class T>
void print_tuple(ostream&, const T&) {}
template <ll i, class T, class H, class... Args>
void print_tuple(ostream& os, const T& t) {
  if (i) os << ",";
  os << get<i>(t);
  print_tuple<i + 1, T, Args...>(os, t);
}
template <class... Args>
ostream& operator<<(ostream& os, const tuple<Args...>& t) {
  os << "{";
  print_tuple<0, tuple<Args...>, Args...>(os, t);
  return os << "}";
}
template <class t>
void print(t x, ll suc = 1) {
  cout << x;
  if (suc == 1) cout << "\n";
  if (suc == 2) cout << " ";
}
ll read() {
  ll i;
  cin >> i;
  return i;
}
vi readvi(ll n, ll off = 0) {
  vi v(n);
  for (ll i = ll(0); i < ll(n); i++) v[i] = read() + off;
  return v;
}
template <class T>
void print(const vector<T>& v, ll suc = 1) {
  for (ll i = ll(0); i < ll(v.size()); i++)
    print(v[i], i == ll(v.size()) - 1 ? suc : 2);
}
string readString() {
  string s;
  cin >> s;
  return s;
}
template <class T>
T sq(const T& t) {
  return t * t;
}
void yes(bool ex = true) {
  cout << "Yes"
       << "\n";
  if (ex) exit(0);
}
void no(bool ex = true) {
  cout << "No"
       << "\n";
  if (ex) exit(0);
}
void possible(bool ex = true) {
  cout << "Possible"
       << "\n";
  if (ex) exit(0);
}
void impossible(bool ex = true) {
  cout << "Impossible"
       << "\n";
  if (ex) exit(0);
}
constexpr ll ten(ll n) { return n == 0 ? 1 : ten(n - 1) * 10; }
const ll infLL = LLONG_MAX / 3;
const ll inf = infLL;
ll topbit(signed t) { return t == 0 ? -1 : 31 - __builtin_clz(t); }
ll topbit(ll t) { return t == 0 ? -1 : 63 - __builtin_clzll(t); }
ll botbit(signed first) { return first == 0 ? 32 : __builtin_ctz(first); }
ll botbit(ll first) { return first == 0 ? 64 : __builtin_ctzll(first); }
ll popcount(signed t) { return __builtin_popcount(t); }
ll popcount(ll t) { return __builtin_popcountll(t); }
bool ispow2(ll i) { return i && (i & -i) == i; }
ll mask(ll i) { return (ll(1) << i) - 1; }
bool inc(ll first, ll second, ll c) { return first <= second && second <= c; }
template <class t>
void mkuni(vc<t>& v) {
  sort(v.begin(), v.end());
  v.erase(unique(v.begin(), v.end()), v.end());
}
ll rand_int(ll l, ll r) {
  static mt19937_64 gen(chrono::steady_clock::now().time_since_epoch().count());
  return uniform_int_distribution<ll>(l, r)(gen);
}
template <class t>
void myshuffle(vc<t>& first) {
  for (ll i = ll(0); i < ll(ll(first.size())); i++)
    swap(first[i], first[rand_int(0, i)]);
}
template <class t>
ll lwb(const vc<t>& v, const t& first) {
  return lower_bound(v.begin(), v.end(), first) - v.begin();
}
template <class N, class E>
struct treedp {
  const vvc<E>& g;
  vc<N> first, second, res, sub, bus;
  void dfs1(ll v, ll p) {
    first[v].init(v);
    E up;
    for (auto e : g[v])
      if (e != p) {
        dfs1(e, v);
        second[e] = first[v];
        first[v] = first[v] + first[e];
      } else
        up = e;
    sub[v] = first[v];
    if (p != -1) first[v] = first[v].up(up);
  }
  void dfs2(ll v, ll p, N cur) {
    for (ll i = ll(g[v].size()) - 1; i >= ll(0); i--) {
      auto e = g[v][i];
      if (e == p) continue;
      bus[e] = cur + second[e];
      dfs2(e, v, bus[e].up(e));
      cur = cur + first[e];
    }
    res[v] = cur;
  }
  treedp(const vvc<E>& gg)
      : g(gg),
        first(ll(g.size())),
        second(ll(g.size())),
        res(ll(g.size())),
        sub(ll(g.size())),
        bus(ll(g.size())) {
    dfs1(0, -1);
    N tmp;
    tmp.init(0);
    dfs2(0, -1, tmp);
  }
};
struct N {
  signed v[2][2], s;
  void init(ll) {
    v[0][0] = 1;
    v[0][1] = 0;
    v[1][0] = 0;
    v[1][1] = 0;
    s = 1;
  }
  N up(ll) const {
    N res{};
    res.v[0][0] = v[1][0];
    res.v[0][1] = v[0][0] + v[1][1];
    res.v[1][0] = v[0][0];
    res.v[1][1] = v[0][1];
    res.s = s + 1;
    return res;
  }
  N operator+(const N& r) const {
    N res{};
    for (ll first = ll(0); first < ll(2); first++)
      for (ll second = ll(0); second < ll(2 - first); second++) {
        for (ll c = ll(0); c < ll(2); c++)
          for (ll d = ll(0); d < ll(2 - c); d++) {
            res.v[first + second][c + d] += v[first][c] * r.v[second][d];
          }
      }
    res.s = s + r.s - 1;
    return res;
  }
  ll get() { return v[0][0] + v[1][1]; }
  ll get2() { return v[1][0] * s; }
  void show() const {
    for (ll i = ll(0); i < ll(2); i++)
      for (ll j = ll(0); j < ll(2); j++) void(0);
  }
};
signed main() {
  cin.tie(0);
  ios::sync_with_stdio(0);
  cout << fixed << setprecision(20);
  ll n;
  cin >> n;
  vvc<ll> t(n);
  for (ll i = ll(0); i < ll(n - 1); i++) {
    ll first, second;
    cin >> first >> second;
    first--;
    second--;
    t[first].push_back(second);
    t[second].push_back(first);
  }
  treedp<N, ll> dp(t);
  ll ans = 0;
  for (ll i = ll(1); i < ll(n); i++) {
    ans += dp.sub[i].get() * dp.bus[i].get();
    ans += dp.sub[i].get2() * dp.bus[i].get2();
  }
  print(ans);
}

### Prompt

Develop a solution in CPP to the problem described below:

Sloth is bad, mkay? So we decided to prepare a problem to punish lazy guys.

You are given a tree, you should count the number of ways to remove an edge from it and then add an edge to it such that the final graph is a tree and has a perfect matching. Two ways of this operation are considered different if their removed edges or their added edges aren't the same. The removed edge and the added edge can be equal.

A perfect matching is a subset of edges such that each vertex is an endpoint of exactly one of these edges.

Input

The first line contains n (2 ≤ n ≤ 5·105) — the number of vertices.

Each of the next n - 1 lines contains two integers a and b (1 ≤ a, b ≤ n) — the endpoints of one edge. It's guaranteed that the graph is a tree.

Output

Output a single integer — the answer to the problem.

Examples

Input

4
1 2
2 3
3 4


Output

8


Input

5
1 2
2 3
3 4
3 5


Output

0


Input

8
1 2
2 3
3 4
1 5
5 6
6 7
1 8


Output

22

Note

In first sample, there are 8 ways:

  * edge between 2 and 3 turns to edge between 1 and 3, 
  * edge between 2 and 3 turns to edge between 1 and 4, 
  * edge between 2 and 3 turns to edge between 2 and 3, 
  * edge between 2 and 3 turns to edge between 2 and 4, 
  * edge between 1 and 2 turns to edge between 1 and 2, 
  * edge between 1 and 2 turns to edge between 1 and 4, 
  * edge between 3 and 4 turns to edge between 1 and 4, 
  * edge between 3 and 4 turns to edge between 3 and 4. 

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
template <class t, class u>
void chmax(t& first, u second) {
  if (first < second) first = second;
}
template <class t, class u>
void chmin(t& first, u second) {
  if (second < first) first = second;
}
template <class t>
using vc = vector<t>;
template <class t>
using vvc = vc<vc<t>>;
using pi = pair<ll, ll>;
using vi = vc<ll>;
template <class t, class u>
ostream& operator<<(ostream& os, const pair<t, u>& p) {
  return os << "{" << p.first << "," << p.second << "}";
}
template <class t>
ostream& operator<<(ostream& os, const vc<t>& v) {
  os << "{";
  for (auto e : v) os << e << ",";
  return os << "}";
}
using uint = unsigned;
using ull = unsigned long long;
template <class t, size_t n>
ostream& operator<<(ostream& os, const array<t, n>& first) {
  return os << vc<t>(first.begin(), first.end());
}
template <ll i, class T>
void print_tuple(ostream&, const T&) {}
template <ll i, class T, class H, class... Args>
void print_tuple(ostream& os, const T& t) {
  if (i) os << ",";
  os << get<i>(t);
  print_tuple<i + 1, T, Args...>(os, t);
}
template <class... Args>
ostream& operator<<(ostream& os, const tuple<Args...>& t) {
  os << "{";
  print_tuple<0, tuple<Args...>, Args...>(os, t);
  return os << "}";
}
template <class t>
void print(t x, ll suc = 1) {
  cout << x;
  if (suc == 1) cout << "\n";
  if (suc == 2) cout << " ";
}
ll read() {
  ll i;
  cin >> i;
  return i;
}
vi readvi(ll n, ll off = 0) {
  vi v(n);
  for (ll i = ll(0); i < ll(n); i++) v[i] = read() + off;
  return v;
}
template <class T>
void print(const vector<T>& v, ll suc = 1) {
  for (ll i = ll(0); i < ll(v.size()); i++)
    print(v[i], i == ll(v.size()) - 1 ? suc : 2);
}
string readString() {
  string s;
  cin >> s;
  return s;
}
template <class T>
T sq(const T& t) {
  return t * t;
}
void yes(bool ex = true) {
  cout << "Yes"
       << "\n";
  if (ex) exit(0);
}
void no(bool ex = true) {
  cout << "No"
       << "\n";
  if (ex) exit(0);
}
void possible(bool ex = true) {
  cout << "Possible"
       << "\n";
  if (ex) exit(0);
}
void impossible(bool ex = true) {
  cout << "Impossible"
       << "\n";
  if (ex) exit(0);
}
constexpr ll ten(ll n) { return n == 0 ? 1 : ten(n - 1) * 10; }
const ll infLL = LLONG_MAX / 3;
const ll inf = infLL;
ll topbit(signed t) { return t == 0 ? -1 : 31 - __builtin_clz(t); }
ll topbit(ll t) { return t == 0 ? -1 : 63 - __builtin_clzll(t); }
ll botbit(signed first) { return first == 0 ? 32 : __builtin_ctz(first); }
ll botbit(ll first) { return first == 0 ? 64 : __builtin_ctzll(first); }
ll popcount(signed t) { return __builtin_popcount(t); }
ll popcount(ll t) { return __builtin_popcountll(t); }
bool ispow2(ll i) { return i && (i & -i) == i; }
ll mask(ll i) { return (ll(1) << i) - 1; }
bool inc(ll first, ll second, ll c) { return first <= second && second <= c; }
template <class t>
void mkuni(vc<t>& v) {
  sort(v.begin(), v.end());
  v.erase(unique(v.begin(), v.end()), v.end());
}
ll rand_int(ll l, ll r) {
  static mt19937_64 gen(chrono::steady_clock::now().time_since_epoch().count());
  return uniform_int_distribution<ll>(l, r)(gen);
}
template <class t>
void myshuffle(vc<t>& first) {
  for (ll i = ll(0); i < ll(ll(first.size())); i++)
    swap(first[i], first[rand_int(0, i)]);
}
template <class t>
ll lwb(const vc<t>& v, const t& first) {
  return lower_bound(v.begin(), v.end(), first) - v.begin();
}
template <class N, class E>
struct treedp {
  const vvc<E>& g;
  vc<N> first, second, res, sub, bus;
  void dfs1(ll v, ll p) {
    first[v].init(v);
    E up;
    for (auto e : g[v])
      if (e != p) {
        dfs1(e, v);
        second[e] = first[v];
        first[v] = first[v] + first[e];
      } else
        up = e;
    sub[v] = first[v];
    if (p != -1) first[v] = first[v].up(up);
  }
  void dfs2(ll v, ll p, N cur) {
    for (ll i = ll(g[v].size()) - 1; i >= ll(0); i--) {
      auto e = g[v][i];
      if (e == p) continue;
      bus[e] = cur + second[e];
      dfs2(e, v, bus[e].up(e));
      cur = cur + first[e];
    }
    res[v] = cur;
  }
  treedp(const vvc<E>& gg)
      : g(gg),
        first(ll(g.size())),
        second(ll(g.size())),
        res(ll(g.size())),
        sub(ll(g.size())),
        bus(ll(g.size())) {
    dfs1(0, -1);
    N tmp;
    tmp.init(0);
    dfs2(0, -1, tmp);
  }
};
struct N {
  signed v[2][2], s;
  void init(ll) {
    v[0][0] = 1;
    v[0][1] = 0;
    v[1][0] = 0;
    v[1][1] = 0;
    s = 1;
  }
  N up(ll) const {
    N res{};
    res.v[0][0] = v[1][0];
    res.v[0][1] = v[0][0] + v[1][1];
    res.v[1][0] = v[0][0];
    res.v[1][1] = v[0][1];
    res.s = s + 1;
    return res;
  }
  N operator+(const N& r) const {
    N res{};
    for (ll first = ll(0); first < ll(2); first++)
      for (ll second = ll(0); second < ll(2 - first); second++) {
        for (ll c = ll(0); c < ll(2); c++)
          for (ll d = ll(0); d < ll(2 - c); d++) {
            res.v[first + second][c + d] += v[first][c] * r.v[second][d];
          }
      }
    res.s = s + r.s - 1;
    return res;
  }
  ll get() { return v[0][0] + v[1][1]; }
  ll get2() { return v[1][0] * s; }
  void show() const {
    for (ll i = ll(0); i < ll(2); i++)
      for (ll j = ll(0); j < ll(2); j++) void(0);
  }
};
signed main() {
  cin.tie(0);
  ios::sync_with_stdio(0);
  cout << fixed << setprecision(20);
  ll n;
  cin >> n;
  vvc<ll> t(n);
  for (ll i = ll(0); i < ll(n - 1); i++) {
    ll first, second;
    cin >> first >> second;
    first--;
    second--;
    t[first].push_back(second);
    t[second].push_back(first);
  }
  treedp<N, ll> dp(t);
  ll ans = 0;
  for (ll i = ll(1); i < ll(n); i++) {
    ans += dp.sub[i].get() * dp.bus[i].get();
    ans += dp.sub[i].get2() * dp.bus[i].get2();
  }
  print(ans);
}

```