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 MAXN = 1e6 + 10, MAXM = 2e6 + 10;
const int INF = INT_MAX, SINF = 0x3f3f3f3f;
const long long llINF = LLONG_MAX;
const int MOD = 1e9 + 7, mod = 998244353;
int head[MAXN], to[MAXN], _next[MAXN], ecnt;
void add_Edge(int u, int v) {
  _next[++ecnt] = head[u];
  to[ecnt] = v;
  head[u] = ecnt;
}
int l[MAXM], r[MAXM], sz[MAXM];
void dd(int u, int f) {
  sz[u] = 1;
  for (int i = head[u]; i; i = _next[i])
    if (to[i] != f) {
      dd(to[i], u);
      sz[u] += sz[to[i]];
    }
}
void dfs(int u, int f, int c) {
  int cnt = 0;
  for (int i = head[u]; i; i = _next[i])
    if (to[i] != f) {
      cnt++;
    }
  r[u] = c + cnt;
  int p = r[u] + 1, q = r[u];
  for (int i = head[u]; i; i = _next[i])
    if (to[i] != f) {
      l[to[i]] = --q;
      dfs(to[i], u, p);
      p += 2 * sz[to[i]] - 1;
    }
}
int n, u, v;
int main() {
  scanf("%d", &n);
  for (int i = 1; i < n; i++) {
    scanf("%d%d", &u, &v);
    add_Edge(u, v);
    add_Edge(v, u);
  }
  dd(1, 0);
  l[1] = 1;
  dfs(1, 0, 2);
  for (int i = 1; i <= n; ++i) printf("%d %d\n", l[i], r[i]);
  return 0;
}