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Codeforces Round 190 (Div. 1) |
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Finished |

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constructive algorithms

dfs and similar

divide and conquer

greedy

trees

*2100

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C. Ciel the Commander

time limit per test

1 secondmemory limit per test

256 megabytesinput

standard inputoutput

standard outputNow Fox Ciel becomes a commander of Tree Land. Tree Land, like its name said, has *n* cities connected by *n* - 1 undirected roads, and for any two cities there always exists a path between them.

Fox Ciel needs to assign an officer to each city. Each officer has a rank — a letter from 'A' to 'Z'. So there will be 26 different ranks, and 'A' is the topmost, so 'Z' is the bottommost.

There are enough officers of each rank. But there is a special rule must obey: if *x* and *y* are two distinct cities and their officers have the same rank, then on the simple path between *x* and *y* there must be a city *z* that has an officer with higher rank. The rule guarantee that a communications between same rank officers will be monitored by higher rank officer.

Help Ciel to make a valid plan, and if it's impossible, output "Impossible!".

Input

The first line contains an integer *n* (2 ≤ *n* ≤ 10^{5}) — the number of cities in Tree Land.

Each of the following *n* - 1 lines contains two integers *a* and *b* (1 ≤ *a*, *b* ≤ *n*, *a* ≠ *b*) — they mean that there will be an undirected road between *a* and *b*. Consider all the cities are numbered from 1 to *n*.

It guaranteed that the given graph will be a tree.

Output

If there is a valid plane, output *n* space-separated characters in a line — *i*-th character is the rank of officer in the city with number *i*.

Otherwise output "Impossible!".

Examples

Input

4

1 2

1 3

1 4

Output

A B B B

Input

10

1 2

2 3

3 4

4 5

5 6

6 7

7 8

8 9

9 10

Output

D C B A D C B D C D

Note

In the first example, for any two officers of rank 'B', an officer with rank 'A' will be on the path between them. So it is a valid solution.

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