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.)

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.

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.

$L_1$ $R_1$ $L_2$ $R_2$ $\\vdots$ $L_N$ $R_N$

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