codeforces#P1926B. Vlad and Shapes
Vlad and Shapes
Description
Vladislav has a binary square grid of $n \times n$ cells. A triangle or a square is drawn on the grid with symbols $\texttt{1}$. As he is too busy being cool, he asks you to tell him which shape is drawn on the grid.
- A triangle is a shape consisting of $k$ ($k>1$) consecutive rows, where the $i$-th row has $2 \cdot i-1$ consecutive characters $\texttt{1}$, and the central 1s are located in one column. An upside down triangle is also considered a valid triangle (but not rotated by 90 degrees).
- A square is a shape consisting of $k$ ($k>1$) consecutive rows, where the $i$-th row has $k$ consecutive characters $\texttt{1}$, which are positioned at an equal distance from the left edge of the grid.
For the given grid, determine the type of shape that is drawn on it.
The first line contains a single integer $t$ ($1 \leq t \leq 100$) — the number of test cases.
The first line of each test case contains a single integer $n$ ($2 \leq n \leq 10$) — the size of the grid.
The next $n$ lines each contain $n$ characters $\texttt{0}$ or $\texttt{1}$.
The grid contains exactly one triangle or exactly one square that contains all the $\texttt{1}$s in the grid. It is guaranteed that the size of the triangle or square is greater than $1$ (i.e., the shape cannot consist of exactly one 1).
For each test case, output "SQUARE" if all the $\texttt{1}$s in the grid form a square, and "TRIANGLE" otherwise (without quotes).
Input
The first line contains a single integer $t$ ($1 \leq t \leq 100$) — the number of test cases.
The first line of each test case contains a single integer $n$ ($2 \leq n \leq 10$) — the size of the grid.
The next $n$ lines each contain $n$ characters $\texttt{0}$ or $\texttt{1}$.
The grid contains exactly one triangle or exactly one square that contains all the $\texttt{1}$s in the grid. It is guaranteed that the size of the triangle or square is greater than $1$ (i.e., the shape cannot consist of exactly one 1).
Output
For each test case, output "SQUARE" if all the $\texttt{1}$s in the grid form a square, and "TRIANGLE" otherwise (without quotes).
6
3
000
011
011
4
0000
0000
0100
1110
2
11
11
5
00111
00010
00000
00000
00000
10
0000000000
0000000000
0000000000
0000000000
0000000000
1111111110
0111111100
0011111000
0001110000
0000100000
3
111
111
111
SQUARE
TRIANGLE
SQUARE
TRIANGLE
TRIANGLE
SQUARE