Problem 1: Draw Fixing, *(K Narayan
Kumar, CMI)*

Siruseri happens to have some of the best chess players in India and one of the most important events in the Siruseri sports calendar is the Annual Chess Challenge where teams from Siruseri and Navalur compete.

The event is held alternately at Siruseri and Navalur. This year
the tournament is to be held at Sirseri and the Secretary of the
Siruseri, who is up for re-election this year, would like to ensure
a win for Siruseri. Since starting a war or accusing Navalur of
possessing weapons of mass destruction is beyond his scope (and he
also has a few more brain cells than the average leader of the free
world) he decided to do something clever. *Draw
Fixing*!!

To understand what he intended to do, we need to know how the
Chess Challege match is organised. Both Siruseri and Navalur are
required to send *N* players. Every player from both teams
participates in exactly one game (and so exactly *N* games
are played). The host is expected to draw lots to determine who
plays who. Our secretary plans to fix this draw so that the
pairings are exactly as he wants them to be.

Each chess player has a ELO rating indicating how good he is. The higher the rating the better the player. The secretary knows the rating of each of the players in the Siruseri and Navalur teams and he would like to pair them up so that the number of pairs in which the Siruseri player has a higher ELO rating is maximised.

For example, suppose that *N* is 4 and the ratings of the
players are as below:

Siruseri Team | ELO Rating | Navalur Team | ELO Rating |

Player 1 | 1873 | Player 1 | 2450 |

Player 2 | 2134 | Player 2 | 1860 |

Player 3 | 1900 | Player 3 | 1700 |

Player 4 | 1600 | Player 4 | 2120 |

Then the secretary can arrange for Siruseri to have the higher
rating in 3 out of 4 games. He can do this, for example, by pairing
them as (1,2), (2,4), (3,3) and (4,1), where (*i,j*) means
Player *i* from Siruseri plays Player *j* from
Navalur. This is the best he can do as no player from Siruseri can
beat Player 1 from Navalur.

Your task is help the secretary to find a pairing that maximises the number of pairs with higher rating for Siruseri.

Input format

The first line of the input contains a single integer
*N*, denoting the number of players in each team. The next
*N* lines (lines 2 through *N*+1) list the ratings of
the *N* players in the Siruseri team and the *N*
following lines (lines *N*+2 through 2*N*+1) denote
the ratings of the players in the Navalur team.

Output format

The first line of the output is an integer *N* (0 ≤
*N* ≤ *N*) representing the number of pairs where the
Siruseri player has a higher rating in the optimal pairing. This
should be followed by *N* lines, each containing an integer
*n _{i}* indicating the player chosen from the
Navalur team to play against the

*i*th player from Siruseri.

Test Data

You may assume that 1 ≤ *N* ≤ 50000. Further you may
assume that in 50% of the inputs *N* ≤ 5000.

Example:

We illustrate the input and output format using the example above.

Sample input

4 1873 2134 1900 1600 2450 1860 1700 2120

Sample output

3 2 4 3 1

Test data:

- Some test inputs admit multiple correct solutions. Here is a C program to check if a given output is correct for a given input.

CPU Timelimit: | 3 seconds |

Memory limit: | 64M |

Grading style: | ioi |