The package for this problem was not updated by the problem writer or Codeforces administration after we've upgraded the judging servers. To adjust the time limit constraint, a solution execution time will be multiplied by 2. For example, if your solution works for 400 ms on judging servers, then the value 800 ms will be displayed and used to determine the verdict.

Codeforces Round 205 (Div. 2) |
---|

Finished |

Virtual contest is a way to take part in past contest, as close as possible to participation on time. It is supported only ICPC mode for virtual contests.
If you've seen these problems, a virtual contest is not for you - solve these problems in the archive.
If you just want to solve some problem from a contest, a virtual contest is not for you - solve this problem in the archive.
Never use someone else's code, read the tutorials or communicate with other person during a virtual contest.

combinatorics

constructive algorithms

greedy

implementation

math

sortings

*1900

No tag edit access

The problem statement has recently been changed. View the changes.

×
B. Two Heaps

time limit per test

1 secondmemory limit per test

256 megabytesinput

standard inputoutput

standard outputValera has 2·*n* cubes, each cube contains an integer from 10 to 99. He arbitrarily chooses *n* cubes and puts them in the first heap. The remaining cubes form the second heap.

Valera decided to play with cubes. During the game he takes a cube from the first heap and writes down the number it has. Then he takes a cube from the second heap and write out its two digits near two digits he had written (to the right of them). In the end he obtained a single fourdigit integer — the first two digits of it is written on the cube from the first heap, and the second two digits of it is written on the second cube from the second heap.

Valera knows arithmetic very well. So, he can easily count the number of distinct fourdigit numbers he can get in the game. The other question is: how to split cubes into two heaps so that this number (the number of distinct fourdigit integers Valera can get) will be as large as possible?

Input

The first line contains integer *n* (1 ≤ *n* ≤ 100). The second line contains 2·*n* space-separated integers *a*_{i} (10 ≤ *a*_{i} ≤ 99), denoting the numbers on the cubes.

Output

In the first line print a single number — the maximum possible number of distinct four-digit numbers Valera can obtain. In the second line print 2·*n* numbers *b*_{i} (1 ≤ *b*_{i} ≤ 2). The numbers mean: the *i*-th cube belongs to the *b*_{i}-th heap in your division.

If there are multiple optimal ways to split the cubes into the heaps, print any of them.

Examples

Input

1

10 99

Output

1

2 1

Input

2

13 24 13 45

Output

4

1 2 2 1

Note

In the first test case Valera can put the first cube in the first heap, and second cube — in second heap. In this case he obtain number 1099. If he put the second cube in the first heap, and the first cube in the second heap, then he can obtain number 9910. In both cases the maximum number of distinct integers is equal to one.

In the second test case Valera can obtain numbers 1313, 1345, 2413, 2445. Note, that if he put the first and the third cubes in the first heap, he can obtain only two numbers 1324 and 1345.

Codeforces (c) Copyright 2010-2023 Mike Mirzayanov

The only programming contests Web 2.0 platform

Server time: Jun/08/2023 15:04:51 (k2).

Desktop version, switch to mobile version.

Supported by

User lists

Name |
---|