Description

From your point of view, Vincent’s skyscrapers are rectangles whose sides are parallel to the coordinate axes, with one side lying on the $x$-axis. In the picture, the $x$-axis should be drawn using the character *, the outline of the skyscrapers using #, and everything else using .. The left edge of the picture must start with a skyscraper, and the right edge of the picture must end with a skyscraper. Also, to verify the result obtained by mathematicians, output the perimeter of the given outline, instead of counting the side that lies on the $x$-axis.

Input Format

The first line contains an integer $n$, the number of skyscrapers.

Each of the next $n$ lines contains three integers $l_i, r_i$ and $h_i$, describing the position of the $i$-th skyscraper. In the Cartesian coordinate system, the skyscraper is treated as a rectangle with the bottom-left corner at $(l_i, 0)$ and the top-right corner at $(r_i, h_i)$.

Output Format

Output an integer on the first line, the perimeter of the skyscraper outline.

In the next $h + 1$ lines, where $h + 1$ is the height of the tallest skyscraper, output Vincent’s drawing as described above.

3
1 5 4
7 11 3
9 13 5

28
........####
####....#..#
#..#..###..#
#..#..#....#
#..#..#....#
************

6
2 8 7
5 13 5
2 18 3
23 26 5
20 31 7
21 30 10

61
...................#########.
...................#.......#.
...................#.......#.
######............##.......##
#....#............#.........#
#....######.......#.........#
#.........#.......#.........#
#.........######..#.........#
#..............#..#.........#
#..............#..#.........#
*****************************

Hint

Explanation of Sample Input/Output 1

In the figure below, blue shows the skyscraper outline (character #), and yellow is the part of the $x$-axis in Vincent’s painting (character *).

Constraints

• For $50\%$ of the testdata, $1 \le n \le 100$, and $1 \le l_i, r_i, h_i \le 100$.
• For $100\%$ of the testdata, $1 \le n \le 10^4$, $1 \le l_i, r_i, h_i \le 10^3$, and $3 \leq r_i - l_i \leq 10^3$.

Translated by ChatGPT 5