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;
pair<int, int> ans[500100];
int num[500100];
vector<int> node[500100], t[500100];
void dfs(int x, int p) {
  num[x] = 2;
  for (int i = 0; i < t[x].size(); i++) {
    if (t[x][i] == p) continue;
    node[x].push_back(t[x][i]);
    dfs(t[x][i], x);
    num[x] += num[t[x][i]];
  }
}
void f(int x, int a, int b) {
  int sum = b + node[x].size() + 1;
  ans[x].first = a;
  ans[x].second = b + node[x].size();
  for (int i = 0; i < node[x].size(); i++) {
    f(node[x][i], b + node[x].size() - i - 1, sum);
    sum += num[node[x][i]] - 1;
  }
}
int main() {
  int n, a, b;
  scanf("%d", &n);
  for (int i = 1; i < n; i++) {
    scanf("%d%d", &a, &b);
    t[a].push_back(b);
    t[b].push_back(a);
  }
  dfs(1, 0);
  f(1, 1, 2);
  for (int i = 1; i <= n; i++) printf("%d %d\n", ans[i].first, ans[i].second);
  return 0;
}