#include <bits/stdc++.h>
clock_t t = clock();
namespace my_std {
using namespace std;
mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());
template <typename T>
inline T rnd(T l, T r) {
  return uniform_int_distribution<T>(l, r)(rng);
}
template <typename T>
inline bool chkmax(T& x, T y) {
  return x < y ? x = y, 1 : 0;
}
template <typename T>
inline bool chkmin(T& x, T y) {
  return x > y ? x = y, 1 : 0;
}
template <typename T>
inline void read(T& t) {
  t = 0;
  char f = 0, ch = getchar();
  double d = 0.1;
  while (ch > '9' || ch < '0') f |= (ch == '-'), ch = getchar();
  while (ch <= '9' && ch >= '0') t = t * 10 + ch - 48, ch = getchar();
  if (ch == '.') {
    ch = getchar();
    while (ch <= '9' && ch >= '0') t += d * (ch ^ 48), d *= 0.1, ch = getchar();
  }
  t = (f ? -t : t);
}
template <typename T, typename... Args>
inline void read(T& t, Args&... args) {
  read(t);
  read(args...);
}
char __sr[1 << 21], __z[20];
int __C = -1, __zz = 0;
inline void Ot() { fwrite(__sr, 1, __C + 1, stdout), __C = -1; }
inline void print(register int x) {
  if (__C > 1 << 20) Ot();
  if (x < 0) __sr[++__C] = '-', x = -x;
  while (__z[++__zz] = x % 10 + 48, x /= 10)
    ;
  while (__sr[++__C] = __z[__zz], --__zz)
    ;
  __sr[++__C] = '\n';
}
void file() {}
inline void chktime() {}
long long ksm(long long x, int y) {
  long long ret = 1;
  for (; y; y >>= 1, x = x * x)
    if (y & 1) ret = ret * x;
  return ret;
}
}  // namespace my_std
using namespace my_std;
int n;
struct hh {
  int t, nxt;
} edge[500101 << 1];
int head[500101], ecnt;
void make_edge(int f, int t) {
  edge[++ecnt] = (hh){t, head[f]};
  head[f] = ecnt;
  edge[++ecnt] = (hh){f, head[t]};
  head[t] = ecnt;
}
int size[500101];
int up[500101], dn[500101];
void dfs1(int x, int fa) {
  size[x] = 1;
  int c = 0;
  for (int i = head[x]; i; i = edge[i].nxt)
    if (edge[i].t != fa)
      dfs1(edge[i].t, x), c += (dn[edge[i].t] == -1 ? 233 : dn[edge[i].t]),
          size[x] += size[edge[i].t];
  if (c > 1)
    dn[x] = -1;
  else
    dn[x] = c ^ 1;
}
void dfs2(int x, int fa) {
  if (!fa) up[x] = 1;
  int c = 0;
  for (int i = head[x]; i; i = edge[i].nxt)
    if (edge[i].t != fa) c += (dn[edge[i].t] == -1 ? 233 : dn[edge[i].t]);
  for (int i = head[x]; i; i = edge[i].nxt)
    if (edge[i].t != fa) {
      if (up[x] == -1) {
        up[edge[i].t] = -1;
        dfs2(edge[i].t, x);
        continue;
      }
      int cc = c - (dn[edge[i].t] == -1 ? 233 : dn[edge[i].t]);
      if (cc == 0)
        up[edge[i].t] = up[x] ^ 1;
      else if (cc == 1 && up[x])
        up[edge[i].t] = 1;
      else
        up[edge[i].t] = -1;
      dfs2(edge[i].t, x);
    }
}
long long F[500101][2], G[500101][2];
void dfs3(int x, int fa) {
  int c = 0;
  for (int i = head[x]; i; i = edge[i].nxt)
    if (edge[i].t != fa) c += (dn[edge[i].t] == -1 ? 233 : dn[edge[i].t]);
  for (int i = head[x]; i; i = edge[i].nxt)
    if (edge[i].t != fa) {
      dfs3(edge[i].t, x);
      int cc = c - (dn[edge[i].t] == -1 ? 233 : dn[edge[i].t]);
      if (cc > 1) continue;
      if (cc == 0)
        F[x][0] += F[edge[i].t][1], F[x][1] += F[edge[i].t][0];
      else
        F[x][0] += F[edge[i].t][0];
    }
  if (c == 0) ++F[x][0];
}
long long sum[500101][4][2];
void dfs4(int x, int fa) {
  int c = 0;
  for (int i = head[x]; i; i = edge[i].nxt)
    if (edge[i].t != fa) c += (dn[edge[i].t] == -1 ? 2 : dn[edge[i].t]);
  if (c <= 3)
    for (int k = (0); k <= (1); k++) sum[x][c][k] += G[x][k];
  c += (up[x] == -1 ? 2 : (up[x] ^ 1));
  for (int i = head[x]; i; i = edge[i].nxt)
    if (edge[i].t != fa) {
      int cc = c - (dn[edge[i].t] == -1 ? 2 : dn[edge[i].t]);
      if (cc <= 3)
        for (int k = (0); k <= (1); k++) sum[x][cc][k] += F[edge[i].t][k];
    }
  for (int i = head[x]; i; i = edge[i].nxt)
    if (edge[i].t != fa) {
      int cc = c - (dn[edge[i].t] == -1 ? 2 : dn[edge[i].t]);
      if (cc <= 3)
        for (int k = (0); k <= (1); k++) sum[x][cc][k] += -F[edge[i].t][k];
      for (int c = ((dn[edge[i].t] == -1 ? 2 : dn[edge[i].t])); c <= (3); c++) {
        int cc = c - (dn[edge[i].t] == -1 ? 2 : dn[edge[i].t]);
        if (cc > 1) continue;
        if (cc == 0)
          G[edge[i].t][0] += sum[x][c][1], G[edge[i].t][1] += sum[x][c][0];
        else
          G[edge[i].t][0] += sum[x][c][0];
      }
      if (cc == 0) ++G[edge[i].t][0];
      dfs4(edge[i].t, x);
      if (cc <= 3)
        for (int k = (0); k <= (1); k++) sum[x][cc][k] += F[edge[i].t][k];
    }
}
int main() {
  file();
  read(n);
  int x, y;
  for (int i = (1); i <= (n - 1); i++) read(x, y), make_edge(x, y);
  dfs1(1, 0), dfs2(1, 0);
  dfs3(1, 0);
  dfs4(1, 0);
  long long ans = 0;
  for (int x = (2); x <= (n); x++)
    if (!dn[x] && up[x] == 1)
      ans += 1ll * size[x] * (n - size[x]);
    else
      ans += 1ll * F[x][0] * G[x][0];
  cout << ans;
  return 0;
}

### Prompt

Please formulate a Cpp solution to the following problem:

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>
clock_t t = clock();
namespace my_std {
using namespace std;
mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());
template <typename T>
inline T rnd(T l, T r) {
  return uniform_int_distribution<T>(l, r)(rng);
}
template <typename T>
inline bool chkmax(T& x, T y) {
  return x < y ? x = y, 1 : 0;
}
template <typename T>
inline bool chkmin(T& x, T y) {
  return x > y ? x = y, 1 : 0;
}
template <typename T>
inline void read(T& t) {
  t = 0;
  char f = 0, ch = getchar();
  double d = 0.1;
  while (ch > '9' || ch < '0') f |= (ch == '-'), ch = getchar();
  while (ch <= '9' && ch >= '0') t = t * 10 + ch - 48, ch = getchar();
  if (ch == '.') {
    ch = getchar();
    while (ch <= '9' && ch >= '0') t += d * (ch ^ 48), d *= 0.1, ch = getchar();
  }
  t = (f ? -t : t);
}
template <typename T, typename... Args>
inline void read(T& t, Args&... args) {
  read(t);
  read(args...);
}
char __sr[1 << 21], __z[20];
int __C = -1, __zz = 0;
inline void Ot() { fwrite(__sr, 1, __C + 1, stdout), __C = -1; }
inline void print(register int x) {
  if (__C > 1 << 20) Ot();
  if (x < 0) __sr[++__C] = '-', x = -x;
  while (__z[++__zz] = x % 10 + 48, x /= 10)
    ;
  while (__sr[++__C] = __z[__zz], --__zz)
    ;
  __sr[++__C] = '\n';
}
void file() {}
inline void chktime() {}
long long ksm(long long x, int y) {
  long long ret = 1;
  for (; y; y >>= 1, x = x * x)
    if (y & 1) ret = ret * x;
  return ret;
}
}  // namespace my_std
using namespace my_std;
int n;
struct hh {
  int t, nxt;
} edge[500101 << 1];
int head[500101], ecnt;
void make_edge(int f, int t) {
  edge[++ecnt] = (hh){t, head[f]};
  head[f] = ecnt;
  edge[++ecnt] = (hh){f, head[t]};
  head[t] = ecnt;
}
int size[500101];
int up[500101], dn[500101];
void dfs1(int x, int fa) {
  size[x] = 1;
  int c = 0;
  for (int i = head[x]; i; i = edge[i].nxt)
    if (edge[i].t != fa)
      dfs1(edge[i].t, x), c += (dn[edge[i].t] == -1 ? 233 : dn[edge[i].t]),
          size[x] += size[edge[i].t];
  if (c > 1)
    dn[x] = -1;
  else
    dn[x] = c ^ 1;
}
void dfs2(int x, int fa) {
  if (!fa) up[x] = 1;
  int c = 0;
  for (int i = head[x]; i; i = edge[i].nxt)
    if (edge[i].t != fa) c += (dn[edge[i].t] == -1 ? 233 : dn[edge[i].t]);
  for (int i = head[x]; i; i = edge[i].nxt)
    if (edge[i].t != fa) {
      if (up[x] == -1) {
        up[edge[i].t] = -1;
        dfs2(edge[i].t, x);
        continue;
      }
      int cc = c - (dn[edge[i].t] == -1 ? 233 : dn[edge[i].t]);
      if (cc == 0)
        up[edge[i].t] = up[x] ^ 1;
      else if (cc == 1 && up[x])
        up[edge[i].t] = 1;
      else
        up[edge[i].t] = -1;
      dfs2(edge[i].t, x);
    }
}
long long F[500101][2], G[500101][2];
void dfs3(int x, int fa) {
  int c = 0;
  for (int i = head[x]; i; i = edge[i].nxt)
    if (edge[i].t != fa) c += (dn[edge[i].t] == -1 ? 233 : dn[edge[i].t]);
  for (int i = head[x]; i; i = edge[i].nxt)
    if (edge[i].t != fa) {
      dfs3(edge[i].t, x);
      int cc = c - (dn[edge[i].t] == -1 ? 233 : dn[edge[i].t]);
      if (cc > 1) continue;
      if (cc == 0)
        F[x][0] += F[edge[i].t][1], F[x][1] += F[edge[i].t][0];
      else
        F[x][0] += F[edge[i].t][0];
    }
  if (c == 0) ++F[x][0];
}
long long sum[500101][4][2];
void dfs4(int x, int fa) {
  int c = 0;
  for (int i = head[x]; i; i = edge[i].nxt)
    if (edge[i].t != fa) c += (dn[edge[i].t] == -1 ? 2 : dn[edge[i].t]);
  if (c <= 3)
    for (int k = (0); k <= (1); k++) sum[x][c][k] += G[x][k];
  c += (up[x] == -1 ? 2 : (up[x] ^ 1));
  for (int i = head[x]; i; i = edge[i].nxt)
    if (edge[i].t != fa) {
      int cc = c - (dn[edge[i].t] == -1 ? 2 : dn[edge[i].t]);
      if (cc <= 3)
        for (int k = (0); k <= (1); k++) sum[x][cc][k] += F[edge[i].t][k];
    }
  for (int i = head[x]; i; i = edge[i].nxt)
    if (edge[i].t != fa) {
      int cc = c - (dn[edge[i].t] == -1 ? 2 : dn[edge[i].t]);
      if (cc <= 3)
        for (int k = (0); k <= (1); k++) sum[x][cc][k] += -F[edge[i].t][k];
      for (int c = ((dn[edge[i].t] == -1 ? 2 : dn[edge[i].t])); c <= (3); c++) {
        int cc = c - (dn[edge[i].t] == -1 ? 2 : dn[edge[i].t]);
        if (cc > 1) continue;
        if (cc == 0)
          G[edge[i].t][0] += sum[x][c][1], G[edge[i].t][1] += sum[x][c][0];
        else
          G[edge[i].t][0] += sum[x][c][0];
      }
      if (cc == 0) ++G[edge[i].t][0];
      dfs4(edge[i].t, x);
      if (cc <= 3)
        for (int k = (0); k <= (1); k++) sum[x][cc][k] += F[edge[i].t][k];
    }
}
int main() {
  file();
  read(n);
  int x, y;
  for (int i = (1); i <= (n - 1); i++) read(x, y), make_edge(x, y);
  dfs1(1, 0), dfs2(1, 0);
  dfs3(1, 0);
  dfs4(1, 0);
  long long ans = 0;
  for (int x = (2); x <= (n); x++)
    if (!dn[x] && up[x] == 1)
      ans += 1ll * size[x] * (n - size[x]);
    else
      ans += 1ll * F[x][0] * G[x][0];
  cout << ans;
  return 0;
}

```