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;
namespace {
using Integer = long long;
template <class T, class S>
istream& operator>>(istream& is, pair<T, S>& p) {
  return is >> p.first >> p.second;
}
template <class T>
istream& operator>>(istream& is, vector<T>& vec) {
  for (T& val : vec) is >> val;
  return is;
}
template <class T>
istream& operator,(istream& is, T& val) {
  return is >> val;
}
template <class T, class S>
ostream& operator<<(ostream& os, const pair<T, S>& p) {
  return os << p.first << " " << p.second;
}
template <class T>
ostream& operator<<(ostream& os, const vector<T>& vec) {
  for (size_t i = 0; i < vec.size(); i++)
    os << vec[i] << (i == vec.size() - 1 ? "" : " ");
  return os;
}
template <class T>
ostream& operator,(ostream& os, const T& val) {
  return os << " " << val;
}
template <class H>
void print(const H& head) {
  cout << head;
}
template <class H, class... T>
void print(const H& head, const T&... tail) {
  cout << head << " ";
  print(tail...);
}
template <class... T>
void println(const T&... values) {
  print(values...);
  cout << endl;
}
template <class H>
void eprint(const H& head) {
  cerr << head;
}
template <class H, class... T>
void eprint(const H& head, const T&... tail) {
  cerr << head << " ";
  eprint(tail...);
}
template <class... T>
void eprintln(const T&... values) {
  eprint(values...);
  cerr << endl;
}
class range {
  Integer start_, end_, step_;

 public:
  struct range_iterator {
    Integer val, step_;
    range_iterator(Integer v, Integer step) : val(v), step_(step) {}
    Integer operator*() { return val; }
    void operator++() { val += step_; }
    bool operator!=(range_iterator& x) {
      return step_ > 0 ? val < x.val : val > x.val;
    }
  };
  range(Integer len) : start_(0), end_(len), step_(1) {}
  range(Integer start, Integer end) : start_(start), end_(end), step_(1) {}
  range(Integer start, Integer end, Integer step)
      : start_(start), end_(end), step_(step) {}
  range_iterator begin() { return range_iterator(start_, step_); }
  range_iterator end() { return range_iterator(end_, step_); }
};
inline string operator"" _s(const char* str, size_t size) {
  return move(string(str));
}
constexpr Integer my_pow(Integer x, Integer k, Integer z = 1) {
  return k == 0    ? z
         : k == 1  ? z * x
         : (k & 1) ? my_pow(x * x, k >> 1, z * x)
                   : my_pow(x * x, k >> 1, z);
}
constexpr Integer my_pow_mod(Integer x, Integer k, Integer M, Integer z = 1) {
  return k == 0    ? z % M
         : k == 1  ? z * x % M
         : (k & 1) ? my_pow_mod(x * x % M, k >> 1, M, z * x % M)
                   : my_pow_mod(x * x % M, k >> 1, M, z);
}
constexpr unsigned long long operator"" _ten(unsigned long long value) {
  return my_pow(10, value);
}
inline int k_bit(Integer x, int k) { return (x >> k) & 1; }
mt19937 mt(chrono::duration_cast<chrono::nanoseconds>(
               chrono::steady_clock::now().time_since_epoch())
               .count());
template <class T>
string join(const vector<T>& v, const string& sep) {
  stringstream ss;
  for (size_t i = 0; i < v.size(); i++) {
    if (i > 0) ss << sep;
    ss << v[i];
  }
  return ss.str();
}
inline string operator*(string s, int k) {
  string ret;
  while (k) {
    if (k & 1) ret += s;
    s += s;
    k >>= 1;
  }
  return ret;
}
}  // namespace
constexpr long long mod = 9_ten + 7;
vector<int> nex;
int rec(vector<vector<int>>& g, int pos, int last) {
  nex[pos] = pos + g.size();
  nex[pos + g.size()] = -1;
  int head = pos;
  int tail = pos + g.size();
  for (int ch : g[pos]) {
    if (ch == last) continue;
    auto ch_tail = rec(g, ch, pos);
    int ch_head = ch;
    int ch_head_next = nex[ch];
    nex[ch_head] = nex[head];
    nex[head] = ch_head;
    nex[tail] = ch_head_next;
    tail = ch_tail;
  }
  return tail;
}
int main() {
  int n;
  cin >> n;
  nex = vector<int>(2 * n);
  vector<vector<int>> g(n);
  for (int i = 0; i < n - 1; i++) {
    int a, b;
    scanf("%d%d", &a, &b);
    a--;
    b--;
    g[a].push_back(b);
    g[b].push_back(a);
  }
  rec(g, 0, -1);
  vector<int> ans;
  for (int k = 0, pos = 0; k < 2 * n; k++) {
    ans.push_back(pos);
    pos = nex[pos];
  }
  vector<int> loc(2 * n);
  for (int i = 0; i < 2 * n; i++) {
    loc[ans[i]] = i;
  }
  for (int i = 0; i < n; i++) {
    printf("%d %d\n", loc[i] + 1, loc[i + n] + 1);
  }
  return 0;
}