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 PYTHON):

Solution:
import os
import sys
from atexit import register
from io import BytesIO
sys.stdin = BytesIO(os.read(0, os.fstat(0).st_size))
sys.stdout = BytesIO()
register(lambda: os.write(1, sys.stdout.getvalue()))
input = lambda: sys.stdin.readline().rstrip('\r\n')
raw_input = lambda: sys.stdin.readline().rstrip('\r\n')

n = int(input())
edges = {}
for i in range(1,n+1):
    edges[i] = []
for i in range(n-1):
    x,y = map(int,raw_input().split(" "))
    edges[x].append(y)
    edges[y].append(x)
visited = [0]*(1+n)
root = 1
stack = [root]
visited[root] = 1
ans = [[0]*2 for i in range(n+1)]
status = [0]*(n+1)
fa = [0]*(n+1)
R = 1
status[0] = 1
while stack:
    node = stack.pop()
    cnt = 0
    for v in edges[node]:
        if not visited[v]:
            stack.append(v)
            visited[v] = 1
            cnt += 1
        else:
            fa[node] = v
    ans[node][0] = status[fa[node]]
    status[fa[node]] -= 1
    ans[node][1] = R+cnt+1
    R = R+cnt+1
    status[node] = ans[node][1]-1
for i in range(1,n+1):
    print ans[i][0],ans[i][1]