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>
#pragma GCC optimize("-O3")
using namespace std;
const int N = 1e6 + 5;
void pairsort(int a[], int b[], int n) {
  pair<int, int> pairt[n];
  for (int i = 0; i < n; i++) {
    pairt[i].first = a[i];
    pairt[i].second = b[i];
  }
  sort(pairt, pairt + n);
  for (int i = 0; i < n; i++) {
    a[i] = pairt[i].first;
    b[i] = pairt[i].second;
  }
}
int gcd(int a, int b) {
  if (b == 0) return a;
  return gcd(b, a % b);
}
int isPrime(int n) {
  if (n < 2) return 0;
  if (n < 4) return 1;
  if (n % 2 == 0 or n % 3 == 0) return 0;
  for (int i = 5; i * i <= n; i += 6)
    if (n % i == 0 or n % (i + 2) == 0) return 0;
  return 1;
}
long long C(int n, int r) {
  if (r > n - r) r = n - r;
  long long ans = 1;
  for (int i = 1; i <= r; i++) {
    ans *= n - r + i;
    ans /= i;
  }
  return ans;
}
int mod = 1e9 + 7;
int modexpo(int x, int p) {
  int res = 1;
  x = x % mod;
  while (p) {
    if (p % 2) res = res * x;
    p >>= 1;
    x = x * x % mod;
    res %= mod;
  }
  return res;
}
int n, x, y, a[N];
vector<int> v[N], vv;
vector<vector<int>> ans(N, vector<int>(2, 0));
void dfs(int x, int y) {
  for (int i = 0; i < v[x].size(); i++) {
    if (v[x][i] == y) continue;
    vv.push_back(v[x][i]);
  }
  vv.push_back(x);
  for (int i = (int)v[x].size() - 1; i >= 0; i--) {
    if (v[x][i] == y) continue;
    dfs(v[x][i], x);
  }
}
int32_t main() {
  ios::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  ;
  cin >> n;
  for (int i = 1; i < n; i++)
    cin >> x >> y, v[x].push_back(y), v[y].push_back(x);
  vv.push_back(1), dfs(1, 1);
  for (int i = 0; i < vv.size(); i++) ans[vv[i]][a[vv[i]]++] = (i + 1);
  for (int i = 1; i <= n; i++) cout << ans[i][0] << " " << ans[i][1] << "\n";
  return 0;
}