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;
vector<int> adj[500100];
int L[500100], R[500100];
int place_segments(int u, int l, int r, int par = 0) {
  L[u] = l;
  R[u] = r;
  int R = r;
  for (int i = 0, nl = r - 1; i < adj[u].size(); i++) {
    int v = adj[u][i];
    if (v == par) continue;
    R = place_segments(v, nl--, R + (int)adj[v].size(), u);
  }
  return R;
}
int main() {
  int n;
  while (scanf("%d", &n) > 0) {
    for (int i = 0; i < n - 1; i++) {
      int x, y;
      scanf("%d%d", &x, &y);
      adj[x].push_back(y);
      adj[y].push_back(x);
    }
    place_segments(1, 1, (int)adj[1].size() + 2);
    for (int i = 1; i <= n; i++) {
      printf("%d %d\n", L[i], R[i]);
    }
    for (int i = 1; i <= n; i++) {
      adj[i].clear();
    }
  }
}