Problem Statement

You are given a rooted tree with N vertices. The root is Vertex 1.
For each $i = 1, 2, \ldots, N-1$, the i-th edge connects Vertex u_i and Vertex v_i.
For each $i = 1, 2, \ldots, N$, let S_i denote the set of all vertices in the subtree rooted at Vertex i. (Each vertex is in the subtree rooted at itself, that is$, i \in$ S_i.)
Additionally, for integers l and r, let [l, r] denote the set of all integers between l and r, that is$, [l, r] = \lbrace l, l+1, l+2, \ldots, r \rbrace$.
Consider a sequence of N pairs of integers $\big((L_1, R_1), (L_2, R_2), \ldots, (L_N, R_N)\big)$ that satisfies the conditions below.

• $1 \leq L_i \leq R_i$ for every integer i such that $1 \leq i \leq N$.
• The following holds for every pair of integers (i, j) such that $1 \leq i, j \leq N$.
• $[L_i, R_i] \subseteq [L_j, R_j]$ if $S_i \subseteq S_j$
• $[L_i, R_i] \cap [L_j, R_j] = \emptyset$ if $S_i \cap S_j = \emptyset$

It can be shown that there is at least one sequence $\big((L_1, R_1), (L_2, R_2), \ldots, (L_N, R_N)\big)$.
Among those sequences, print one that minimizes $\max \lbrace L_1, L_2, \ldots, L_N, R_1, R_2, \ldots, R_N \rbrace$, the maximum integer used. (If there are multiple such sequences, you may print any of them.)

Input

Input is given from Standard Input in the following format:
N
u_1 v_1
u_2 v_2
$\vdots$
u_{N-1} v_{N-1}

Output

Print N lines in the format below. That is, for each $i = 1, 2, \ldots, N$, the i-th line should contain L_i and R_i separated by a space.
L_1 R_1
L_2 R_2
$\vdots$
L_N R_N

Constraints

• $2 \leq N \leq 2 \times 10^5$
• $1 \leq u_i, v_i \leq N$
• All values in input are integers.
• The given graph is a tree.

Sample Input 1

3
2 1
3 1

Sample Output 1

1 2
2 2
1 1

(L_1, R_1) = (1, 2), (L_2, R_2) = (2, 2), (L_3, R_3) = (1, 1) satisfies the conditions.
Indeed, we have $[L_2, R_2] \subseteq [L_1, R_1], [L_3, R_3] \subseteq [L_1, R_1], [L_2, R_2] \cap [L_3, R_3] = \emptyset$.
Additionally, $\max \lbrace L_1, L_2, L_3, R_1, R_2, R_3 \rbrace = 2$ is the minimum possible value.

Sample Input 2

5
3 4
5 4
1 2
1 4

Sample Output 2

1 3
3 3
2 2
1 2
1 1

Sample Input 3

5
4 5
3 2
5 2
3 1

Sample Output 3

1 1
1 1
1 1
1 1
1 1

见题面 Input 部分

见题面 Output 部分