An by
grid of characters is called good if it satisfies these three conditions:
- Each character is either
A
,B
, orC
. - Every
by
subgrid contains all three different letters.
- Any two cells that share exactly one corner contain different letters.
Let denote the cell in the
-th row from the top and
-th column from the left.
You want to construct a good grid that satisfies some of constraints. Each constraint consists of a positive integer value
and two cells
and
that share an edge. You will get
points if your good grid has the same letter in cells
and
.
Find a good grid that gets the most total number of points.
Constraints
For all :
Input Specification
The first line contains three space-separated integers: ,
, and
.
The next lines contain five space-separated integers:
,
,
,
, and
.
Output Specification
On the first line, output the maximum total number of points obtainable by a good grid.
On the next lines, output a good grid that obtains this total number of points. If there are many possible good grids, output any of them.
Scoring
For each test case:
- You will receive
of the points if your first line of output contains the correct answer and the remaining lines contain a correctly formatted good grid that obtains this total number of points.
- Otherwise, you will receive
of the points if your first line of output contains the correct answer. You do not need to print anything after the first line if you are aiming for these partial points, as long as you ensure that the first line is terminated by a
\n
character. You will still receive these partial points if you output a malformatted or incorrect grid. - Otherwise, you will receive
points.
Your final score is the minimum score over all test cases.
Sample Input
3 4 6
3 1 2 1 3
1 2 3 1 3
4 3 4 2 4
1 2 2 3 2
5 2 1 2 2
9 2 1 2 2
Sample Output
21
BAAA
CCBC
BAAC
Explanation
This grid is good and satisfies the st,
rd,
th, and
th constraints, for a total of
points. It can be proven that it is impossible to obtain more than
points.
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