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 = (int)1e9 + 7;
const int MX = 1073741822;
const long long MXLL = 4e18;
const int Sz = 1110111;
inline void Read_rap() {
  ios_base ::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
}
inline void randomizer3000() {
  unsigned int seed;
  asm("rdtsc" : "=A"(seed));
  srand(seed);
}
void files(string problem) {
  if (fopen((problem + ".in").c_str(), "r")) {
    freopen((problem + ".in").c_str(), "r", stdin);
    freopen((problem + ".out").c_str(), "w", stdout);
  }
}
void localInput(const char in[] = "s") {
  if (fopen(in, "r")) {
    freopen(in, "r", stdin);
  } else
    cerr << "Warning: Input file not found" << endl;
}
int n;
int l[Sz], r[Sz];
int pt[Sz];
int sz[Sz];
vector<int> g[Sz];
void dfs(int v, int pr, int pos) {
  sz[v] = 1;
  for (int to : g[v]) {
    if (to != pr) {
      dfs(to, v, pos);
      sz[v] += sz[to];
      pos += sz[to] * 2 - 1;
    }
  }
  pt[pos++] = v;
  l[v] = pos - 1;
  for (int i = (int)(g[v].size()) - 1; i >= 0; i--) {
    int to = g[v][i];
    if (to != pr) {
      pt[pos++] = to;
      r[to] = pos - 1;
    }
  }
}
int main() {
  Read_rap();
  cin >> n;
  for (int i = 1; i < n; i++) {
    int a, b;
    cin >> a >> b;
    g[a].push_back(b);
    g[b].push_back(a);
  }
  dfs(1, 1, 1);
  r[1] = 2 * n;
  for (int i = 1; i <= n; i++) {
    cout << l[i] << ' ' << r[i] << endl;
  }
  return 0;
}