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.

No tag edit access

В условии задачи недавно были сделаны правки. Просмотреть изменения.

×
F. Football

time limit per test

1 secondmemory limit per test

256 megabytesinput

standard inputoutput

standard outputThere are $$$n$$$ football teams in the world.

The Main Football Organization (MFO) wants to host at most $$$m$$$ games. MFO wants the $$$i$$$-th game to be played between the teams $$$a_i$$$ and $$$b_i$$$ in one of the $$$k$$$ stadiums.

Let $$$s_{ij}$$$ be the numbers of games the $$$i$$$-th team played in the $$$j$$$-th stadium. MFO does not want a team to have much more games in one stadium than in the others. Therefore, for each team $$$i$$$, the absolute difference between the maximum and minimum among $$$s_{i1}, s_{i2}, \ldots, s_{ik}$$$ should not exceed $$$2$$$.

Each team has $$$w_i$$$ — the amount of money MFO will earn for each game of the $$$i$$$-th team. If the $$$i$$$-th team plays $$$l$$$ games, MFO will earn $$$w_i \cdot l$$$.

MFO needs to find what games in what stadiums they need to host in order to earn as much money as possible, not violating the rule they set.

However, this problem is too complicated for MFO. Therefore, they are asking you to help them.

Input

The first line contains three integers $$$n$$$, $$$m$$$, $$$k$$$ ($$$3 \leq n \leq 100$$$, $$$0 \leq m \leq 1\,000$$$, $$$1 \leq k \leq 1\,000$$$) — the number of teams, the number of games, and the number of stadiums.

The second line contains $$$n$$$ integers $$$w_1, w_2, \ldots, w_n$$$ ($$$1 \leq w_i \leq 1\,000$$$) — the amount of money MFO will earn for each game of the $$$i$$$-th game.

Each of the following $$$m$$$ lines contains two integers $$$a_i$$$ and $$$b_i$$$ ($$$1 \leq a_i, b_i \leq n$$$, $$$a_i \neq b_i$$$) — the teams that can play the $$$i$$$-th game. It is guaranteed that each pair of teams can play at most one game.

Output

For each game in the same order, print $$$t_i$$$ ($$$1 \leq t_i \leq k$$$) — the number of the stadium, in which $$$a_i$$$ and $$$b_i$$$ will play the game. If the $$$i$$$-th game should not be played, $$$t_i$$$ should be equal to $$$0$$$.

If there are multiple answers, print any.

Example

Input

7 11 3 4 7 8 10 10 9 3 6 2 6 1 7 6 4 3 4 6 3 1 5 3 7 5 7 3 4 2 1 4

Output

3 2 1 1 3 1 2 1 2 3 2

Note

One of possible solutions to the example is shown below:

Codeforces (c) Copyright 2010-2020 Mike Mirzayanov

The only programming contests Web 2.0 platform

Server time: Sep/27/2020 10:16:42 (h3).

Desktop version, switch to mobile version.

Supported by

User lists

Name |
---|