#include <bits/stdc++.h>
inline __attribute__((always_inline)) void init_io() {
  std::ios_base::sync_with_stdio(false);
  std::cin.tie(nullptr);
  std::cout.tie(nullptr);
  std::fixed(std::cout).precision(10);
}
template <typename... Args>
inline __attribute__((always_inline)) bool read(Args&... args) {
  return (bool)(std::cin >> ... >> args);
}
template <typename... Args>
inline __attribute__((always_inline)) void write(Args&&... args) {
  (std::cout << ... << std::forward<Args>(args));
}
template <class... Args>
inline __attribute__((always_inline)) void writeln(Args&&... args) {
  write(std::forward<Args>(args)..., '\n');
}
inline __attribute__((always_inline)) void flush() { std::flush(std::cout); }
constexpr int8_t operator""_i8(unsigned long long val) { return val; }
constexpr uint8_t operator""_u8(unsigned long long val) { return val; }
constexpr int16_t operator""_i16(unsigned long long val) { return val; }
constexpr uint16_t operator""_u16(unsigned long long val) { return val; }
constexpr int32_t operator""_i32(unsigned long long val) { return val; }
constexpr uint32_t operator""_u32(unsigned long long val) { return val; }
constexpr int64_t operator""_i64(unsigned long long val) { return val; }
constexpr uint64_t operator""_u64(unsigned long long val) { return val; }
using graph_t = std::vector<std::vector<int>>;
bool is_all_path_to_leafs_even(const graph_t& g, int v, int p,
                               bool even = true) {
  if (g[v].size() == 1 && !even) return false;
  for (int u : g[v]) {
    if (u == p) continue;
    if (!is_all_path_to_leafs_even(g, u, v, !even)) return false;
  }
  return true;
}
int main() {
  init_io();
  int n;
  read(n);
  graph_t g(n);
  for (int i = 1; i < n; ++i) {
    int a, b;
    read(a, b);
    --a, --b;
    g[a].push_back(b);
    g[b].push_back(a);
  }
  std::vector<char> is_leaf(n, false);
  int leaf = -1;
  int leaf_cnt = 0;
  for (int i = 0; i < n; ++i) {
    if (g[i].size() == 1) {
      leaf = i;
      leaf_cnt += 1;
      is_leaf[i] = true;
    }
  }
  assert(leaf != -1);
  int max_res = n - leaf_cnt - 1;
  for (int i = 0; i < n; ++i) {
    int leaf_neighbours = 0;
    for (int u : g[i]) leaf_neighbours += is_leaf[u];
    if (leaf_neighbours == 0) continue;
    max_res += 1;
  }
  const int min_res = 3 - 2 * is_all_path_to_leafs_even(g, leaf, -1);
  writeln(min_res, ' ', max_res);
  return 0;
}

### Prompt

Your task is to create a Cpp solution to the following problem:

You have unweighted tree of n vertices. You have to assign a positive weight to each edge so that the following condition would hold:

  * For every two different leaves v_{1} and v_{2} of this tree, [bitwise XOR](https://en.wikipedia.org/wiki/Bitwise_operation#XOR) of weights of all edges on the simple path between v_{1} and v_{2} has to be equal to 0. 



Note that you can put very large positive integers (like 10^{(10^{10})}).

It's guaranteed that such assignment always exists under given constraints. Now let's define f as the number of distinct weights in assignment.

<image> In this example, assignment is valid, because bitwise XOR of all edge weights between every pair of leaves is 0. f value is 2 here, because there are 2 distinct edge weights(4 and 5).

<image> In this example, assignment is invalid, because bitwise XOR of all edge weights between vertex 1 and vertex 6 (3, 4, 5, 4) is not 0. 

What are the minimum and the maximum possible values of f for the given tree? Find and print both.

Input

The first line contains integer n (3 ≤ n ≤ 10^{5}) — the number of vertices in given tree.

The i-th of the next n-1 lines contains two integers a_{i} and b_{i} (1 ≤ a_{i} < b_{i} ≤ n) — it means there is an edge between a_{i} and b_{i}. It is guaranteed that given graph forms tree of n vertices.

Output

Print two integers — the minimum and maximum possible value of f can be made from valid assignment of given tree. Note that it's always possible to make an assignment under given constraints.

Examples

Input


6
1 3
2 3
3 4
4 5
5 6


Output


1 4


Input


6
1 3
2 3
3 4
4 5
4 6


Output


3 3


Input


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


Output


1 6

Note

In the first example, possible assignments for each minimum and maximum are described in picture below. Of course, there are multiple possible assignments for each minimum and maximum. 

<image>

In the second example, possible assignments for each minimum and maximum are described in picture below. The f value of valid assignment of this tree is always 3. 

<image>

In the third example, possible assignments for each minimum and maximum are described in picture below. Of course, there are multiple possible assignments for each minimum and maximum. 

<image>

### Response

```cpp
#include <bits/stdc++.h>
inline __attribute__((always_inline)) void init_io() {
  std::ios_base::sync_with_stdio(false);
  std::cin.tie(nullptr);
  std::cout.tie(nullptr);
  std::fixed(std::cout).precision(10);
}
template <typename... Args>
inline __attribute__((always_inline)) bool read(Args&... args) {
  return (bool)(std::cin >> ... >> args);
}
template <typename... Args>
inline __attribute__((always_inline)) void write(Args&&... args) {
  (std::cout << ... << std::forward<Args>(args));
}
template <class... Args>
inline __attribute__((always_inline)) void writeln(Args&&... args) {
  write(std::forward<Args>(args)..., '\n');
}
inline __attribute__((always_inline)) void flush() { std::flush(std::cout); }
constexpr int8_t operator""_i8(unsigned long long val) { return val; }
constexpr uint8_t operator""_u8(unsigned long long val) { return val; }
constexpr int16_t operator""_i16(unsigned long long val) { return val; }
constexpr uint16_t operator""_u16(unsigned long long val) { return val; }
constexpr int32_t operator""_i32(unsigned long long val) { return val; }
constexpr uint32_t operator""_u32(unsigned long long val) { return val; }
constexpr int64_t operator""_i64(unsigned long long val) { return val; }
constexpr uint64_t operator""_u64(unsigned long long val) { return val; }
using graph_t = std::vector<std::vector<int>>;
bool is_all_path_to_leafs_even(const graph_t& g, int v, int p,
                               bool even = true) {
  if (g[v].size() == 1 && !even) return false;
  for (int u : g[v]) {
    if (u == p) continue;
    if (!is_all_path_to_leafs_even(g, u, v, !even)) return false;
  }
  return true;
}
int main() {
  init_io();
  int n;
  read(n);
  graph_t g(n);
  for (int i = 1; i < n; ++i) {
    int a, b;
    read(a, b);
    --a, --b;
    g[a].push_back(b);
    g[b].push_back(a);
  }
  std::vector<char> is_leaf(n, false);
  int leaf = -1;
  int leaf_cnt = 0;
  for (int i = 0; i < n; ++i) {
    if (g[i].size() == 1) {
      leaf = i;
      leaf_cnt += 1;
      is_leaf[i] = true;
    }
  }
  assert(leaf != -1);
  int max_res = n - leaf_cnt - 1;
  for (int i = 0; i < n; ++i) {
    int leaf_neighbours = 0;
    for (int u : g[i]) leaf_neighbours += is_leaf[u];
    if (leaf_neighbours == 0) continue;
    max_res += 1;
  }
  const int min_res = 3 - 2 * is_all_path_to_leafs_even(g, leaf, -1);
  writeln(min_res, ' ', max_res);
  return 0;
}

```