Problem: We had a really tough time generating tests for problem D. In order to prepare strong tests, we had to solve the following problem.

Given an undirected labeled tree consisting of n vertices, find a set of segments such that:

  1. both endpoints of each segment are integers from 1 to 2n, and each integer from 1 to 2n should appear as an endpoint of exactly one segment; 
  2. all segments are non-degenerate; 
  3. for each pair (i, j) such that i ≠ j, i ∈ [1, n] and j ∈ [1, n], the vertices i and j are connected with an edge if and only if the segments i and j intersect, but neither segment i is fully contained in segment j, nor segment j is fully contained in segment i. 



Can you solve this problem too?

Input

The first line contains one integer n (1 ≤ n ≤ 5 ⋅ 10^5) — the number of vertices in the tree.

Then n - 1 lines follow, each containing two integers x_i and y_i (1 ≤ x_i, y_i ≤ n, x_i ≠ y_i) denoting the endpoints of the i-th edge.

It is guaranteed that the given graph is a tree.

Output

Print n pairs of integers, the i-th pair should contain two integers l_i and r_i (1 ≤ l_i < r_i ≤ 2n) — the endpoints of the i-th segment. All 2n integers you print should be unique.

It is guaranteed that the answer always exists.

Examples

Input


6
1 2
1 3
3 4
3 5
2 6


Output


9 12
7 10
3 11
1 5
2 4
6 8


Input


1


Output


1 2

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
const int MOD = 1000000007;
const int INTMAX = numeric_limits<int>::max();
void writeln() { cout << "\n"; }
template <class T>
inline void print(T&& a);
template <class T>
inline void priws(T&& a);
template <class T>
inline void read(T& a);
template <class... Args>
inline void readln(Args&... args) {
  (read(args), ...);
}
template <class H, class... T>
inline void writeln(H&& h, T&&... t) {
  priws(h);
  (print(t), ...);
  writeln();
}
vector<string> split(string& s, string d) {
  vector<string> v;
  size_t p = 0;
  while ((p = s.find(d)) != string::npos)
    v.push_back(s.substr(0, p)), s.erase(0, p + d.length());
  v.push_back(s);
  return v;
}
template <class... Args>
inline void err(string v, Args... args) {
  auto vv = split(v, ", ");
  auto it = vv.begin();
  (writeln(*it++, "=", args), ...);
}
void run() {
  int n;
  readln(n);
  vector<vector<int>> edges(n);
  int x, y;
  for (int i = 0; i < (int)(n - 1); ++i)
    readln(x, y), --x, --y, edges[x].push_back(y), edges[y].push_back(x);
  vector<vector<int>> ans(n);
  int counter = 0;
  auto addInAns = [&](int c) { ans[c].push_back(++counter); };
  function<void(int, int)> dfs = [&](int u, int p) {
    for (int& v : edges[u])
      if (v != p) dfs(v, u);
    addInAns(u);
    reverse(begin(edges[u]), end(edges[u]));
    for (int& v : edges[u])
      if (v != p) addInAns(v);
  };
  dfs(0, -1);
  addInAns(0);
  writeln(ans);
}
int main() {
  ios_base::sync_with_stdio(false);
  run();
  cerr << fixed << setprecision(0)
       << "Execution time = " << 1000.0 * clock() / CLOCKS_PER_SEC << "ms\n";
  return 0;
}
template <class T1, class T2>
inline ostream& operator<<(ostream& os, pair<T1, T2> const& _a);
template <
    typename T, typename D = decltype(*begin(declval<T>())),
    typename enable_if<!is_same<T, basic_string<char>>::value>::type* = nullptr>
ostream& operator<<(ostream& os, T const& _a) {
  auto it = begin(_a);
  if (it != end(_a)) os << *it++;
  while (it != end(_a))
    os << "\n "[is_fundamental<typename T::value_type>::value] << *it++;
  return os;
}
template <class T1, class T2>
inline ostream& operator<<(ostream& os, pair<T1, T2> const& _a) {
  return os << _a.first << " " << _a.second;
}
template <class T1, class T2>
inline istream& operator>>(istream& is, pair<T1, T2>& _a) {
  return is >> _a.first >> _a.second;
}
template <class T>
inline istream& operator>>(istream& is, vector<T>& _a) {
  for (int i = 0; i < (int)(_a.size()); ++i) is >> _a[i];
  return is;
}
template <class T>
inline void print(T&& _a) {
  cout << " " << _a;
}
template <class T>
inline void priws(T&& _a) {
  cout << _a;
}
template <class T>
inline void read(T& _a) {
  cin >> _a;
}