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;
long long int mul(long long int x, long long int y) {
  long long int ans = 1;
  while (y > 0) {
    if (y & 1) ans = (ans * x) % 1000000007;
    y /= 2;
    x = (x * x) % 1000000007;
  }
  return ans;
};
vector<vector<long long int> > v(500005);
vector<vector<long long int> > vv(500005);
vector<long long int> fin;
void go(long long int x, long long int p) {
  long long int size = v[x].size(), i;
  for (i = 0; i < size; i++)
    if (v[x][i] != p) go(v[x][i], x);
  fin.push_back(x);
  for (i = size - 1; i >= 0; i--)
    if (v[x][i] != p) fin.push_back(v[x][i]);
  return;
}
int main() {
  long long int n, i, x, y;
  scanf("%lld", &n);
  for (i = 1; i < n; i++) {
    scanf("%lld", &x);
    scanf("%lld", &y);
    v[x].push_back(y);
    v[y].push_back(x);
  }
  fin.push_back(1);
  go(1, 0);
  for (i = 0; i < 2 * n; i++) vv[fin[i] - 1].push_back(i + 1);
  for (i = 0; i < n; i++) cout << vv[i][0] << " " << vv[i][1] << "\n";
  return 0;
}