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 double pi = 2 * acos(0.0);
double inff = 1.0 / 0.0;
mt19937_64 rng(chrono::steady_clock::now().time_since_epoch().count());
long long int x, y, n, i, z, j, k, w, u, q, m, t;
vector<pair<long long int, long long int> > res;
vector<long long int> adj[1000002];
long long int last;
bool sortcol(long long int x, long long int y) {
  return (int)adj[x].size() < (int)adj[y].size();
}
void dfs(long long int src, long long int p, long long int first) {
  last = last + (int)adj[src].size() - (p != 0) + 1;
  res[src - 1] = make_pair(first, last);
  long long int temp = last, z = 0;
  for (auto a : adj[src]) {
    if (a == p) continue;
    z++;
    dfs(a, src, temp - z);
  }
}
void solve() {
  cin >> n;
  for (i = (int)1; i < (int)n; i++) {
    cin >> x >> y;
    adj[x].push_back(y);
    adj[y].push_back(x);
  }
  for (i = (int)1; i < (int)n + 1; i++) {
    if ((int)adj[i].size() != 0) sort(adj[i].begin(), adj[i].end(), sortcol);
  }
  last = 1;
  res.resize(n);
  dfs(1, 0, 1);
  for (auto a : res) {
    cout << a.first << " " << a.second << "\n";
  }
}
int main() {
  int TESTS = 1;
  ios::sync_with_stdio(false), cout.tie(0), cin.tie(0);
  ;
  while (TESTS--) {
    solve();
  }
}